feature selection and parameters optimization of svm using...

Research ArticleFeature Selection and Parameters Optimization ofSVM Using Particle Swarm Optimization for Fault Classificationin Power Distribution Systems

Ming-Yuan Cho and Thi ThomHoang

Department of Electrical Engineering National Kaohsiung University of Applied Sciences Kaohsiung Taiwan

Correspondence should be addressed toThiThom Hoang thomhtntueduvn

Received 25 March 2017 Accepted 28 May 2017 Published 11 July 2017

Academic Editor Fabio La Foresta

Copyright copy 2017 Ming-Yuan Cho andThiThom Hoang This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

Fast and accurate fault classification is essential to power system operations In this paper in order to classify electrical faultsin radial distribution systems a particle swarm optimization (PSO) based support vector machine (SVM) classifier has beenproposed The proposed PSO based SVM classifier is able to select appropriate input features and optimize SVM parametersto increase classification accuracy Further a time-domain reflectometry (TDR) method with a pseudorandom binary sequence(PRBS) stimulus has been used to generate a dataset for purposes of classification The proposed technique has been tested on atypical radial distribution network to identify ten different types of faults considering 12 given input features generated by usingSimulink software andMATLAB ToolboxThe success rate of the SVM classifier is over 97 which demonstrates the effectivenessand high efficiency of the developed method

1 Introduction

Distribution networks deliver electrical energy from trans-mission systems to consumers and are important and integralpart of all power systems Once an electrical fault occurs inany distribution feeder immediate fault classification playsan important role in postfault analysis and power supplyrestorationThe accuracy of the fault type information assiststhe fault diagnosis system not only to locate the electricalfaults promptly but also to ensure power quality as well asreliability of the system [1 2]

A variety of approaches have been developed to buildan effective fault classifier in electrical distribution feed-ers As the amount of power delivered by a distributionsystem significantly increases it is essential to focus onfault classification schemes The studies of fault classificationin distribution feeder can be divided into three separatecategories as follows (1) impedance based method [3 4](2) travelling wave based method [5 6] (3) and artificial

intelligence based method [7 8] The most common methodfor fault classification in power systems is known as time-domain reflectometry (TDR) [9ndash11]

TDR is rather simple to implement however it is nota perfect fault-location method since any single pulse stim-ulus injected into the electrical line is quickly attenuatedalong that line causing fault location and classification tobecome inaccurate To overcome this problem an improvedTDRmethod using incident pseudorandom binary sequence(PRBS) excitation is proposed to locate such faults in [12]however it should be noted that it is only applied for high-power transmission lines Actually it is quite difficult toapply the TDR method to find faults in distribution feedersbecause of the various junctions and ends of branchednetwork involved As a result various reflected responsesmayoccur in the reflectometry trace [13]Therefore an intelligentalgorithm is required to extract fault location informationon a multiple-branched network from the reflectometry

HindawiComputational Intelligence and NeuroscienceVolume 2017 Article ID 4135465 9 pageshttpsdoiorg10115520174135465

2 Computational Intelligence and Neuroscience

trace provided SVM has been used successfully to resolveclassification issues for a wide range of applications becauseof its strongly regularized characteristic and rapid trainingspeed [14ndash16]

To build a SVM classifier the aspect of feature subsetselection plays an important role in detecting relevant vari-ables in classification spaces Principal component analysis(PCA) [17] and multidimensional scaling (MDS) [18] are twotraditional methods applied to remove redundant variablesin the original feature vectors Authors in [19] proposeda Hadoop scheme to extract feature in parallel in whichhundreds of mappers are composed In a recent paper [20]Ma and Niu used the firework algorithm to select inputfeatures by removing redundant influence in order to improvethe icing forecasting of high voltage transmission line

In addition to feature subset selection the optimal setof SVM parameters also plays an important role in thedistribution of samples in a given search space Vapnikshowed that the penalty parameter 119862 and kernel functionparameter such as gamma 120574 for the radial basis function(RBF) significantly affect the performance of SVM [21]Various researches have been proposed to select these twoparameters but there is no general opinion for their settings[22] The grid search method (GSM) is investigated to deter-mine optimal parameters by attempting different values andselecting those values possessing the least amount of testingerror [23] Because of the computational complexity involvedwith GSM genetic algorithm (GA) has been developed toimprove classification accuracy and reduce training time byusing a minimal number of features [24] However it takessignificant amounts of calculation time due to the complexoperational process including inheritance selection recom-bination and mutation To overcome this relative problemKennedy and Eberhart proposed a population-based searchtechnique known as particle swarm optimization (PSO) [25]The primary advantage of the PSO based encoding techniqueis in its capacity to decrease trapped status in local optimaand increase the classification accuracy as well as the trainingspeed

In this paper a novelmethod based upon PSO techniquesis developed to simultaneously optimize input features andSVM parameters in order to classify the fault types found inthe distribution networkThese fault types can be divided intoten classes including single phase-to-ground faults (AG BGandCG) line-to-line faults (AB AC and BC) double line-to-ground faults (ABG ACG and BCG) and three-phase short-circuit faults (ABC) Further this PSO-SVM classifier usesa dataset obtained from TDR analysis with PRBS excitationNot only is the proposed PSO based encoding technique easyto use but it also helps to significantly increase the successrate of the SVM classifier

The remainder of this paper is constructed as follows InSection 2 the theory of the proposed method is discussedincluding TDR SVM and PSO Section 3 presents themodeling of a typical two-branched distribution feeder Thedeveloped PSO based SVM fault diagnosis approach is givenin Section 4 In Section 5 experimental simulation results anddiscussions are presented Finally a conclusion is presented inSection 6

