Research ArticleFault Diagnosis of Batch Reactor Using MachineLearning Methods

Sujatha Subramanian1 Fathima Ghouse2 and Pappa Natarajan3

1 Department of Electronics and Instrumentation Engineering Adhiyamaan College of Engineering Hosur KrishnagiriTamil Nadu 635 109 India

2Department of Information Technology Adhiyamaan College of Engineering Hosur Krishnagiri Tamil Nadu 635 109 India3 Department of Instrumentation Engineering Madras Institute of Technology Anna University ChennaiTamil Nadu 600 044 India

Correspondence should be addressed to Sujatha Subramanian saransakthisifycom

Received 3 January 2014 Accepted 4 March 2014 Published 22 April 2014

Academic Editor Azah Mohamed

Copyright copy 2014 Sujatha Subramanian et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Fault diagnosis of a batch reactor gives the early detection of fault and minimizes the risk of thermal runaway It provides superiorperformance and helps to improve safety and consistency It has becomemore vital in this technical era In this paper support vectormachine (SVM) is used to estimate the heat release (119876

119903) of the batch reactor both normal and faulty conditionsThe signature of the

residual which is obtained from the difference between nominal and estimated faulty119876119903values characterizes the different natures

of faults occurring in the batch reactor Appropriate statistical and geometric features are extracted from the residual signature andthe total numbers of features are reduced using SVM attribute selection filter and principle component analysis (PCA) techniquesartificial neural network (ANN) classifiers like multilayer perceptron (MLP) radial basis function (RBF) and Bayes net are usedto classify the different types of faults from the reduced features It is observed from the result of the comparative study that theproposed method for fault diagnosis with limited number of features extracted from only one estimated parameter (119876

119903) shows that

it is more efficient and fast for diagnosing the typical faults

1 Introduction

Batch and semibatch reactors are extensively used in finechemicals biochemicals pharmaceuticals and food indus-tries for the production of small amounts of products withhigh added value As these processes have become moreautomated and more flexible the demands on their effi-ciency have increased creatingmore complexity in operationand control However the frequency of accidents increasedinvolving important consequences on the human naturaland economic environment [1 2] Therefore fault diagnosishas become a major research topic Batch processes usuallyinvolve a lot of variables that interrelate with one anotherWhen any of these variables diverge away from their specifiedlimits a fault occurs There are a plenty of studies on faultdiagnosis varying from analytical methods to artificial intel-ligence and statistical approaches The approaches of fault

detection are based on the threshold checking in the pastVenkatasubramanian and Chan [3] proposed fault diagnosisto the continuous stirred tank reactors with neural networkand identified six kinds of faults The application of neuralnetworks in fault diagnosis of chemical process focuses onthe following aspects such as using as a classifier usingas a dynamic forecast model and combining with otherdiagnostic methods Later pattern classification and modelidentification [4] EKF based fault detection [5] and faultdiagnosis of ball bearing using machine learning method [6]were used

In this paper SVM model is used to generate theresidual images Fault classification has been done from theextracted image features SVM is a novel machine learningmethod based on statistical learning theoryThe SVMutilizesa hyperplane with maximum margin to produce a goodgeneralization performance by separating different classes As

Hindawi Publishing CorporationModelling and Simulation in EngineeringVolume 2014 Article ID 426402 14 pageshttpdxdoiorg1011552014426402

2 Modelling and Simulation in Engineering

a result SVM has been widely used for many applicationssuch as time series forecasting fault detection modelling ofnonlinear dynamic systems one-class SVM formachine faultdetection and classification [7] SVM for copper clad laminatedefects classification [8] and SVM for fault diagnosis of asteam turbine [9]

For this study different major fault types like actuatorfault sensor fault and process fault are considered Hencethe fault residuals are generated from the output of thenominal model and this faulty model Data based faultdiagnosis method requires a large amount of historical dataTo make this method be more efficient the first step isfeature extraction [10] From the residuals signature themostappropriate statistical and geometrical features are extractedand among these 15 features are selected Through thischaracteristic extraction the data can be transformed to theprior information of fault diagnosis system SVM attributefilter is employed to rank the features in order to reduce theinput data dimension whichmakes the better performance ofthe classifier And its performance is compared based on PCAfeature reduction also

This paper is mainly focused on identifying fault clas-sification of batch reactor from the residual features usingartificial intelligent classifiers such as multilayer perceptron(MLP) radial basis function (RBF) and Bayes net Thepaper is organized as follows Section 2 describes machinelearning methods used in this work Section 3 explains thecase study of the well-known batch reactor Section 4 givesfault identificationmethod Section 5 shows and discusses thesimulation results Finally the conclusion from this work ispresented in Section 6

2 Machine Learning Methods

In this paper the machine learning methods like SVM ANNlike MLP and RBF are used SVM is a supervised learningmethod which is motivated in maximizing the ability togeneralize well from a small number of training samples bymapping the original space into a high dimensional innerproduct space called feature space via a kernel The SVMformulation follows structural risk minimization (SRM)principle in which an upper bound on the generalizationerror is minimized whereas the error risk minimization(ERM) minimizes the prediction error on the training dataThis equips the SVMwith a greater potential to generalize theinput-output relationship learnt during its training phase formaking good predictions for new input data [11]

SVMrsquos solutions are characterized by convex optimizationproblems So it can be applied in settling pattern recogni-tion problems with small samples nonlinearity and higherdimensions SVM can easily be introduced into learningproblems such as function estimation

In the batch reactor the heat released by the reactionaffects the dynamics of the reactor temperature This termdepends on the initial concentration which is usually mea-surable at a very low sampling rate not suitable for real timecontrol or estimation So any fault occurring in the batchreactor will have the impact on the heat release of the reactor

FeedStir Vent controller

Coolantsteam outlet

Coolantsteam inlet

Product

Tr VrQr

Tj

Figure 1 Schematic diagram of a jacketed batch reactor

So a model developed based on the heat release of the reactor(119876119903) which can predict the type of fault occurred But the

quantity of119876119903is not directly measurable one So an estimator

is required to estimate it Here SVM is used to build theestimator model

Similarly for classification of different faults the usualANN classifiers are used in this work There are variousneural network architectures but the application consideredin this work has used MLP with back propagation learningalgorithm RBF and the Bayes net [12ndash16]

3 Case Study

The proposed fault diagnosis scheme is applied to the batchreactor by Cott and Macchietto [17] Aziz et al [18] Mujtabaet al [19] and Sujatha and Pappa [20] The complex reactionscheme of a batch reactor is a representative of manyindustrial reactions as shown in Figure 1 The batch reactoris inherently a dynamic process The reactions I and II of thebatch reactor are given in the following equation

119860 + 119861 997888rarr 119862

119860 + 119862 997888rarr 119863(1)

where 119860 119861 are the raw materials 119862 is the desired productand119863 is the waste product

This benchmark model is given on the basis of reactionequation (1) competent of simulating the reactions like thereactor temperature jacket temperature and heat release ofreactor under nominal operating conditions and also undervarious faulty conditions

These simulations are run under closed loop control withgeneric model controller (GMC) [20 21] The total runningtime of the batch process is 120 minutes (2 hours) The batchreactor model equations are given below

119889119872119860

119889119905= minus 119877

1minus 1198772

Modelling and Simulation in Engineering 3

119889119872119861

119889119905= minus 119877

1

119889119872119862

119889119905= 1198771minus 1198772

119889119872119863

119889119905= 1198772

1198771= 1198961119872119860119872119861

1198772= 1198962119872119860119872119862

1198961= exp(

1198961

1minus 1198962

1

(119879119903+ 27315)

)

1198962= exp(

1198961

2minus 1198962

2

(119879119903+ 27315)

)

