research article estimating concrete workability based on...

Research ArticleEstimating Concrete Workability Based on Slump Test withLeast Squares Support Vector Regression

Nhat-Duc Hoang1 and Anh-Duc Pham2

1 Institute of Research and Development Faculty of Civil Engineering Duy Tan UniversityP809-K725 Quang Trung Danang 550000 Vietnam2Faculty of Project Management the University of Danang-University of Science and Technology54 Nguyen Luong Bang Danang 550000 Vietnam

Correspondence should be addressed to Nhat-Duc Hoang hoangnhatducdtueduvn

Received 23 August 2016 Accepted 8 November 2016

Academic Editor Khandaker Hossain

Copyright copy 2016 N-D Hoang and A-D Pham 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

Concrete workability quantified by concrete slump is an important property of a concrete mixture Concrete slump is generallyknown to affect the consistency flowability pumpability compactibility and harshness of a concrete mix Hence an accurateprediction of this property is a practical need of construction engineers This research proposes a machine learning model forpredicting concrete slump based on the Least Squares Support Vector Regression (LS-SVR) LS-SVR is employed to model thenonlinear mapping between the mix components and slump values Since the learning process of the LS-SVR necessitates twohyperparameters the regularization and the kernel parameters the grid search method is employed search for the most desirableset of hyperparameters Furthermore to construct the hybrid model this research collected a dataset including actual concreteslump tests from a hydroelectric dam construction project in Vietnam Experimental results show that the proposed model iscapable of predicting concrete slump accurately

1 Introduction

Concrete workability is defined as the effort required tomanipulate a freshly mixed quantity of concrete with min-imum loss of homogeneity [1] This property of concreteis generally known to affect the consistency flowabilitypumpability compactibility and harshness of a concrete mixThus concrete workability is a very crucial factor thatmust beconsidered in order to produce high quality concrete [2ndash4]

The slump test is the most commonmethod for assessingthe flow properties of fresh concrete the slump providesa measure of workability [5] Using this test the slumpcan be derived by measuring the drop from the top of theslumped fresh concrete In the task of concrete mixturedesign the prediction of concrete flowability is criticalfor on-site construction As the complexity of concreteconstruction escalates there is an increasing pressure onmaterial engineers to achieve high workability as well as to

maintain the necessary mechanical properties to meet designspecifications

Concrete has been increasingly utilized in high-risebuilding and infrastructure development projects and specialingredients are often employed to make the material satisfya specific set of performance requirements [6] Superplasti-cizers are often included to enhance the concrete workability[7ndash9] This situation makes the concrete mixes to be highlycomplex materials and modeling their properties becomesa very challenging task There are complex and nonlinearrelationships between the characteristics and the componentsthat constitute the concrete mixes [8 10 11]

Due to the importance of the research topic variousstudies have been dedicated to concrete slump predictionTraditional statistical models and machine learning are pre-vailing approaches to tackle the problem at hand Oztas etal [2] Yeh [1 3] Chine et al [12] and Bilgil [13] employedthe regression analysis and Artificial Neural Network (ANN)

Hindawi Publishing CorporationJournal of Construction EngineeringVolume 2016 Article ID 5089683 8 pageshttpdxdoiorg10115520165089683

2 Journal of Construction Engineering

Figure 1 Concrete slump test (image source httpxaydungth-anhvinhvn)

models to estimate concrete slump the common finding isthat ANN is an effective nonlinear modeling method andits results are more accurate than the models based on thetraditional regression analysis approach

Baykasoglu et al [14] utilized the gene expression pro-gramming (GEP) to model high-strength concrete slumpChen et al [15] constructed a parallel hypercubic GEPto forecast the slump of high-performance concrete thisresearch showed that the improved method is better than theGEP and similar to the performance of ANN Chandwaniet al [16] proposed a Genetic Algorithm assisted ANN thestudy showed that the integrated approach can enhance theconvergence speed of ANN and its prediction accuracy

Due to the popularity of concrete in the constructionindustry better alternatives for concrete slump prediction areof practical need for construction engineers in concrete mixdesign This research contributes to the body of knowledgeby proposing a new approach for improving the accuracyof concrete slump prediction which is based on the LeastSquares Support Vector Regression (LS-SVR) LS-SVR is anadvanced machine learning method which is designed fornonlinear modeling [17] the superiority of the approach hasbeen illustrated in recent applications [18ndash22]

Furthermore a dataset that contains slump test recordscollected from a hydroelectric dam construction project incentral Vietnam is used to establish and verify the proposedapproach The rest of the article is organized as follows thesecond section presents the research method The proposedslump prediction model is described in the third sectionThenext section reports the experimental results The conclusionof this study is stated in the final section

2 Research Method

21 The Concrete Slump Test Dataset This research recordedtesting results of 95 concrete mixes during the constructionprogress of the Song Bung 2 hydroelectric dam constructionproject in central Vietnam (httpwwwsb2vn) The test isin conformity with the Vietnamese standard (TCVN-3106)for slump test which is equivalent to the ASTM-C-143 Theequipment for the slump test includes a hollow frustum ofa cone and a ruler as the measuring device (see Figure 1)