L2dz L2dzR2dz R2dz

Cdz Gdz

Figure 1 The classical model for a lumped section

2 Basic Theory of the Proposed Method

21 Time-Domain Reflectometry Time-domain reflectome-try (TDR) is widely used for fault classification and locationof faults in electrical transmission and distribution lines TDRis based on a single pulse being injected into the given line orcable to be examined Afterwards some of the pulse energyis reflected back to source whenever it reaches the point ofany discontinuities such as electrical faults tee joints or lineterminals Since the propagation velocity is assumed to beconstant the fault distance can be measured based on theexpected pulse transit time Hence the reflectometry tracewill not only display the desired information of the fault typebut also determine the fault location

Assume a distribution line is modeled by a lumped-parameter equivalent circuit as shown in Figure 1 with adistributed series inductance 119871 resistance 119877 capacitance 119862and conductance 119866

A voltage introduced at the generator will require a cer-tain amount of time to propagate along the line representedin the following equation

120597V (119909 119905)120597119909 = minus119877119894 (119909 119905) minus 119871120597119894 (119909 119905)120597119905 120597119894 (119909 119905)120597119909 = minus119866V (119909 119905) minus 119862120597V (119909 119905)120597119905

(1)

where V(119909 119905) and 119894(119909 119905) are the forward travelling voltageand current waves respectively The amplitude of incidentpulse will be attenuated along the line and the phase of thevoltage travelling along the line will be distorted resultingfrom varying frequency [26]The attenuation and phase shiftare determined by the propagation coefficient as shown in

120574 = radic(119877 + 119895120596119871) (119866 + 119895120596119862) = 120572 + 119895120573 (2)

where 120572 and 120573 are the attenuation coefficient and the phasechange coefficient respectively The velocity at which thevoltage moves down the line can be defined in

120592 = 120596120573 (3)

From (1) using the Laplace transform and differentialequation we can obtain

V (119909 119905) = V+ (119905 minus 119909120592) + Vminus (119905 + 119909120592) 119894 (119909 119905) = 119894+ (119905 minus 119909120592) + 119894minus (119905 + 119909120592)

(4)

Computational Intelligence and Neuroscience 3

where V+(119905 minus 119909120592) and 119894+(119905 minus 119909120592) are the forward travellingvoltage and current waves respectively Vminus(119905+119909120592) and 119894minus(119905+119909120592) are the backward travelling voltage and current wavesrespectively Equating the coefficients of 119890minus119904119909120592 (4) can berewritten as

119868 (119909 119904) = 1119885119862 [119881+ (119904) 119890minus119904119909120592 minus 119881minus (119904) 119890+119904119909120592]

119885119862 = radic 119871119862(5)

where 119885119862 is called the characteristic impedance When theline is terminated with any load whose impedance value isother than the characteristic impedance a reflected wave willoccur at the load and then propagate back toward the sourceThe voltage moving down the line in this case is given bymeans of

119881 (119897 119904) = 119885119877 (119904) lowast 119868 (119897 119904) (6)

where 119885119877 is called the load impedance This reflected wave isrelated to the incident wave by representation in the followingequation

119881minus (119897 119904) = Γ (119904) 119881+ (119904) 119890minus2119904120591Γ = 119885119877 minus 119885119862119885119877 + 119885119862 120591 = 119897120592

(7)

where Γ is called the receiving-end voltage reflection coeffi-cient and 120591 is called the transit time

TDR is quite simple to implement but it is not a perfecttechnique since the use of single pulse excitation that isquickly attenuated along the line In addition the pulsewidth is one of the factors that affect the accuracy rateof the reflectometry method TDR method using incidentpseudorandom binary sequence (PRBS) excitation can solvethese problems by using cross-correlation (CCR) functionbetween the reflected wave and incident wave given by (8)for fault diagnosis in distribution feeders

119862119909119910 (119896) = 1119871119871sum119894=1

119909 (119894) 119910 (119894 + 119896) (8)

where 119862119909119910 is the cross-correlation (CCR) function betweenthe reflected wave and incident wave 119909119894 is the forward signaland 119910119894 is the feedback signal

As previously mentioned a variety of different compo-nents exist along electrical distribution lines like transform-ers capacitors tap changers phase splitters and so forthso it is not easy to extract fault locations from variousreflections observed in the reflectometry trace In this studya multilayer SVM classifier is proposed as a supportingtechnique for the TDR method to provide fault diagnosis inmultibranch distribution networks including single phase-to-ground faults (AG BG and CG) line-to-line faults (ABAC and BC) double line-to-ground faults (ABG ACG andBCG) and three-phase faults (ABC)

22 Support Vector Machine A support vector machine(SVM) was first mentioned by Vapnik in 1995 and ithas become one of the most optimal techniques for dataclassification It has a solid theoretical foundation basedon a combination between the structural risk minimizationprinciple and statistical machine learning theory (SLR) Themain advantages of SVM are the global optimization andhigh generalization ability Further it overcomes overfittingproblems and provides sparse solutions in comparison toexisting methods such as artificial neuron network (ANN)and refined genetic algorithm (RGA) in fault classification

In standard linear classification problem for exampleone should separate the set of training data (119909119894 119910119894) 119894 =1 2 119898119898 is the number of given observations where 119909119894 isin119877119899 are feature vectors and 119910119894 isin (minus1 +1) are label vectors Abinary classification problem can be posed as an optimizationproblem in the following way

Min 12 11990822 + 119862 119898sum119894=1

120585119894 (9)

Subjected to 119910119894 (119908 times 119909119894) + 119887 ge 1 minus 120585119894120585119894 ge 0 119894 = 1 119898 (10)

where 119862 is the regularization parameter 120585119894 the penalizingrelaxation variables Equation (10) means