119889119879119903

119889119905=(119876119903+ 119876119895)

119872119903119862119901119903

119889119879119895

119889119905=(119879119904119901

119895minus 119879119895)

120591119895

minus119876119895

119881119895120588119895119862119901119895

119876119903= minus Δ119867

11198771minus Δ11986721198772

119872119903= 119872119860+119872119861+119872119862+119872119863

119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863

119872119903

119876119895= 119880119860(119879

119895minus 119879119903)

(2)

The initial values of the above mentioned process param-eters of [119872

119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00

200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1

4 Fault Diagnosis of the Batch Reactor

Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2

Table 1 Nominal values of the parameters

Constant parameters Values

119862119901119860

Specific heat capacity of component119860

180 kcalkmol∘C

119862119901119861

Specific heat capacity of component119861

400 kcalkmol∘C

119862119901119862

Specific heat capacity of component119862

520 kcalkmol∘C

119862119901119863

Specific heat capacity of component119863

800 kcalkmol∘C

Δ1198671

Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672

Heat of reaction of reaction 2 minus60000 kcalkmol119862119901

Mass heat capacity of reactant 045 kcalkg∘C119862119901119895

Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895

Density 10000 kgm3

1198961

1

Preexponential rate constant forreaction 1 209057

1198962

1

Preexponential rate constant forreaction 1 10000

1198961

2

Preexponential rate constant forreaction 2 389057

1198962

2

Preexponential rate constant forreaction 2 17000

119881119895

Jacket volume 06921m3

119860 Heat transfer area 624m2

119872119903

Number of moles of component 1560 kg120591119895

Jacket time constant 30min

Actuator Process Sensor

Faults Faults Faults

Figure 2 Types of faults

Faults can be defined as follows

(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults

(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors

Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906

119886(119905) = 119906(119905) + 119891

119886(119905) where 119891

119886(119905) is the actuator

fault vector Abrupt constant bias has been given via thevector 119891

119886(119905) = 120575119906 so that the actuator action becomes

4 Modelling and Simulation in Engineering

100999897969594939291

0 20 40 60 80 100 120

Actu

ator

inpu

t

Time (min)

Added actuatorbias

(with

bia

s add

ition

)

Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes

Actuator freezing

936

932

928

924

920 20 40 60 80 100 120

Time (min)

Actu

ator

inpu

t(w

ith fr

eezi

ng)

Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)

Tr(k minus 1) Tr(k)

Tj(k)Tj(k minus 1)

Qr(k minus 1)

Tr(k minus 2)

Qr(k)

Input Output

Figure 5 Inputoutput mapping of the SVM heat release estimator

119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing

of the actuator at certain time has been shown as 119891119886(119905) =

minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in

Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor

41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876

119903) which is not ameasurable parameter is estimated

through the SVMmodel

42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which

SVM estimator

Batch reactor y(k)u(k)

zminus1

zminus1

zminus2

zminus2

Qr(k)

Figure 6 Training method for the heat release estimator

0 20 40 60 80 100 120

Time (min)

Predicted (SVM)Actual

1600

1400

1200

1000

800

600

400

200

0

minus200Qr

(kJm

in)

Figure 7 Response of SVM 119876119903estimator under normal condition

the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown

in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is

developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7

The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876

119903) which is

the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers

43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876

119903) Each fault is introduced through simulation and

the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work

431 Process Fault

(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation

Modelling and Simulation in Engineering 5

(nominal)

Faults

Residual (faulty)

Signature window

Features extraction

Feature reduction bySVM attribute

Batch reactor

SVM estimator model (under faulty

condition) SVM estimator model

ANN classifiers

Faults

Qr

Qr (in presenceof fault)

ip

minus

+

Figure 8 Block diagram of fault diagnosis process

Table 2 Fault description

Slnumber

Faulttypes Fault description Category

1 Fault1 Δ119867mdashheat of reactionchange Process fault

2 Fault2119872119886119872119887change (initial

values of input componentfeed change)

Process fault

3 Fault3 Heat transfer coefficientchange (119880) Process fault

4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault

6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault

in 119876119903residual for 10 20 30 and 40 increase

and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value

of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876

119903residual for the heat

of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10

(iii) Change in initial charge of reactants (119872119860 119872119861) a

change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876

119903residual for 10 20

25 and 30 decrease and increase in initial chargeare as shown in Figure 11

In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed

432 Actuator Fault The actuator fault considered here is asfollows

(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3

(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4

The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13

From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary

433 Sensor Faults The following sensor faults are consid-ered in this work

(i) jacket temperature and reactor temperature measure-ments with the white noise

(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876

119903residual for the sensor faults is shown in

Figure 14The signature of the sensor fault pattern is varying with

respect to the sources of different components and at the timeof fault

From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below

(i) Mean average value of a signal is termed as meanvalue as given in

120583119862=

1

119872119873sum

119894

sum

119895

119875119888

119894119895 (3)

(ii) Standard deviation it is a measure of energy contentin the fault signature shown in

SD = radic119899sum1199092

minus (sum119909)2

119899 (119899 minus 1) (4)

(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in

skewness = 119899

(119899 minus 1) (119899 minus 2)sum(

119909119894minus 119909

119904)

3

(5)

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

2 Modelling and Simulation in Engineering

a result SVM has been widely used for many applicationssuch as time series forecasting fault detection modelling ofnonlinear dynamic systems one-class SVM formachine faultdetection and classification [7] SVM for copper clad laminatedefects classification [8] and SVM for fault diagnosis of asteam turbine [9]

For this study different major fault types like actuatorfault sensor fault and process fault are considered Hencethe fault residuals are generated from the output of thenominal model and this faulty model Data based faultdiagnosis method requires a large amount of historical dataTo make this method be more efficient the first step isfeature extraction [10] From the residuals signature themostappropriate statistical and geometrical features are extractedand among these 15 features are selected Through thischaracteristic extraction the data can be transformed to theprior information of fault diagnosis system SVM attributefilter is employed to rank the features in order to reduce theinput data dimension whichmakes the better performance ofthe classifier And its performance is compared based on PCAfeature reduction also

This paper is mainly focused on identifying fault clas-sification of batch reactor from the residual features usingartificial intelligent classifiers such as multilayer perceptron(MLP) radial basis function (RBF) and Bayes net Thepaper is organized as follows Section 2 describes machinelearning methods used in this work Section 3 explains thecase study of the well-known batch reactor Section 4 givesfault identificationmethod Section 5 shows and discusses thesimulation results Finally the conclusion from this work ispresented in Section 6

2 Machine Learning Methods

In this paper the machine learning methods like SVM ANNlike MLP and RBF are used SVM is a supervised learningmethod which is motivated in maximizing the ability togeneralize well from a small number of training samples bymapping the original space into a high dimensional innerproduct space called feature space via a kernel The SVMformulation follows structural risk minimization (SRM)principle in which an upper bound on the generalizationerror is minimized whereas the error risk minimization(ERM) minimizes the prediction error on the training dataThis equips the SVMwith a greater potential to generalize theinput-output relationship learnt during its training phase formaking good predictions for new input data [11]

SVMrsquos solutions are characterized by convex optimizationproblems So it can be applied in settling pattern recogni-tion problems with small samples nonlinearity and higherdimensions SVM can easily be introduced into learningproblems such as function estimation

In the batch reactor the heat released by the reactionaffects the dynamics of the reactor temperature This termdepends on the initial concentration which is usually mea-surable at a very low sampling rate not suitable for real timecontrol or estimation So any fault occurring in the batchreactor will have the impact on the heat release of the reactor