Table 1 Statistical description

Factors Notation Min Mean Std dev MaxCement (kgm3) 1199091 2010 3386 623 4463Natural sand (kgm3) 1199092 3840 6901 1542 8270Crushed sand (kgm3) 1199093 00 816 1590 3990Coarse aggregate (kgm3) 1199094 11070 11557 330 12180Water (literm3) 1199095 1640 1742 64 1860Superplasticizer (literm3) 1199096 10 31 09 45Concrete slump (cm) 119910 80 102 29 190

Table 2 The dataset of concrete slump test

Mix 1199091 1199092 1199093 1199094 1199095 1199096 1199101 2610 3970 3970 12000 1760 13 802 2480 3990 3990 12080 1760 12 803 3200 3880 3880 11540 1790 32 904 3040 3910 3910 11620 1790 30 905 3360 3850 3850 11480 1780 34 956 3560 7690 00 11540 1700 32 100 90 3390 7650 00 11540 1770 34 8591 3750 7700 00 11440 1670 34 10092 3930 7570 00 11440 1660 35 11093 4040 7670 00 11240 1660 40 9094 3780 7510 00 11080 1860 38 18095 3591 7650 00 11110 1860 36 190

The height of the cone is 30 cm The diameter of the top andbottom of the cone is 10 cm and 20 cm respectivelyThe coneis filled with fresh concrete and then lifted vertically Theheight difference between the concrete and the cone is theslump value

In this study the concrete slump conditioning factors areselected based on reviewing previous works [1 12 16 23]on slump flow modeling and the availability of measuringequipment The amounts of cement (kgm3) natural sand(kgm3) crushed sand (kgm3) coarse aggregate (kgm3)water (literm3) and superplasticizer (literm3) are mixingredients For each mix design the slump value obtainedfrom the actual slump test experiment is recorded Statisticaldescriptions of all specimens are shown in Table 1 The wholedataset is partially described in Table 2 It is noted that theamounts of cement (1199091) natural sand (1199092) crushed sand (1199093)coarse aggregate (1199094) water (1199095) and superplasticizer (1199096)are used as input factors to predict the outputs which are theconcrete slump (119910)22 Least Squares Support Vector Regression (LS-SVR) LS-SVR proposed by Suykens et al [17] is an advancedmachinelearning algorithm which is constructed on the principalof structural risk minimization This approach has beenproved to be very efficient in nonlinear modeling Notably

Journal of Construction Engineering 3

x (concrete mix components)

y

(Concrete slump)y

(Concrete slump)Kernel mapping

Input space

Feature space

y(x) =N

sumk=1

120572kK(xk xl) + b120601(x)

120601(x)

120601(xu)

Figure 2 LS-SVR for concrete slump modeling

the learning process of the LS-SVR is very fast since it onlyrequires solving a set of linear equations

To construct the predictionmodel it is needed to preparea dataset of slump test record in the form 119863 = 119909119896 119910119896119896 = 1 2 119873 Herein 119896 denotes the 119896th data sample and119873 is the total number of data samples It is noted that 119909119896is a vector with six elements 1199091198961 1199091198962 1199091198963 1199091198964 1199091198965 and 1199091198966denote the amount of cement natural sand crushed sandcoarse aggregate water and superplasticizer respectivelyMeanwhile 119910119896 is the output of concrete slump of the 119896th datasample

We aim to establish a mapping function 119910(119909) that derivesthe output of concrete slump based on the input vectorx that describes the concrete mix components Since thefunctional mapping between concrete mix components (119909)and slump value (119910) is possibly nonlinear LS-SVR first mapsthe data from the original input space to a high-dimensionalfeature space via a mapping function 120601(119909) Accordinglylinear regression analysis can be possibly performed in suchhigh-dimensional feature space The operation of LS-SVR inconcrete slump modeling is illustrated in Figure 2

In the training phase of LS-SVR the learning objectivecan be formulated as the following optimization problem [1724]

Minimize 119869119901 (119908 119890) = 12119908119879119908 + 12057412119873sum119896=1

1198902119896Subjected to 119910119896 = 119908119879120601 (119909119896) + 119887 + 119890119896 119896 = 1 119873

(1)

where 119890119896 isin 119877 are error variables 120574 gt 0 denotes a regulariza-tion constant

In order to solve the above optimization problem theLagrangian function is formulated as [17]

119871 (119908 119887 119890 120572) = 119869119901 (119908 119890)minus 119873sum119896=1

120572119896 119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 (2)

where 120572119896 are Lagrange multipliers

The KarushndashKuhnndashTucker conditions for optimality areused by differentiating the Lagrangian function 119871(119908 119887 119890 120572)with the variables as follows [17]

120597119871120597119908 = 0 997888rarr119908 = 119873sum119896=1

120572119896120601 (119909119896) 120597119871120597119887 = 0 997888rarr119873sum119896=1

120572119896 = 0120597119871120597119890119896 = 0 997888rarr120572119896 = 120574119890119896 119896 = 1 119873120597119871120597120572119896 = 0 997888rarr