119908 times 120601 (119909119894) + 119887 ge +1 if 119910119894 = +1119908 times 120601 (119909119894) + 119887 ge minus1 if 119910119894 = minus1 (11)

It is to be noted that the nonlinear classifier may bedenoted in the input space as

119891 (119909) = sign( 119898sum119894=1

120572119894lowast times 119910119894 times 119870 (119909119894 119910119894) + 119887lowast) (12)

where 119891(119909) is the decision function and the bias 119887lowast iscalculated by the Karush-Kuhn-Tucker (KKT) conditions119870(119909119894 119910119894) is the kernel function that produces the innerproduct for this feature space In this paper the followingradial basis function (RBF) is used

119870(119909 119910) = exp (minus120574 1003817100381710038171003817119909 minus 11991010038171003817100381710038172) (13)

where 120574 is the kernel parameterTo obtain optimum performance some SVM parameters

need to be select property including the regularizationparameter 119862 and the kernel parameter 120574 In this workPSO technique is applied to optimize these two parametersaccordingly

23 Particle Swarm Optimization Particle swarm optimiza-tion (PSO) is inspired by the social and cooperative behaviordisplayed by various species to fill their needs in the searchspaceThis algorithm is guided by personal experience119875119887119890119904119905overall experience 119866119887119890119904119905 and the present movement of theparticles to decide their next positions in the search space


Vpk

Xpk

Vpk+1

Xpk+1

Pbestpk

GbestkVpGbest

VpPbest

Figure 2 The PSO search mechanism 119901th particle at 119896th iteration

Further the experiences are accelerated by two factors 1198881 and1198882 and two random numbers 1199031 and 1199032 generated between[0 1] whereas the present movement is multiplied by aninertia factor 119908 Mathematically updated positions of eachparticle in the search space can be expressed using the twoequations discussed below

The initial population (swarm) of size 119873 and dimension119863 is denoted as 119883 = [1198831 1198832 119883119873]119879 where 119879 denotesthe transpose operator Each individual particle 119883119875 (119901 =1 2 119873) is given as 119883119875 = [1198831199011 1198831199012 119883119901119863]119879 Alsothe initial velocity of the population is denoted as 119881 =[1198811 1198812 1198813]119879 Thus the velocity of each particle 119883119875 (119901 =1 2 119873) is given as119881119901 = [1198811199011 1198811199012 119881119901119863] The index 119901varies from 1 to119873 whereas the index 119902 varies from 1 to119863

119881119896+1119901119902 = 119908 times 119881119896119901119902 + 11988811199031 (119875119887119890119904119905119896119901119902 minus 119883119896119901119902)+ 11988821199032 (119866119887119890119904119905119896119902 minus 119883119896119901119902)

(14)

119883119896+1119901119902 = 119883119896119901119902 + 119881119896+1119901119902 (15)

In (14) 119875119887119890119904119905119896119901119902 represents personal best 119902th componentof 119901th individual whereas 119866119887119890119904119905119896119902 represents 119902th componentof the best individual of population up to iteration 119896 Figure 2shows the search mechanism of PSO in a multidimensionalsearch space

The initial 119875119887119890119904119905 of each particle is their initial positionwhereas the initial 119866119887119890119904119905 is the initial best particle positionamong randomly initialized populationThe119875119887119890119904119905 and119866119887119890119904119905of each particle are updated as follows

At iteration 119896If 119891 (X119896+1119901 ) lt 119891 (119875119887119890119904119905119896119901) then 119875119887119890119904119905119896+1119901

= X119896+1119901 else 119875119887119890119904119905119896+1119901 = 119875119887119890119904119905119896119901If 119891 (X119896+1119901 ) lt 119891 (119866119887119890119904119905119896) then 119866119887119890119904119905119896

= X119896+1119901 else 119866119887119890119904119905119896+1 = 119866119887119890119904119905119896(16)

where119891(119883) is the objective function subject tominimizationThe updating procedure should be repeated until a stop con-dition is reached such as a prespecified number of iterations

PRBS

SSMain feeder

Figure 3 A two-branched distribution line diagram of the samplesystem

are met Once terminated the 119866119887119890119904119905119896 and 119891(119866119887119890119904119905119896) arereported as the solution of PSO techniqueMore details aboutthe basic concept of PSO can be found in [27ndash30]

3 System Modeling

An equivalentmodel has to be constructed by using Simulinksoftware and MATLAB Toolbox to simulate a typical two-branched distribution feeder shown in Figure 3 inwhich dotsrepresent the distribution transformers and their loads

Two distribution transformers in the sample system areused to reduce the voltage on the distribution line to thelevel of customers that are distributed along a feeder Theirparameters and connection phases are shown in Table 1 [31]It is noted that these distribution transformers are operatedin a full-load condition with 08 lagging power factor asa result the sample distribution system is operated withunbalanced conditions in occurrence The main feeder andlaterals are constructed by means of overhead lines whosepositive-sequence impedance is 0131 + 1198950364Ωkm [31]

4 Developed PSO Based SVM FaultDiagnosis Approach

Since the TDR technique does not diagnose fault easily inthe distribution networks hence it requires to be supportedfrom other intelligent techniques in order to obtain the bestresults This paper proposes a PSO based SVM classifierto improve the performance of the TDR method in faultclassification in electrical distribution feeders The overallstructure of SVM short-circuit classifier is shown in Figure 4in which PSO is performed to optimize the feature subsetand SVM parameters For this the data acquisition for datapreprocessing is mentioned first

41 Data Acquisition To obtain a suitable dataset for clas-sification process PRBS disturbance is injected directly intothe secondary circuit of the current transformer (CT) 2005Awhich is placed at the beginning of the line under test Theprimary circuit of the CT is connected to the main feederthus the amplified PRBS is propagated along the line todiagnose any faults which may occur