FeedStir Vent controller

Coolantsteam outlet

Coolantsteam inlet

Product

Tr VrQr

Tj

Figure 1 Schematic diagram of a jacketed batch reactor

So a model developed based on the heat release of the reactor(119876119903) which can predict the type of fault occurred But the

quantity of119876119903is not directly measurable one So an estimator

is required to estimate it Here SVM is used to build theestimator model

Similarly for classification of different faults the usualANN classifiers are used in this work There are variousneural network architectures but the application consideredin this work has used MLP with back propagation learningalgorithm RBF and the Bayes net [12ndash16]

3 Case Study

The proposed fault diagnosis scheme is applied to the batchreactor by Cott and Macchietto [17] Aziz et al [18] Mujtabaet al [19] and Sujatha and Pappa [20] The complex reactionscheme of a batch reactor is a representative of manyindustrial reactions as shown in Figure 1 The batch reactoris inherently a dynamic process The reactions I and II of thebatch reactor are given in the following equation

119860 + 119861 997888rarr 119862

119860 + 119862 997888rarr 119863(1)

where 119860 119861 are the raw materials 119862 is the desired productand119863 is the waste product

This benchmark model is given on the basis of reactionequation (1) competent of simulating the reactions like thereactor temperature jacket temperature and heat release ofreactor under nominal operating conditions and also undervarious faulty conditions

These simulations are run under closed loop control withgeneric model controller (GMC) [20 21] The total runningtime of the batch process is 120 minutes (2 hours) The batchreactor model equations are given below

119889119872119860

119889119905= minus 119877

1minus 1198772

Modelling and Simulation in Engineering 3

119889119872119861

119889119905= minus 119877

1

119889119872119862

119889119905= 1198771minus 1198772

119889119872119863

119889119905= 1198772

1198771= 1198961119872119860119872119861

1198772= 1198962119872119860119872119862

1198961= exp(

1198961

1minus 1198962

1

(119879119903+ 27315)

)

1198962= exp(

1198961

2minus 1198962

2

(119879119903+ 27315)

)

119889119879119903

119889119905=(119876119903+ 119876119895)

119872119903119862119901119903

119889119879119895

119889119905=(119879119904119901

119895minus 119879119895)

120591119895

minus119876119895

119881119895120588119895119862119901119895

119876119903= minus Δ119867

11198771minus Δ11986721198772

119872119903= 119872119860+119872119861+119872119862+119872119863

119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863

119872119903

119876119895= 119880119860(119879

119895minus 119879119903)

(2)

The initial values of the above mentioned process param-eters of [119872

119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00

200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1

4 Fault Diagnosis of the Batch Reactor

Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2

Table 1 Nominal values of the parameters

Constant parameters Values

119862119901119860

Specific heat capacity of component119860

180 kcalkmol∘C

119862119901119861

Specific heat capacity of component119861

400 kcalkmol∘C

119862119901119862

Specific heat capacity of component119862

520 kcalkmol∘C

119862119901119863

Specific heat capacity of component119863

800 kcalkmol∘C

Δ1198671

Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672

Heat of reaction of reaction 2 minus60000 kcalkmol119862119901

Mass heat capacity of reactant 045 kcalkg∘C119862119901119895

Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895

Density 10000 kgm3

1198961

1

Preexponential rate constant forreaction 1 209057

1198962

1

Preexponential rate constant forreaction 1 10000

1198961

2

Preexponential rate constant forreaction 2 389057

1198962

2

Preexponential rate constant forreaction 2 17000

119881119895

Jacket volume 06921m3

119860 Heat transfer area 624m2

119872119903

Number of moles of component 1560 kg120591119895

Jacket time constant 30min

Actuator Process Sensor

Faults Faults Faults

Figure 2 Types of faults

Faults can be defined as follows

(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults

(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors

Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906

119886(119905) = 119906(119905) + 119891

119886(119905) where 119891

119886(119905) is the actuator

fault vector Abrupt constant bias has been given via thevector 119891

119886(119905) = 120575119906 so that the actuator action becomes

4 Modelling and Simulation in Engineering

100999897969594939291

0 20 40 60 80 100 120

Actu

ator

inpu

t

Time (min)

Added actuatorbias

(with

bia

s add

ition

)

Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes

Actuator freezing

936

932

928

924

920 20 40 60 80 100 120

Time (min)

Actu

ator

inpu

t(w

ith fr

eezi

ng)

Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)

Tr(k minus 1) Tr(k)

Tj(k)Tj(k minus 1)

Qr(k minus 1)

Tr(k minus 2)

Qr(k)

Input Output

Figure 5 Inputoutput mapping of the SVM heat release estimator

119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing

of the actuator at certain time has been shown as 119891119886(119905) =

minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in

Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor

41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876

119903) which is not ameasurable parameter is estimated

through the SVMmodel

42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which

SVM estimator

Batch reactor y(k)u(k)

zminus1

zminus1

zminus2

zminus2

Qr(k)

Figure 6 Training method for the heat release estimator

0 20 40 60 80 100 120

Time (min)

Predicted (SVM)Actual

1600

1400

1200

1000

800

600

400

200

0

minus200Qr

(kJm

in)

Figure 7 Response of SVM 119876119903estimator under normal condition

the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown

in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is

developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7

The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876

119903) which is

the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers

43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876

119903) Each fault is introduced through simulation and

the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work

431 Process Fault

(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation

Modelling and Simulation in Engineering 5

(nominal)

Faults

Residual (faulty)

Signature window

Features extraction

Feature reduction bySVM attribute

Batch reactor

SVM estimator model (under faulty

condition) SVM estimator model

ANN classifiers

Faults

Qr

Qr (in presenceof fault)

ip

minus

+

Figure 8 Block diagram of fault diagnosis process

Table 2 Fault description

Slnumber

Faulttypes Fault description Category

1 Fault1 Δ119867mdashheat of reactionchange Process fault

2 Fault2119872119886119872119887change (initial

values of input componentfeed change)

Process fault

3 Fault3 Heat transfer coefficientchange (119880) Process fault

4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault

6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault

in 119876119903residual for 10 20 30 and 40 increase

and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value

of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876

119903residual for the heat

of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10

(iii) Change in initial charge of reactants (119872119860 119872119861) a

change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876

119903residual for 10 20

25 and 30 decrease and increase in initial chargeare as shown in Figure 11

In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed

432 Actuator Fault The actuator fault considered here is asfollows

(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3

(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4

The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13

From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary

433 Sensor Faults The following sensor faults are consid-ered in this work

(i) jacket temperature and reactor temperature measure-ments with the white noise

(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876

119903residual for the sensor faults is shown in

Figure 14The signature of the sensor fault pattern is varying with

respect to the sources of different components and at the timeof fault

From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below

(i) Mean average value of a signal is termed as meanvalue as given in

120583119862=

1

119872119873sum

119894

sum

119895

119875119888

119894119895 (3)

(ii) Standard deviation it is a measure of energy contentin the fault signature shown in

SD = radic119899sum1199092

minus (sum119909)2

119899 (119899 minus 1) (4)

(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in

skewness = 119899

(119899 minus 1) (119899 minus 2)sum(

119909119894minus 119909

119904)

3

(5)

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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RotatingMachinery

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 3

119889119872119861

119889119905= minus 119877

1

119889119872119862

119889119905= 1198771minus 1198772

119889119872119863

119889119905= 1198772

1198771= 1198961119872119860119872119861

1198772= 1198962119872119860119872119862

1198961= exp(

1198961

1minus 1198962

1

(119879119903+ 27315)

)

1198962= exp(

1198961

2minus 1198962

2

(119879119903+ 27315)

)

119889119879119903

119889119905=(119876119903+ 119876119895)

119872119903119862119901119903

119889119879119895

119889119905=(119879119904119901

119895minus 119879119895)

120591119895

minus119876119895

119881119895120588119895119862119901119895

119876119903= minus Δ119867

11198771minus Δ11986721198772

119872119903= 119872119860+119872119861+119872119862+119872119863

119862119901119903=119862119901119860119872119860+ 119862119901119861119872119861+ 119862119901119862119872119862+ 119862119901119863119872119863

119872119903

119876119895= 119880119860(119879

119895minus 119879119903)

(2)

The initial values of the above mentioned process param-eters of [119872

119860 119872119861 119872119862 119872119863 119879119895 119879119903] are [120 120 00 00

200 200] at 119905 = 0 The reactor temperature is used as thecontrol variable and is bounded between 20∘ and 100∘C andthe jacket temperature is the manipulated variable and it isbounded between 20∘ and 120∘C All the nominal parametersand constant values used in themodel equations (2) are givenin Table 1

4 Fault Diagnosis of the Batch Reactor

Fault can be defined as any nonpermitted deviation of processbehaviour from an acceptable one So fault diagnosis is theproblem of identifying and isolating unanticipated changesin a process Diagnosis is a challenging problem due toseveral factors such as monitoring the number of variablesoccurrences of the process complexity and the variety ofprocess failures The failures can be broadly categorized intothree types such as actuator faults sensor faults and processfaultsThe fault types are inspired from the relevant literature[22] presented in Figure 2

Table 1 Nominal values of the parameters

Constant parameters Values

119862119901119860

Specific heat capacity of component119860

180 kcalkmol∘C

119862119901119861

Specific heat capacity of component119861

400 kcalkmol∘C

119862119901119862

Specific heat capacity of component119862

520 kcalkmol∘C

119862119901119863

Specific heat capacity of component119863

800 kcalkmol∘C

Δ1198671

Heat of reaction of reaction 1 minus100000 kcalkmolΔ1198672

Heat of reaction of reaction 2 minus60000 kcalkmol119862119901

Mass heat capacity of reactant 045 kcalkg∘C119862119901119895

Molar heat capacity of component 119895 045 kcalkg∘C119880 Heat transfer coefficient 976 kcalminm2 ∘C120588119895

Density 10000 kgm3

1198961

1

Preexponential rate constant forreaction 1 209057

1198962

1

Preexponential rate constant forreaction 1 10000

1198961

2

Preexponential rate constant forreaction 2 389057

1198962

2

Preexponential rate constant forreaction 2 17000

119881119895

Jacket volume 06921m3

119860 Heat transfer area 624m2

119872119903

Number of moles of component 1560 kg120591119895

Jacket time constant 30min

Actuator Process Sensor

Faults Faults Faults

Figure 2 Types of faults

Faults can be defined as follows

(i) Process faults processes that occur below a certainlevel of detail are generally represented as lumpedparameters in process models An example of such alumped parameter in this batch reactor is the foulingfactor Changes in these parameters are termed asprocess or parametric faults

(ii) Sensor failure while all sensors have random errorssensor failures refer to gross errors such as biasmeasurement with noise and frozen sensors

Controller and actuator fault the actuator faults aremostly caused by the nonlinear characteristics of the controlvalve by hysteresis stiction friction and poor controllertuning Actuator action in the presence of fault can berepresented as 119906

119886(119905) = 119906(119905) + 119891

119886(119905) where 119891

119886(119905) is the actuator

fault vector Abrupt constant bias has been given via thevector 119891

119886(119905) = 120575119906 so that the actuator action becomes

4 Modelling and Simulation in Engineering

100999897969594939291

0 20 40 60 80 100 120

Actu

ator

inpu

t

Time (min)

Added actuatorbias

(with

bia

s add

ition

)

Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes

Actuator freezing

936

932

928

924

920 20 40 60 80 100 120

Time (min)

Actu

ator

inpu

t(w

ith fr

eezi

ng)

Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)

Tr(k minus 1) Tr(k)

Tj(k)Tj(k minus 1)

Qr(k minus 1)

Tr(k minus 2)

Qr(k)

Input Output

Figure 5 Inputoutput mapping of the SVM heat release estimator

119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing

of the actuator at certain time has been shown as 119891119886(119905) =

minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in

Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor

41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876

119903) which is not ameasurable parameter is estimated

through the SVMmodel

42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which

SVM estimator

Batch reactor y(k)u(k)

zminus1

zminus1

zminus2

zminus2

Qr(k)

Figure 6 Training method for the heat release estimator

0 20 40 60 80 100 120

Time (min)

Predicted (SVM)Actual

1600

1400

1200

1000

800

600

400

200

0

minus200Qr

(kJm

in)

Figure 7 Response of SVM 119876119903estimator under normal condition

the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown

in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is

developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7

The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876

119903) which is

the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers

43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876

119903) Each fault is introduced through simulation and

the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work

431 Process Fault

(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation

Modelling and Simulation in Engineering 5

(nominal)

Faults

Residual (faulty)

Signature window

Features extraction

Feature reduction bySVM attribute

Batch reactor

SVM estimator model (under faulty

condition) SVM estimator model

ANN classifiers

Faults

Qr

Qr (in presenceof fault)

ip

minus

+

Figure 8 Block diagram of fault diagnosis process

Table 2 Fault description

Slnumber

Faulttypes Fault description Category

1 Fault1 Δ119867mdashheat of reactionchange Process fault

2 Fault2119872119886119872119887change (initial

values of input componentfeed change)

Process fault

3 Fault3 Heat transfer coefficientchange (119880) Process fault

4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault

6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault

in 119876119903residual for 10 20 30 and 40 increase

and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value

of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876

119903residual for the heat

of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10

(iii) Change in initial charge of reactants (119872119860 119872119861) a

change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876

119903residual for 10 20

25 and 30 decrease and increase in initial chargeare as shown in Figure 11

In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed

432 Actuator Fault The actuator fault considered here is asfollows

(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3

(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4

The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13

From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary

433 Sensor Faults The following sensor faults are consid-ered in this work

(i) jacket temperature and reactor temperature measure-ments with the white noise

(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876

119903residual for the sensor faults is shown in

Figure 14The signature of the sensor fault pattern is varying with

respect to the sources of different components and at the timeof fault

From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below

(i) Mean average value of a signal is termed as meanvalue as given in

120583119862=

1

119872119873sum

119894

sum

119895

119875119888

119894119895 (3)

(ii) Standard deviation it is a measure of energy contentin the fault signature shown in

SD = radic119899sum1199092

minus (sum119909)2

119899 (119899 minus 1) (4)

(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in

skewness = 119899

(119899 minus 1) (119899 minus 2)sum(

119909119894minus 119909

119904)

3

(5)

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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DistributedSensor Networks

International Journal of

4 Modelling and Simulation in Engineering

100999897969594939291

0 20 40 60 80 100 120

Actu

ator

inpu

t

Time (min)

Added actuatorbias

(with

bia

s add

ition

)

Figure 3 Simulated actuator fault by introducing bias at the time of80 minutes

Actuator freezing

936

932

928

924

920 20 40 60 80 100 120

Time (min)

Actu

ator

inpu

t(w

ith fr

eezi

ng)

Figure 4 Simulated actuator fault by introducing freezing at thetime interval (80ndash100 minutes)

Tr(k minus 1) Tr(k)

Tj(k)Tj(k minus 1)

Qr(k minus 1)

Tr(k minus 2)

Qr(k)

Input Output

Figure 5 Inputoutput mapping of the SVM heat release estimator

119906119886(119905) = 119906(119905) + 120575119906 as shown in Figure 3 Similarly the freezing

of the actuator at certain time has been shown as 119891119886(119905) =

minus119906(119905) so that the actuator action is 119906119886(119905) = 0 as shown in