Once a fault occurs in the distribution feeder it causesproducing a reflected signal that travels between the faultlocation and the substation Then these reflected responsesare cross-correlated with the incident impulse by (8) in orderto reduce the impact of noise as well as surmount amplitudeattenuation It is worth noting that for each of the fault types


Table 1 Parameters and connection phases of distribution transformers in the sample system

Number Windings connection Phases Secondary voltages (V) Capacity (kVA) Impedance (119885)1 Delta-Wye-Gnd A B C 220 500 1892 Delta-Delta A B C 220 500 189

Testing dataset

Training dataset

Reflected data acquisition

Selection of feature set and SVMparameters using PSO

Optimum SVM

ABCBCGACGABGBCACABCGBGAG

Figure 4 Block diagram of the proposed PSO based SVM classifier

specified the magnitudes of the feedback waves are differentat the shortage time as a result the peaks of the CCR are notfound to be the sameHence the reflected responses andCCRbetween the reflected wave and the incident wave are used asinput feature vectors for the training phaseThe total numberof feature vectors is 12 and they comprise a feature vector119881 = [V1 V2 V12]119879 in which V1ndashV6 are the reflected voltageand current obtained at the substation and V7ndashV12 are thepeaks of CCR between the reflected and the incident waves

42 Feature Extraction For utilization of the reflectometrymethod various echo responses are collected in whichsome irrelevant data may be confusing to the SVM clas-sifier and subsequently increase the training time Featureextraction is the best effective method to select appropriateinput features in order to improve the speed of trainingas well as to ensure the success rate of classification Foroptimum feature selection in this work PSO is employedto improve the performance of the SVM classifier To selectoptimum features of the given dataset a binary string hasbeen optimized using PSO where each bit represents a givenfeature of the dataset In the binary string a ldquo0rdquo representsan ignored feature whereas a ldquo1rdquo represents a selected featureof the dataset The optimum features are those features takenfrom the given dataset which correspond to the optimizedbinary string having its bit as a ldquo1rdquo For this a given setof predefined SVM parameters has been used while theselection of features of the given dataset usingPSO ismadeAtthe end of feature selection stage the selected strings providethe information regarding the features needed for optimizingthe SVM parameters

43 Optimum SVM Parameters The performance of SVM issusceptible to kernel function parameter 120574 and the regular-ization parameter 119862 so these parameters must be carefully

selected to increase the classification accuracy In this paperPSO technique is used to select the parameters of the SVMclassifier Performance is measured according to the classifi-cation accuracy on unseen testing data In the learning stagethe PSO based encoding SVM model is trained based onstructural risk minimization to minimize the training errorWhile training error improvement occurs penalty parameter119862 and kernel function parameter 120574 are regulated by meansof PSO The regulated parameters with minimal error arereported as the most suitable parameters As a result theoptimal parameters (119862 and 120574) are to be obtained

Once the optimized parameters of the SVM are obtainedthen it is used for the retraining of the SVM model Afterthe training phase the SVM classifier is ready to identify newsamples in the testing phase The testing set is also chosen bymeans of the above feature selection from the original datasetobtained by theTDR traceThen testing patterns are inputtedto the trained multilayer SVM classifier which can identifyall the 10 types of faults including single-phase-to-groundfaults (AG BG and CG) line-to-line faults (AB AC andBC) double-line-to-ground faults (ABG ACG and BCG)and three-phase faults (ABC)

Detailed experiment procedure for feature extractionand SVM parameter selection using PSO algorithm can beexpressed using the following steps

(1) Read complete data and set 119908 1198881 and 1198882 parameters(2) Initialize positions X and velocitiesV of each particle

of population(3) Initialize sets of SVM parameters within its ranges as

particle position and velocity(4) Form SVM using training dataset and initialized

positions of each particle(5) Evaluate fitness of each particle 119865119901119896 = 119891(X119901119896) forall119901

and find the best particle index 119887


Form SVM using training datasets and initialized position of each particle

Initialize sets of SVM parameters within its ranges as particle positions and velocity

Print optimum values of SVM

Update velocity and position of each particle

Evaluate initial fitness of each particle

Evaluate fitness of each particle

No

Yes

Read complete datasets and set PSO parameters

Testing datasetTraining dataset

Data acquisition

Trained SVM classifier with optimum feature and parameters

SVM Output

Various faults types

Set iteration count k = 1

k = k + 1

and update Pbest and Gbest

and select Pbest and Gbest

parameters as Gbest

If k le ＧＲＣＮ

Figure 5 Flowchart of the proposed approach

(6) Select 119875119887119890119904119905119901119896 = X119901119896 and 119866119887119890119904119905119896 = X119887119896(7) Set iteration count 119896 = 1(8) 119908 = 119908max minus (119908max minus 119908min) times itemax ite(9) Update velocity and position of each particle using

(14) and (15)(10) Evaluate updated fitness of each particle 119865119901119896+1 =

119891(X119901119896+1) forall119901 and find the best particle index 1198871(11) Update 119875119887119890119904119905 of each particle forall119901

If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896

(12) Update 119866119887119890119904119905 of populationIf 1198651198871119896+1 lt 119865119887119896 then 119866119887119890119904119905119896+1 lt 1198751198871198901199041199051198871119896+1 and set119887 = 1198871 else 119866119887119890119904119905119896+1 lt 119866119887119890119904119905119896

(13) If 119896max ite then 119896 = 119896 + 1 and go to step (6) else goto step (14)

(14) Optimum solution obtained print the results ofoptimum generation as 119866119887119890119904119905119896