Figure 4 The faults that occurred in the batch reactor have arelationship with the heat release of the reactor

41 SVM Estimator Model Based Fault Detection Modelbased fault detection method is developed based on theassumption that the developed model is replica of the realplant dynamics The input-output data are obtained by simu-lating the batch reactor with nominal operating conditionsThe different faults have been introduced in the reactorthrough simulation by using MATLAB software From thesimulated input and output data SVM estimator model isdeveloped using LIBSVM toolbox The heat release of thereactor (119876

119903) which is not ameasurable parameter is estimated

through the SVMmodel

42 Training and Testing of the Estimator Training the SVMestimator as shown in Figure 6 is an iterative process in which

SVM estimator

Batch reactor y(k)u(k)

zminus1

zminus1

zminus2

zminus2

Qr(k)

Figure 6 Training method for the heat release estimator

0 20 40 60 80 100 120

Time (min)

Predicted (SVM)Actual

1600

1400

1200

1000

800

600

400

200

0

minus200Qr

(kJm

in)

Figure 7 Response of SVM 119876119903estimator under normal condition

the SVM is given inputs along with the desired outputs Inthis work the SVM estimates the heat release of the reactor(119876119903)The input and outputmapping of the estimator is shown

in Figure 5 where the past and present values of the reactortemperature and jacket temperature and the past values of the119876119903are considered as the input data The estimator model is

developed by selecting the SVM parameters such as 120574 = 90120590 = 100 and the Radial Basis Function (RBF) as kernel tobuild and train the estimator as shown in Figure 6 Withoutany fault the response of the estimator is shown in Figure 7

The estimator models are developed under both normaland faulty conditions The difference between faulty andnominal model is called residual (in terms of 119876

119903) which is

the important part of the fault diagnosing method as shownin Figure 8 Based on the residual patterns the faults areidentified through ANN classifiers

43 Different Faults Three different types of faults such asprocess fault sensor fault and actuator fault are introducedand data is collected for estimation of heat release of thereactor (119876

119903) Each fault is introduced through simulation and

the respective plant input and output data are collected everytime Table 2 shows the assigned fault for this work

431 Process Fault

(i) Change in heat transfer coefficient (119880) because of thefouling effect present in the heat exchanger119880 changesfrom its nominal value from batch to batch Variation

Modelling and Simulation in Engineering 5

(nominal)

Faults

Residual (faulty)

Signature window

Features extraction

Feature reduction bySVM attribute

Batch reactor

SVM estimator model (under faulty

condition) SVM estimator model

ANN classifiers

Faults

Qr

Qr (in presenceof fault)

ip

minus

+

Figure 8 Block diagram of fault diagnosis process

Table 2 Fault description

Slnumber

Faulttypes Fault description Category

1 Fault1 Δ119867mdashheat of reactionchange Process fault

2 Fault2119872119886119872119887change (initial

values of input componentfeed change)

Process fault

3 Fault3 Heat transfer coefficientchange (119880) Process fault

4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault

6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault

in 119876119903residual for 10 20 30 and 40 increase

and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value

of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876

119903residual for the heat

of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10

(iii) Change in initial charge of reactants (119872119860 119872119861) a

change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876

119903residual for 10 20

25 and 30 decrease and increase in initial chargeare as shown in Figure 11

In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed

432 Actuator Fault The actuator fault considered here is asfollows

(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3

(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4

The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13

From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary

433 Sensor Faults The following sensor faults are consid-ered in this work

(i) jacket temperature and reactor temperature measure-ments with the white noise

(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876

119903residual for the sensor faults is shown in

Figure 14The signature of the sensor fault pattern is varying with

respect to the sources of different components and at the timeof fault

From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below

(i) Mean average value of a signal is termed as meanvalue as given in

120583119862=

1

119872119873sum

119894

sum

119895

119875119888

119894119895 (3)

(ii) Standard deviation it is a measure of energy contentin the fault signature shown in

SD = radic119899sum1199092

minus (sum119909)2

119899 (119899 minus 1) (4)

(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in

skewness = 119899

(119899 minus 1) (119899 minus 2)sum(

119909119894minus 119909

119904)

3

(5)

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 5

(nominal)

Faults

Residual (faulty)

Signature window

Features extraction

Feature reduction bySVM attribute

Batch reactor

SVM estimator model (under faulty

condition) SVM estimator model

ANN classifiers

Faults

Qr

Qr (in presenceof fault)

ip

minus

+

Figure 8 Block diagram of fault diagnosis process

Table 2 Fault description

Slnumber

Faulttypes Fault description Category

1 Fault1 Δ119867mdashheat of reactionchange Process fault

2 Fault2119872119886119872119887change (initial

values of input componentfeed change)

Process fault

3 Fault3 Heat transfer coefficientchange (119880) Process fault

4 Fault4 Actuator freezing Actuator fault5 Fault5 Actuator biasing Actuator fault

6 Fault6 Sensor abrupt zero biasingand addition of white noise Sensor fault

in 119876119903residual for 10 20 30 and 40 increase

and decrease in 119880 are shown in Figure 9(ii) Change in heat of reaction (Δ119867) the actual value

of heat of reaction may not be available in theopen literature and subsequently it can be the basicfor model mismatch due to change in unmeasuredparameter The variation in 119876

119903residual for the heat

of the reaction is reduced and increased by 10 and25 from the nominal value as shown in Figure 10

(iii) Change in initial charge of reactants (119872119860 119872119861) a

change in product demand and accidental failure ofthe charging system or scale-up issues at the designstage will be the causes for the change in the operatingconditionsThe variation in119876

119903residual for 10 20

25 and 30 decrease and increase in initial chargeare as shown in Figure 11

In the heat release of the reactor residual patterns forthe process fault the differences in sign of magnitudesluggishness of the response decrease of the magnitude andchange of the starting position of the curve are observed

432 Actuator Fault The actuator fault considered here is asfollows

(i) The addition of bias in the actuator shows the stickingnature of the actuator as shown in Figure 3

(ii) The actuator freezing occurred in the time interval 80to 100 minutes as shown in Figure 4

The residuals from the actuator faults as freezing at thedifferent time intervals and biasing are shown in Figures 12and 13

From the actuator fault of both freezing and biasingsignatures abrupt change is identified at the moment of faultoccurring and based on the duration the magnitude and thepattern of the residual vary

433 Sensor Faults The following sensor faults are consid-ered in this work

(i) jacket temperature and reactor temperature measure-ments with the white noise

(ii) abrupt bias at sensor(iii) abrupt zero at sensorVariation in 119876

119903residual for the sensor faults is shown in

Figure 14The signature of the sensor fault pattern is varying with

respect to the sources of different components and at the timeof fault

From the fault signatures the relevant statistical andgeometrical features are extracted Here 15 features suchas area mean standard deviation skew kurtosis fractionalarea Feretrsquos diameter integrated density and raw integrateddensity are extracted by using Image J software Few of thefeatures are explained below

(i) Mean average value of a signal is termed as meanvalue as given in

120583119862=

1

119872119873sum

119894

sum

119895

119875119888

119894119895 (3)

(ii) Standard deviation it is a measure of energy contentin the fault signature shown in

SD = radic119899sum1199092

minus (sum119909)2

119899 (119899 minus 1) (4)

(iii) Skewness it is a measure of symmetry or moreprecisely the lack of symmetry as expressed in

skewness = 119899

(119899 minus 1) (119899 minus 2)sum(

119909119894minus 119909

119904)

3

(5)

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

6 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

20

40

Time (min)

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 1200

200

400

600

800

1000

1200

1400

1600

Time (min)

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

20

40

60

80

100

120

Time (min)

minus40

minus20

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

Time (min)

minus1400

minus1200

minus1000

minus800

minus600

minus400

minus200

Qr

resid

ual

(d)

Figure 9 Residual (in terms of119876119903) due to change in heat transfer (a) Residual (in terms of119876

119903) due to 10 sudden increase in the heat transfer

coefficient (119880) (b) Residual (in terms of 119876119903) due to 20 reduction in the heat transfer coefficient (119880) (c) Residual (in terms of 119876

119903) due to

40 increase in the heat transfer coefficient (119880) (d) Residual (in terms of 119876119903) due to 30 increase in the heat transfer coefficient (119880)

(iv) Kurtosis it is a measure of whether the data arepeaked or flat relative to the normal distribution asgiven in

kurtosis = [119899 (119899 + 1)

(119899 minus 1) (119899 minus 2) (119899 minus 3)sum(

119909119894minus 119909

119904)

4

]

minus 3(119899 minus 1)

2

(119899 minus 2) (119899 minus 3)

(6)

where 119899 is the sample size and 119904 is the standard deviation

5 Results and Discussion

The extracted features from the 24 simulated fault instancesare listed in Table 3 The instance means the number of datapoints in the input data The listed features are reduced todecrease the computational complexityThe feature reductionas well as fault classification is carried out by using WEKAsoftware

51 SVM Attribute Filter Based Feature Selection SVMattribute filter is used to reduce the number of features byranking method Intuitively the SVM model is a represen-tation of the points in space mapped so that the featuresof separate categories are divided by a clear gap The newfeatures are then mapped into the same space and predictedto belong to a category based on which side of the gapthey fall on The features are given as the input to the SVMattribute filter The attributes are ranked by the square ofthe weight assigned by the SVM An attribute selection formulticlass problem is handled by ranking attributes for eachclass separately using a one-versus-all method Based onthe attribute ranking Table 4 the number of input featuresis selected for the classifier to improve the performance ofit

52 Classifier Performance After selecting the fault as anattribute for class the classification is carried out with theANN classifiers The output of the WEKA software gives

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 7

Table3Ex

tractedfeatures

from119876119903resid

ual

Class

Area

Mean

StdD

ev119883

119884119883119872

119884119872

Major

Minor

Feret

IntD

enSkew

Kurt

fArea

RawIntD

enFA

ULT

15344

652499

83542

6645

3165

66570

31624

112725

60368

113323

133605465

minus6915

45815

98031

133605465

FAULT

15396

4825032

3422

6650

3090

66569

3091

8111935

61383

113137

135084975

minus7177

49512

9816

5135084975

FAULT

1547120

2516

12918

6605

2970

6615

429830

110242

6318

9112611

137664

045

minus8507

70364

98673

137664

045

FAULT

2502824

2514

13001

6620

3205

66289

32061

111032

57660

110877

1264

18800

minus8258

6619

598595

1264

18800

FAULT

2511160

2514

82974

6655

3170

66639

3170

7110919

58675

111206

128548050

minus8338

67519

98621

128548050

FAULT

2543240

25056

3335

6690

3080

67012

30825

113514

6093

2114

176

136114410

minus7379

52455

98259

136114410

FAULT

2543510

25041

3390

6630

3235

66415

32340

111709

6194

8113203

136100130

minus725

50569

982

136100130

FAULT

2506430

2512

03087

6605

3170

6619

131695

112048

57547

111631

127218225

minus8014

62225

98512

127218225

FAULT

3522080

25093

3193

6700

3180

67070

31860

113289

58675

113067

131008800

minus7731

5776

698406

131008800

FAULT

3524365

25023

3454

6625

3125

66383

31287

112273

59465

112594

1312117

80minus7105

48477

9812

91312117

80FA

ULT

3523566

25079

3246

6590

3115

66066

31211

111258

5991

6111989

131309190

minus7596

55699

98352

131309190

FAULT

3525616

25086

3220

6620

3110

66303

3112

8111483

60029

112212

131858715

minus7661

56687

9837

8131858715

FAULT

4493968

2498

53583

6610

3270

6595

33274

8111032

56644

110465

123422550

minus6828

44626

97984

123422550

FAULT

4516780

24875

3941

6630

3150

6599

031550

111709

5890

1111918

128551365

minus6153

35855

97551

128551365

FAULT

4490539

2491

53815

6625

3205

6615

03214

8111371

56080

110506

122220990

minus6377

38662

97708

122220990

FAULT

4503296

25023

3453

6605

3240

6590

532492

110919

5777

3110834

125941950

minus7108

4852

79813

1125941950

FAULT

55144

8525000

3535

6655

3155

66409

31753

112725

58111

112393

12862200

0minus6931

46035

9804

12862200

0FA

ULT

5502892

25090

3205

6620

3225

6613

532334

111483

57434

111140

126178590

minus7701

57302

9839

4126178590

FAULT

5520676

25065

3301

6640

3165

66356

31526

111483

59465

111976

130508235

minus746

53659

98295

130508235

FAULT

5515840

25095

3186

6640

3180

66258

31858

111935

58675

112002

129452025

minus7748

58039

98413

129452025

FAULT

5519024

23486

6876

6685

3120

67091

31267

11091

959578

111582

121902750

minus3123

7753

9210

6121902750

FAULT

6518000

2414

35722

6540

3230

65845

32111

112837

58450

112619

125065515

minus3983

1386

94682

125065515

FAULT

6517443

24400

5179

6545

3135

66061

31644

112499

58562

112399

126258915

minus4499

18238

95688

126258915

FAULT

6524160

24489

4974

6570

3210

66489

31861

1137406

58675

113422

128365215

minus472

20281

96038

128365215

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Modelling and Simulation in Engineering

0 20 40 60 80 100 1200

50

100

150

200

250

300

350

400

Time (min)

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

Time (min)

minus150

minus100

minus50

Qr

resid

ual

(c)

Figure 10 Residual (in terms of 119876119903) due to change in heat of reaction (a) Residual (in terms of 119876

119903) due to 25 decrease in heat of reaction

(b) Residual (in terms of 119876119903) due to 25 increase in heat of reaction(c) Residual (in terms of 119876

119903) due to 10 increase in heat of reaction

Table 4 SVM ranking table

Sl number Name of the attributes SVM ranking1 Minor 152 Kurt 143 Mean 134 Feret 125 119883 116 119884119872 107 119883119872 98 fArea 89 Skew 710 119884 611 Major 512 StdDev 413 Area 314 RawIntDen 215 IntDen 1

Table 5 Confusion matrix for different classifier

Bayes ANN RBF Classa b c d e f a b c d e f a b c d e f3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 0 0 0 a = FAULT12 0 0 0 3 0 0 5 0 0 0 0 0 50 0 0 0 b = FAULT20 0 4 0 0 0 0 0 4 0 0 0 0 0 4 0 0 0 c = FAULT30 0 0 3 1 0 0 0 0 4 0 0 0 0 0 4 0 0 d = FAULT40 0 0 0 5 0 0 0 0 0 5 0 0 0 0 0 5 0 e = FAULT50 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 2 f = FAULT6

the confusion matrix which shows a detailed accuracy ofthe classifier based on the class and evaluation of the successof the numeric prediction In the multiple classificationthe outcome of this test data displays a two-dimensionalconfusion matrix with a row and column for each class Eachmatrix element shows the number of test examples for whichthe actual class is the row and the predicted class is thecolumn The confusion matrix shows each classifierrsquos abilityto achieve in the classification of faults as shown in Table 5

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

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Civil EngineeringAdvances in

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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International Journal of

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DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 9

0 20 40 60 80 100 120

0

100

Time (min)

minus500

minus400

minus300

minus200

minus100

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

100

200

300

400

500

600

700

Time (min)

minus100

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

50

100

150

200

250

300

350

400

450

Time (min)

minus50

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

50

Time (min)

minus100

minus150

minus50

minus200

minus250

Qr

resid

ual

(d)