(15) Retrain SVMwith optimum features and parametersthen identify unknown samples on testing dataset

The experiment procedure can be visualized in Figure 5


Table 2 Dataset of ten fault types located at distances of 3 km and 4 km from the substation

Va Vb Vc 119894a 119894b 119894c cc-Va cc-Vb cc-Vc cc-119894a cc-119894b cc-119894cAG 19197 minus03071 01245 49815 minus07968 03232 05941 minus00950 00385 00502 minus00080 00033

06990 minus01118 00453 15998 minus02559 01038 35687 minus05708 02315 30765 minus04921 01996

BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

BCG minus82016 96684 162648 minus25267 29785 50107 minus01137 01340 02254 minus01137 01340 02254minus41309 48697 81921 minus07620 08983 15112 minus02446 02884 04852 minus02104 02480 04172

ACG minus12835 25576 48025 minus09796 19519 36650 minus16907 33688 63257 minus14240 28375 53279minus14241 17834 38278 minus10868 13610 29212 minus18757 23491 50419 minus15799 19786 42466

ABG minus11327 00679 26912 minus29393 01763 69832 minus03506 00210 08329 minus00296 00018 00704minus20970 01258 49821 minus16003 00960 38021 minus27621 01657 65623 minus23265 01395 55272

AB minus74589 minus48688 177206 minus13759 minus08981 32688 minus04417 minus02883 10495 minus03798 minus02479 09024minus14121 minus09218 33549 minus36643 minus23918 87055 minus04370 minus02853 10383 minus00369 minus00241 00877

AC minus10143 minus12113 78915 minus07741 minus09244 60225 minus13360 minus15955 103945 minus11253 minus13439 87550minus15121 minus79329 405259 minus04658 minus24439 124847 minus00210 minus01099 05616 minus00210 minus01099 05616

BC 20444 minus42356 235915 03771 minus07813 43518 01211 minus02508 13972 01041 minus02157 1201301409 minus02920 16262 03225 minus06682 37220 07195 minus14907 83028 06203 minus12851 71576

ABC 03508 minus03674 19940 08029 minus08408 45638 17911 minus18757 101807 15440 minus16170 8776517837 minus18679 101386 13612 minus14255 77374 23494 minus24604 133543 19788 minus20723 112480

AG BG and CG are single phase-to-ground faults BCG ACG and ABG are double line-to-ground faults AB AC and BC are line-to-line faults ABC is three-phase faults Va Vb Vc 119894a 119894b and 119894c are magnitudes of reflected voltages and currents respectively cc-Va cc-Vb cc-Vc cc-119894a cc-119894b and cc-119894c are CCR betweenreflected signal and incident signal

Table 3 Results of SVM classification without and with considering PSO optimization techniques

SVM classifier Number of features 119862 120574 Classification accuracy () Training time (s)Without PSO 12 1810193 11212 9300 1348With PSO 8 150381 00334 9715 8354

5 Test Results and Discussion

In this paper the fault types are considered by using a 127-bit PRBS stimulus with frequency 119891 = 1MHz and a velocityof 198000 kms propagated along the sample system givenin Figure 2 The dataset used in this study was obtained atthe substation end by TDR analysis with the number offeatures being 12 in which six features are considered to bethemagnitudes of reflected signals and six remaining featuresare extracted from the peaks of CCR between the feedbackwave and the forward waveThis dataset is comprised of 5700samples generated by creating each type of fault at differentlocations on two laterals with varying fault impedance valueNote that training and test sets are randomly divided from theoriginal dataset in which 4500 and 1200 are used for trainingand testing set respectively Table 2 only gives a few portionsof the dataset for purposes of brevity which were createdby a simulation of the ten types of short-circuit fault on thefirst lateral located at distances of 3 km and 4 km from thesubstation

In this paper PSO technique is used to select the featuresand parameters of the SVM classifier Preliminary experi-ments also permit this study set population size as 10 inertia

weight has been taken into account as between 01 and 05(considered randomly at each iteration) and accelerationfactors (1198881 and 1198882) have been taken as equal to 2 with amaximum iteration set to 1000

Table 3 gives the results of the classification accuracy forthe SVM algorithm using a dataset both with and withoutPSO optimization The optimum values of 119862 and 120574 of SVMclassifier are 1810193 and 11212 without consideration ofPSO and are 150381 and 00334 with consideration of PSOFrom this table it is observed that the classification accuracyin the case of using the entire feature is 93 whereas theclassification accuracy in the case of using a PSO basedencoding technique is found to be 9715 This demonstratesthe optimal efficiency of the proposed method in whichPSO optimization is applied All 12 features are autoselectedfrom the corresponding input and the testing success ratehas been improved significantly The remaining features are8 which are 1ndash7 and 9 Furthermore Table 3 provides thecomputational times for training SVM classifier The overallsimulation time taken by the SVM classifier without PSO is1348 seconds whereas with PSO it is 8354 seconds It shouldbe concluded that the PSO technique takes a relatively shortercomputational time for training


0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40

Number of iterations

Figure 6 Convergence characteristic of the proposed PSO

The convergence characteristic of the proposed PSO isshown in Figure 6 From this figure it is can be observedthat MSE beyond 15 iterations is nondecreasing thus theoptimized SVM parameters can be obtained prior to the totaltraining time taken (8354 sec)