Figure 11 Residual (in terms of 119876119903) due to change in initial values of the raw material (119872

119860119872119861) (a) Residual (in terms of 119876

119903) due to 25

increase in the initial values of the raw material (119872119860119872119861) (b) Residual (in terms of 119876

119903) due to 30 decrease in the initial values of the raw

material (119872119860 119872119861) (c) Residual (in terms of 119876

119903) due to 20 decrease in the initial values of the raw material (119872

119860 119872119861) (d) Residual (in

terms of 119876119903) due to 10 decrease in the initial values of the raw material (119872

119860119872119861)

Table 6 Results for training of fault features

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

TP rate 0542 0542 0583 0917 1 1 1 1 1FP rate 0111 0111 0092 0017 0 0 0 0 0Precision 0399 0399 0384 0927 1 1 1 1 1Recall 0542 0542 0583 0917 1 1 1 1 1119865-measure 0426 0426 045 0917 1 1 1 1 1ROC area 0815 0815 0865 0989 1 1 1 1 1

From this the radial basis function andmultilayer perceptronhave given better results as compared with the Bayes netclassifier

The training parameters for various classifiers for varyingthe number of features as 15 features 9 features and 5 featuresset as the input for the different classifiers are listed in Table 6which denotes the values of the true positive (TP rate) falsepositive (FP rate) precision recall F-measure andROCarea

The values of the TP rate precision recall F-measure andROC area are ldquo1rdquo for RBF and MLP as compared with theBayes net

Classifiers performance criteria are shown in Table 7 forthree sets of training pattern From this table MLP and RBFclassified all instances correctly (100) compared with Bayesnet Comparing MLP and RBF the mean absolute error rootmean square error relative absolute error and root relative

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Modelling and Simulation in Engineering

Table 7 Performance criteria of the classifiers

Classifiers Bayes MLP RBF5 features 9 features 15 features 5 features 9 features 15 features 5 features 9 features 15 features

Correctly classified instance 13 (54) 13 (54) 14 (58) 22 (92) 24 (100) 24 (100) 24 24 24Incorrectly classified instance 11 (45) 11 (45) 10 (42) 2 (8) 0 (0) 0 (0) 0 0 0Kappa statistics 044 044 05 09 1 1 1 1 1Mean absolute error 015 015 014 011 0063 00394 00005 00001 00001Root mean square error () 029 029 027 018 01074 00694 00031 00004 004Relative absolute error () 64 64 58 44 26 16 02068 003 002Root relative squared error () 83 83 79 53 31 20 091 013 011

Total number of instances 24

Table 8 Correlation matrix (PCA)

Correlation Area Mean StdDev 119883 119884 119883119872 119884119872 Major Minor Feret IntDen Skew Kurt fArea RawIntDenmatrixArea 1 minus029 042 1 098 1 098 1 1 1 1 048 minus055 1 1

Mean minus029 1 minus098 minus029 minus03 minus03 minus03 minus03 minus028 minus03 minus025 minus092 086 minus026 minus025

StdDev 042 minus098 1 042 044 043 044 044 041 043 038 098 minus094 04 038

119883 1 minus029 042 1 099 1 099 1 099 1 099 048 minus056 1 099

119884 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

119883119872 1 minus03 043 1 099 1 099 1 099 1 1 049 minus056 1 1

119884119872 098 minus03 044 099 1 099 1 099 096 099 098 05 minus058 099 098

Major 1 minus03 044 1 099 1 099 1 098 1 099 049 minus057 1 099

Minor 1 minus028 041 099 096 099 096 098 1 099 099 046 minus053 098 099

Feret 1 minus03 043 1 099 1 099 1 099 1 1 049 minus057 1 1

IntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Skew 048 minus092 098 048 05 049 05 049 046 049 044 1 minus099 046 044

Kurt minus055 086 minus094 minus056 minus058 minus056 minus058 minus057 minus053 minus057 minus052 minus099 1 minus054 minus052

fArea 1 minus026 04 1 099 1 099 1 098 1 1 046 minus054 1 1

RawIntDen 1 minus025 038 099 098 1 098 099 099 1 1 044 minus052 1 1

Table 9 Eigen vectors for each feature

Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features Eigenvector 1 (1198811) Eigenvector 2 (1198812) Features02743 00889 Area 02705 00977 Minorminus01184 05206 Mean minus02704 minus00589 Circ01543 minus04899 StdDev 02754 00843 Feret0275 0089 119883 02721 01163 IntDen02741 00755 119884 01695 minus04647 Skew02754 00848 119883119872 minus01879 04165 Kurt02741 0077 119884119872 02738 01054 fArea02756 00817 Major 02721 01163 RawIntDen

Table 10 PCA ranked attributes

Attributes Characteristic value Rank0276 Major + 0275 Feret + 0275119883119872 + 0275119883 + 0274 Area 01934 10521 Mean minus 049 StdDev minus 0465 Skew + 0417 Kurt + 0116 IntDen 00151 2

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 11

0 20 40 60 80 100 120

0

10

20

30

40

Time (min)

minus10

minus30

minus20

Qr

resid

ual

(a)

0 20 40 60 80 100 120Time (min)

0

10

20

30

40

minus10

minus30

minus20

Qr

resid

ual

(b)

Time (min)0 20 40 60 80 100 120

0

20

40

60

minus80

minus60

minus40

minus20

Qr

resid

ual

(c)

Figure 12 Residual (in terms of119876119903) due to actuator freezing at different time intervals (a) Residual (in terms of119876

119903) due to actuator freezing

at the time interval (40ndash120min) (b) Residual (in terms of 119876119903) due to actuator freezing at the time interval (80ndash100min) (c) Residual (in

terms of 119876119903) due to actuator freezing at the time interval (40ndash60min)

Table 11 Classifier performance comparison based on PCA and SVM

Classifiers Bayes net MLP RBFSVM PCA SVM PCA SVM PCA

Correctly classified instance 13 (54) 12 (50) 24 (100) 19 (79) 24 (100) 24 (100)Incorrectly classified instance 11 (45) 12 (50) 0 (0) 5 (20) 0 0Kappa statistics 044 039 1 0746 1 1Mean absolute error 015 019 0063 015 00001 00001Root mean square error () 029 03 01074 0245 004 0006Relative absolute error () 64 81 26 62 002 003Root relative squared error () 83 86 31 71 011 031

square error are less for RBF than MLP So RBF classifierperformance is better than MLP for this fault classificationstudy

From the SVM ranked classifierrsquos performance it hasbeen realised that the RBF is performing well even for lessnumber of features and theMLP and Bayes performances are

poor for less data From the results it could be observed that9 features are enough to make all the classifiersrsquo performancegood The SVM attribute filter is used to reduce the numberof input data

The features are reduced by using PCA technique alsoThe correlation is the measure of similarity and the value

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Modelling and Simulation in Engineering

0 20 40 60 80 100 120

0

50

Time (min)

minus400

minus350

minus300

minus250

minus200

minus150

minus100

minus50

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

20

Time (min)

minus160

minus140

minus120

minus100

minus80

minus60

minus40

minus20

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

100

200

300

Time (min)

minus400

minus500

minus600

minus300

minus200

minus100

Qr

resid

ual

(c)

0 20 40 60 80 100 120

0

100

Time (min)

minus400

minus500

minus600

minus700

minus300

minus200

minus100

Qr

resid

ual

(d)

Figure 13 Residual (in terms of 119876119903) due to actuator biasing at different intervals (a) Residual (in terms of 119876