6 Conclusions

In this paper a multilayer support vector machine (SVM)based on optimum parameters optimization and featureselection approach has been developed to classify ten typesof faults in radial distribution feeders Particle swarm opti-mization (PSO) has been used as an optimizer to improvethe performance of SVMclassifier by selecting an appropriatefeature subset and kernel parameters Further time-domainreflectometry (TDR) with pseudorandom binary sequence(PRBS) stimulus has been utilized for generating a faultdataset In the proposed technique not only does using PRBSinjection overcome the stimulus distortion problem but italso surmounts the impact of noise to provide a reliabledataset for SVM classifier The proposed PSO based SVMclassifier has been successfully applied to identify all tentypes of short-circuit faults in the radial distribution networkobserved The achieved high accuracy rate in classifyingfault types (over 97) demonstrates greater effectiveness overexisting fault identifiers

Conflicts of Interest

The authors declare that they have no conflicts of interest

References

[1] JMora-Florez J Cormane-Angarita andGOrdonez-Plata ldquok-means algorithm andmixture distributions for locating faults inpower systemsrdquo Electric Power Systems Research vol 79 no 5pp 714ndash721 2009

[2] M Mirzaei M Z A Ab Kadir E Moazami and H HizamldquoReview of fault location methods for distribution powersystemrdquo Australian Journal of Basic and Applied Sciences vol3 no 3 pp 2670ndash2676 2009

[3] E C Senger G Manassero Jr C Goldemberg and E L PellinildquoAutomated fault location system for primary distributionnetworksrdquo IEEE Transactions on Power Delivery vol 20 no 2pp 1332ndash1340 2005

[4] Y Liao ldquoAlgorithms for power system fault location andline parameter estimationrdquo in Proceedings of the 2007 39thSoutheastern Symposium on System Theory SSST pp 189ndash193usa March 2007

[5] A Sedighi ldquoClassification of transient phenomena in distri-bution system usingwavelet transformrdquo Journal of ElectricalEngineering vol 65 no 3 pp 144ndash150 2014

[6] A Borghetti S Corsi C ANucciM Paolone L Peretto andRTinarelli ldquoOn the use of continuous-wavelet transform for faultlocation in distribution power systemsrdquo International Journal ofElectrical Power and Energy Systems vol 28 no 9 pp 608ndash6172006

[7] Q Yang J Li S Le Blond and C Wang ldquoArtificial NeuralNetwork Based Fault Detection and Fault Location in the DCMicrogridrdquo Energy Procedia vol 103 pp 129ndash134 2016

[8] M Pourahmadi-Nakhli and A A Safavi ldquoPath characteristicfrequency-based fault locating in radial distribution systemsusing wavelets and neural networksrdquo IEEE Transactions onPower Delivery vol 26 no 2 pp 772ndash781 2011

[9] J Wang P E C Stone D Coats Y-J Shin and R A DougalldquoHealth monitoring of power cable via joint time-frequencydomain reflectometryrdquo IEEE Transactions on Instrumentationand Measurement vol 60 no 3 pp 1047ndash1053 2011

[10] A Cataldoa R Persicob G Leuccib et al ldquoTime domain reflec-tometry ground penetrating radar and electrical resistivitytomography a comparative analysis of alternative approachesfor leak detection in underground pipesrdquoNDTamp Internationalvol 62 pp 14ndash28 2014

[11] S Navaneethan J J SoraghanW H Siew F McPherson and PF Gale ldquoAutomatic fault location for underground low voltagedistribution networksrdquo IEEE Transactions on Power Deliveryvol 16 no 2 pp 346ndash351 2001

[12] D M Horan and R A Guinee ldquoA novel pulse echo correlationtool for transmission path testing and fault diagnosisrdquo Journalof Computers vol 1 no 1 pp 31ndash39 2006

[13] X Zhang M Zhang and D Liu ldquoReconstruction of faultycable network using time-domain reflectometryrdquo Progress inElectromagnetics Research vol 136 pp 457ndash478 2013

[14] D Thukaram H P Khincha and H P Vijaynarasimha ldquoArti-ficial neural network and support vector machine approach forlocating faults in radial distribution systemsrdquo IEEE Transactionson Power Delivery vol 20 no 2 I pp 710ndash721 2005

[15] X Deng R Yuan Z Xiao T Li and K L L Wang ldquoFaultlocation in loop distribution network using SVM technologyrdquoInternational Journal of Electrical Power andEnergy Systems vol65 pp 254ndash261 2015

[16] M Fuchida T Pathmakumar R Mohan N Tan and ANakamura ldquoVision-based perception and classification ofmosquitoes using support vector machinerdquo Applied Sciencesvol 7 no 1 pp 1ndash12 2017

[17] S F Yuan and F L Chu ldquoSupport vector machines-based faultdiagnosis for turbo-pump rotorrdquoMechanical Systems and SignalProcessing vol 20 no 4 pp 939ndash952 2006

[18] Z Sun and G Fox ldquoTraffic flow forecasting based on com-bination of multidimensional scaling and SVMrdquo InternationalJournal of Intelligent Transportation SystemsResearch vol 12 no1 pp 20ndash25 2014


[19] Y Lin F Lv S Zhu et al ldquoLarge-scale image classification fastfeature extraction and SVM trainingrdquo in Proceedings of the IEEEConference on Computer Vision and Pattern Recognition (CVPRrsquo11) pp 1689ndash1696 June 2011

[20] T Ma and D Niu ldquoIcing forecasting of high voltage transmis-sion line using weighted least square support vector machinewith fireworks algorithm for feature selectionrdquoApplied Sciencesvol 6 no 12 article 438 2016

[21] VN VapnikTheNature of Statistical LearningTheory SpringerNew York NY USA 1995

[22] V Cherkassky and Y Ma ldquoPractical selection of SVM parame-ters and noise estimation for SVM regressionrdquoNeural Networksvol 17 no 1 pp 113ndash126 2004

[23] C Hsu C Chang and C Lin ldquoA practical guide to support vec-tor classificationrdquo Department of Computer Science NationalTaiwan University 2003

[24] L B Jack andA K Nandi ldquoFault detection using support vectormachines and artificial neural networks augmented by geneticalgorithmsrdquo Mechanical Systems and Signal Processing vol 16no 2-3 pp 373ndash390 2002

[25] J Kennedy R Eberhart and Y Shi Swarm Intelligence MorganKaufmann Publishers Inc San Francisco Calif USA 2001

[26] Time Domain Reflectometry Theory Practical Radio Fre-quency Test and Measurement 1304-2 Agilient TechnologiesSanta Clara Calif USA 2002

[27] Y Shen LWei C Zeng and J Chen ldquoParticle swarm optimiza-tion with double learning patternsrdquo Computational Intelligenceand Neuroscience vol 2016 19 pages 2016

[28] Y del Valle G K Venayagamoorthy S Mohagheghi J-CHernandez and R G Harley ldquoParticle swarm optimizationbasic concepts variants and applications in power systemsrdquoIEEE Transactions on Evolutionary Computation vol 12 no 2pp 171ndash195 2008

[29] M N Alam B Das and V Pant ldquoA comparative study of meta-heuristic optimization approaches for directional overcurrentrelays coordinationrdquo Electric Power Systems Research vol 128article no 4368 pp 39ndash52 2015

[30] J-H Heo J-K Lyu M-K Kim and J-K Park ldquoApplication ofparticle swarm optimization to the reliability centered mainte-nance method for transmission systemsrdquo Journal of ElectricalEngineering and Technology vol 7 no 6 pp 814ndash823 2012

[31] T-H Chen and W-C Yang ldquoAnalysis of multi-grounded four-wire distribution systems considering the neutral groundingrdquoIEEE Transactions on Power Delivery vol 16 no 4 pp 710ndash7172001

Submit your manuscripts athttpswwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

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Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

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HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

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httpwwwhindawicom Volume 2014

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Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

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Computer EngineeringAdvances in



trace provided SVM has been used successfully to resolveclassification issues for a wide range of applications becauseof its strongly regularized characteristic and rapid trainingspeed [14ndash16]

To build a SVM classifier the aspect of feature subsetselection plays an important role in detecting relevant vari-ables in classification spaces Principal component analysis(PCA) [17] and multidimensional scaling (MDS) [18] are twotraditional methods applied to remove redundant variablesin the original feature vectors Authors in [19] proposeda Hadoop scheme to extract feature in parallel in whichhundreds of mappers are composed In a recent paper [20]Ma and Niu used the firework algorithm to select inputfeatures by removing redundant influence in order to improvethe icing forecasting of high voltage transmission line

In addition to feature subset selection the optimal setof SVM parameters also plays an important role in thedistribution of samples in a given search space Vapnikshowed that the penalty parameter 119862 and kernel functionparameter such as gamma 120574 for the radial basis function(RBF) significantly affect the performance of SVM [21]Various researches have been proposed to select these twoparameters but there is no general opinion for their settings[22] The grid search method (GSM) is investigated to deter-mine optimal parameters by attempting different values andselecting those values possessing the least amount of testingerror [23] Because of the computational complexity involvedwith GSM genetic algorithm (GA) has been developed toimprove classification accuracy and reduce training time byusing a minimal number of features [24] However it takessignificant amounts of calculation time due to the complexoperational process including inheritance selection recom-bination and mutation To overcome this relative problemKennedy and Eberhart proposed a population-based searchtechnique known as particle swarm optimization (PSO) [25]The primary advantage of the PSO based encoding techniqueis in its capacity to decrease trapped status in local optimaand increase the classification accuracy as well as the trainingspeed

In this paper a novelmethod based upon PSO techniquesis developed to simultaneously optimize input features andSVM parameters in order to classify the fault types found inthe distribution networkThese fault types can be divided intoten classes including single phase-to-ground faults (AG BGandCG) line-to-line faults (AB AC and BC) double line-to-ground faults (ABG ACG and BCG) and three-phase short-circuit faults (ABC) Further this PSO-SVM classifier usesa dataset obtained from TDR analysis with PRBS excitationNot only is the proposed PSO based encoding technique easyto use but it also helps to significantly increase the successrate of the SVM classifier

The remainder of this paper is constructed as follows InSection 2 the theory of the proposed method is discussedincluding TDR SVM and PSO Section 3 presents themodeling of a typical two-branched distribution feeder Thedeveloped PSO based SVM fault diagnosis approach is givenin Section 4 In Section 5 experimental simulation results anddiscussions are presented Finally a conclusion is presented inSection 6

L2dz L2dzR2dz R2dz

Cdz Gdz

Figure 1 The classical model for a lumped section

2 Basic Theory of the Proposed Method

21 Time-Domain Reflectometry Time-domain reflectome-try (TDR) is widely used for fault classification and locationof faults in electrical transmission and distribution lines TDRis based on a single pulse being injected into the given line orcable to be examined Afterwards some of the pulse energyis reflected back to source whenever it reaches the point ofany discontinuities such as electrical faults tee joints or lineterminals Since the propagation velocity is assumed to beconstant the fault distance can be measured based on theexpected pulse transit time Hence the reflectometry tracewill not only display the desired information of the fault typebut also determine the fault location

Assume a distribution line is modeled by a lumped-parameter equivalent circuit as shown in Figure 1 with adistributed series inductance 119871 resistance 119877 capacitance 119862and conductance 119866

A voltage introduced at the generator will require a cer-tain amount of time to propagate along the line representedin the following equation

120597V (119909 119905)120597119909 = minus119877119894 (119909 119905) minus 119871120597119894 (119909 119905)120597119905 120597119894 (119909 119905)120597119909 = minus119866V (119909 119905) minus 119862120597V (119909 119905)120597119905