119903) due to actuator biasing at the

time interval (80min) (b) Residual (in terms of119876119903) due to actuator biasing at the time interval (80min) (c) Residual (in terms of119876

119903) due to

actuator biasing at the time interval (60min) (d) Residual (in terms of 119876119903) due to actuator biasing at the time interval (90min)

for correlation is 1 and then the patterns are similar Ifthe correlation is ldquo0rdquo or negative then the patterns aredissimilar The diagonal values of the correlation matrixshown in Table 8 are ldquo1rdquo which indicates that the similaritymeasure is calculated for the image with itself (autocorrela-tion) The other entries denote the cross correlation that iscomputed

The eigenvectors of a square matrix are the nonzerovectors after being multiplied by the matrix remainingproportional to the original vector (ie change only inmagnitude not in direction)The eigenvectors correspondingto the features are displayed in Table 9 For each eigenvectorthe corresponding eigenvalue is the factor by which theeigenvector changes when multiplied by the matrix as theyrepresent the characteristic values shown in Table 10

Table 11 shows the classifier performance based on theSVMwith 9 features and PCA with full data as two attributesare more or less same for the RBF classifier But for MLP andalso for Bayes net the SVM attribute filter based classificationresults show its better nature than PCA

6 Conclusion

This paper proposes a method for classification of variousfaults of the batch reactor by using artificial neural network(ANN) classifiers such asmultilayer perceptron (MLP) radialbasis function (RBF) and Bayes net from fault signatures It isbased on the relationship of each faultrsquos impact on heat release(119876119903) of the reactor which is the immeasurable parameter

estimated by SVM estimator The fault signature trend isvarying from fault to fault Most appropriate features areselected from the variety of fault signatures and the numbersof attributes are reduced based on the SVM attribute filter byusing rankingmethod and PCA to reduce the computationaldifficulty of classifiers It is observed that the classificationaccuracy of RBF and MLP is better than the Bayes net fromthe classifiers performance during training Based on theperformance criteria the RBF performs well compared toMLP and Bayes net within 24 instances under the assumptionthat in practical situation less historical data are availableThe results verify that the capability of the proposed faultdiagnosis scheme is efficient and fast by using general ANN

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Modelling and Simulation in Engineering 13

0 20 40 60 80 100 120

0

5

10

15

Time (min)

minus15

minus10

minus5

Qr

resid

ual

(a)

0 20 40 60 80 100 120

0

10

20

Time (min)

minus40

minus30

minus20

minus10

Qr

resid

ual

(b)

0 20 40 60 80 100 120

0

2

4

6

8

10

Time (min)

minus4

minus6

minus2

Qr

resid

ual

(c)

Figure 14 Residual (in terms of 119876119903) due to sensor fault (a) Residual (in terms of 119876

119903) due to reactor temperature sensor measurement with

white noise (b) Residual (in terms of 119876119903) due to abrupt zero in reactor temperature sensor measurement (c) Residual (in terms of 119876

119903) due

to bias in jacket temperature sensor measurement

classifiers It is based on the limited number of featuresextracted and selected from only one estimated parameter(119876119903) itself In future it can be applied to develop a knowledge

based system which is useful for early diagnosis of fault tominimize the risk of thermal runaway for safety purpose ofthe batch reactor as well as to reduce the operating cost

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A M Benkouider J C Buvat J M Cosmao and A SabonildquoFault detection in semi-batch reactor using the EKF andstatistical methodrdquo Journal of Loss Prevention in the ProcessIndustries vol 22 no 2 pp 153ndash161 2009

[2] D Ruiz J M Nougues Z Calderon A Espuna and LPuigjaner ldquoNeural network based framework for fault diagnosisin batch chemical plantsrdquoComputers and Chemical Engineeringvol 24 no 2ndash7 pp 777ndash784 2000

[3] V Venkatasubramanian and K Chan ldquoNeural networkmethodology for process fault diagnosisrdquo AIChE Journal vol35 no 12 pp 1993ndash2002 1989

[4] S Saludes and M J Fuente ldquoSupport vector based noveltydetection for fault tolerant controlrdquo in Proceedings of the 44thIEEE Conference on Decision and Control and the EuropeanControl Conference (CDC-ECC rsquo05) pp 5820ndash5825 SevilleSpain December 2005

[5] I Monroy R Benitez G Escudero and M Graells ldquoA semi-supervised approach to fault diagnosis for chemical processesrdquoComputers andChemical Engineering vol 34 no 5 pp 631ndash6422010

[6] P K Kankar S C Sharma and S P Harsha ldquoFault diagnosis ofball bearings using machine learning methodsrdquo Expert Systemswith Applications vol 38 no 3 pp 1876ndash1886 2011

[7] H J Shin D-H Eom and S-S Kim ldquoOne-class supportvectormachinesmdashan application inmachine fault detection andclassificationrdquo Computers and Industrial Engineering vol 48no 2 pp 395ndash408 2005

[8] T-S Li ldquoApplying wavelets transform and support vectormachine for copper clad laminate defects classificationrdquo Com-puters and Industrial Engineering vol 56 no 3 pp 1154ndash11682009

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Modelling and Simulation in Engineering

[9] K Salahshoor M Kordestani and M S Khoshro ldquoFaultdetection and diagnosis of an industrial steam turbine usingfusion of SVM (support vector machine) and ANFIS (adaptiveneuro-fuzzy inference system) classifiersrdquoEnergy vol 35 no 12pp 5472ndash5482 2010

[10] Q Yang J Guo and X Zhang ldquoFastICA-SVM fault diagnosisfor batch processrdquo in Proceedings of the 7th InternationalConference on Natural Computation (ICNC rsquo11) pp 1649ndash1653July 2011

[11] J A K Suykens and J Vandewalle ldquoLeast squares supportvector machine classifiersrdquo Neural Processing Letters vol 9 no3 pp 293ndash300 1999

[12] J S R Jang C T Sun and E Mizutani Neuro-Fuzzy and SoftComputing Computational Approach to Learning and MachineIntelligence Prentice Hall of India 2002

[13] R E Neapolitan Probabilistic Reasoning in Expert SystemsTheory and Algorithms John Wiley amp Sons 1989

[14] J Pearl Probabilistic Reasoning in Intelligent Systems MorganKaufmann San Francisco Calif USA 1988

[15] H Simon Neural NetworksmdashA Comprehensive FoundationPearson Education San Francisco Calif USA 2005

[16] M J Zurada Introduction to Artificial Neural Systems DelhiJaico Publishing House 1999

[17] B J Cott and S Macchietto ldquoTemperature control of exother-mic batch reactors using generic model controlrdquo Industrial andEngineering Chemistry Research vol 28 no 8 pp 1177ndash11841989

[18] N Aziz M A Hussain and I M Mujtaba ldquoPerformance ofdifferent types of controllers in tracking optimal temperatureprofiles in batch reactorsrdquo Computers and Chemical Engineer-ing vol 24 no 2ndash7 pp 1069ndash1075 2000

[19] I M Mujtaba N Aziz and M A Hussain ldquoNeural networkbased modelling and control in batch reactorrdquo Chemical Engi-neering Research and Design vol 84 no 8 pp 635ndash644 2006

[20] S Sujatha and N Pappa ldquoRealization of non linear controllersin batch reactor using GA and SVMrdquo International Journal ofChemical Reactor Engineering vol 9 no 1 2011

[21] P L Lee and G R Sullivan ldquoGeneric model control (GMC)rdquoComputers andChemical Engineering vol 12 no 6 pp 573ndash5801988

[22] S W Choi J Morris and I-B Lee ldquoNonlinear multiscalemodelling for fault detection and identificationrdquo ChemicalEngineering Science vol 63 no 8 pp 2252ndash2266 2008

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of