(1)

where V(119909 119905) and 119894(119909 119905) are the forward travelling voltageand current waves respectively The amplitude of incidentpulse will be attenuated along the line and the phase of thevoltage travelling along the line will be distorted resultingfrom varying frequency [26]The attenuation and phase shiftare determined by the propagation coefficient as shown in

120574 = radic(119877 + 119895120596119871) (119866 + 119895120596119862) = 120572 + 119895120573 (2)

where 120572 and 120573 are the attenuation coefficient and the phasechange coefficient respectively The velocity at which thevoltage moves down the line can be defined in

120592 = 120596120573 (3)

From (1) using the Laplace transform and differentialequation we can obtain

V (119909 119905) = V+ (119905 minus 119909120592) + Vminus (119905 + 119909120592) 119894 (119909 119905) = 119894+ (119905 minus 119909120592) + 119894minus (119905 + 119909120592)

(4)




119885119862 = radic 119871119862(5)


119881 (119897 119904) = 119885119877 (119904) lowast 119868 (119897 119904) (6)



(7)



119862119909119910 (119896) = 1119871119871sum119894=1

119909 (119894) 119910 (119894 + 119896) (8)





Min 12 11990822 + 119862 119898sum119894=1

120585119894 (9)





119891 (119909) = sign( 119898sum119894=1



119870(119909 119910) = exp (minus120574 1003817100381710038171003817119909 minus 11991010038171003817100381710038172) (13)





Vpk

Xpk

Vpk+1

Xpk+1

Pbestpk

GbestkVpGbest

VpPbest





(14)

119883119896+1119901119902 = 119883119896119901119902 + 119881119896+1119901119902 (15)




= X119896+1119901 else 119875119887119890119904119905119896+1119901 = 119875119887119890119904119905119896119901If 119891 (X119896+1119901 ) lt 119891 (119866119887119890119904119905119896) then 119866119887119890119904119905119896

= X119896+1119901 else 119866119887119890119904119905119896+1 = 119866119887119890119904119905119896(16)


PRBS

SSMain feeder



3 System Modeling










Testing dataset

Training dataset



Optimum SVM





















No

Yes



Data acquisition


SVM Output



k = k + 1



parameters as Gbest






If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896










BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in






119885119862 = radic 119871119862(5)


119881 (119897 119904) = 119885119877 (119904) lowast 119868 (119897 119904) (6)



(7)



119862119909119910 (119896) = 1119871119871sum119894=1

119909 (119894) 119910 (119894 + 119896) (8)





Min 12 11990822 + 119862 119898sum119894=1

120585119894 (9)





119891 (119909) = sign( 119898sum119894=1



119870(119909 119910) = exp (minus120574 1003817100381710038171003817119909 minus 11991010038171003817100381710038172) (13)





Vpk

Xpk

Vpk+1

Xpk+1

Pbestpk

GbestkVpGbest

VpPbest





(14)

119883119896+1119901119902 = 119883119896119901119902 + 119881119896+1119901119902 (15)




= X119896+1119901 else 119875119887119890119904119905119896+1119901 = 119875119887119890119904119905119896119901If 119891 (X119896+1119901 ) lt 119891 (119866119887119890119904119905119896) then 119866119887119890119904119905119896

= X119896+1119901 else 119866119887119890119904119905119896+1 = 119866119887119890119904119905119896(16)


PRBS

SSMain feeder



3 System Modeling










Testing dataset

Training dataset



Optimum SVM





















No

Yes



Data acquisition


SVM Output



k = k + 1



parameters as Gbest






If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896










BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




Vpk

Xpk

Vpk+1

Xpk+1

Pbestpk

GbestkVpGbest

VpPbest





(14)

119883119896+1119901119902 = 119883119896119901119902 + 119881119896+1119901119902 (15)




= X119896+1119901 else 119875119887119890119904119905119896+1119901 = 119875119887119890119904119905119896119901If 119891 (X119896+1119901 ) lt 119891 (119866119887119890119904119905119896) then 119866119887119890119904119905119896

= X119896+1119901 else 119866119887119890119904119905119896+1 = 119866119887119890119904119905119896(16)


PRBS

SSMain feeder



3 System Modeling










Testing dataset

Training dataset



Optimum SVM





















No

Yes



Data acquisition


SVM Output



k = k + 1



parameters as Gbest






If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896










BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in






Testing dataset

Training dataset



Optimum SVM





















No

Yes



Data acquisition


SVM Output



k = k + 1



parameters as Gbest






If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896










BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in










No

Yes



Data acquisition


SVM Output



k = k + 1



parameters as Gbest






If 119865119901119896+1 lt 119865119901119896 then 119875119887119890119904119905119901119896+1 = 119883119901119896+1 else119875119887119890119904119905119901119896+1 = 119875119887119890119904119905119901119896










BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in







BG 14521 07277 05122 37681 18884 13290 04494 02252 01585 00380 00190 0013405287 02650 01865 12101 06064 04268 26995 13528 09521 23271 11662 08208

CG 04648 45783 31718 00857 08445 05851 00275 02711 01878 00237 02331 0161500880 08668 06005 02284 22492 15582 00272 02683 01858 00023 00227 00157

















0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in




0026

00255

0025

00245

0024

00235

0023

00225

0022

Mea

n sq

uare

erro

r

0 5 10 15 20 25 30 35 40




6 Conclusions




References








































Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in
























Advances in

FuzzySystems


Volume 2014












Journal of



Advances in

Multimedia


Biomedical Imaging


Advances in


RoboticsJournal of










Advances in



feature selection and parameters optimization of svm using...

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