119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 = 0 119896 = 1 119873

(3)

By solving linear system (3) the resulting LS-SVR modelis expressed as follows [17 18]

119910 (119909) = 119873sum119896=1

120572119896119870(119909119896 119909119897) + 119887 (4)

where 120572119896 and 119887 are the solution to the linear system 119896 and119873 are the index and the total number of data points in thetraining set 119909119896 and 119909119897 denote an input pattern in the trainingand testing set It is worth reminding that 119909119896 and 119909119897 are bothinput vectors of concrete mix components with six elements119870(sdot) is the kernel function which maps the input data from


Data normalization

LS-SVR training

Grid search

LS-SVR training

Hyperparameters

LS-SVR predicting

LS-SVR predicting

Hyperparameter search

Prediction process

Predicted concrete slump

Dataset

Training data

Testing data

CementNatural sandCrushed sandCoarse aggregateWaterSuperplasticizer

Figure 3 Concrete slump prediction using LS-SVR (CSP-LSSVR)

the feature space into the high-dimensional space The radialbasis kernel function is often employed [17 19]

119870(119909119896 119909119897) = exp(minus1003817100381710038171003817119909119896 minus 1199091198971003817100381710038171003817221205902 ) (5)

where120590 represents the radial basis kernel function parameter

3 The Proposed Model forConcrete Slump Prediction

This section of the article describes the concrete slump pre-diction using LS-SVR (CSP-LSSVR) The prediction modelrelies on LS-SVR to discover the nonlinear mapping relation-ship between the concrete components and the slump Theflowchart of the CSP-LSSVR is demonstrated in Figure 3

Given the input data of concrete mix ingredients (theamounts of cement natural sand crushed sand coarse aggre-gate water and superplasticizer) the first step of themodel isto carry out the data normalization process within which thewhole data is normalized into a (0 1) range This process canhelp prevent the circumstance in which inputs with greatermagnitudes dominate those with smaller magnitudes Thefunction used for normalizing data is provided as follows

119883119899 = 119883119900 minus 119883min119883max minus 119883min (6)

where119883119899 is the normalized data119883119900 is the original data119883maxand 119883min denote the maximum and minimum values of thedata respectively

The dataset featuring six input factors and the outputvariable of concrete slump is then randomly divided into atraining set and a testing setThe training dataset is employedto establish the LS-SVR model Since the LS-SVR withradial basis kernel function is employed the learning processrequires hyperparameters the regularization parameter 120574and the kernel parameter 120590 and the grid search method[17 25] is employed search for the most desirable set ofhyperparameters

In the grid search for tuning parameters various pairs of(120574 and 120575) are tried and the one with the best fivefold cross-validation accuracy is chosen Using exponential growingsequences of 120574 (2minus5 2minus4 215) and 120590 (2minus15 2minus4 23) isa common way to identify good parameters The grid searchapproach is straightforward and easy to implement After thehyperparameters have been determined appropriately andthe training process is finished the proposed CSP-LSSVR canbe used to predict the slump flow values of new concretesamples

4 Experimental Results

When the training process finishes the slump of concretemixin the testing cases can be predicted by providing mixturecomponents for the trained model In the experimentsbesides the proposed CSP-LSSVR the Artificial Neural Net-work (ANN) and the multiple linear regression (MLR) areutilized as benchmark methods In order to measure modelperformance this research employs Root Mean Squared


0 10 20 30 40 50 60 70

8

10

12

14

16

18

20

22

Con

cret

e slu

mp

(cm

)

Actual slumpPredicted slump

Figure 4 The CSP-LSSVR training results

Error (RMSE) Mean Absolute Percentage Error (MAPE)and Coefficient of Determination (1198772)

The motivation for using these benchmark approaches isthat the ANN is an effective tool for nonlinear modeling andhas been successfully employed for predicting concrete slump[3 12 23] The MLR model is a basic statistical predictivemethod and comparing its result with othermachine learningmodels may reveal useful insights [26]

To construct an ANN the user needs to specify the net-work structure and the learning rate Such parameters of theANNmodel are usually selected via a trial-and-error process[26] Based on experiments the network configuration is setas follows the number of hidden layers is set to be 1 thelearning rate is 0001 the number of neurons in the hiddenlayer is set to be 6 The Levenberg-Marquardt algorithm [27]is employed to train the ANNmodel

In the first experiment the dataset is randomly dividedinto 2 sets the training set that occupies 80 of the datasetand the testing set that includes 20 of the dataset In detailthe training and testing sets consist of 76 and 19 mixesrespectively The training and testing results of the CSP-LSSVR are illustrated in Figures 4 and 5 respectively

The MLR model for predicting concrete slump basedon the collected dataset is established via the Least SquaresEstimation method [28] and shown as follows

119910 = 3622 minus 12471199091 minus 27031199092 minus 24561199093 minus 7391199094minus 3001199095 minus 1181199096 (7)

where the symbols of 1199091 1199092 1199093 1199094 1199095 and 1199096 representthe amount of cement natural sand crushed sand coarseaggregate water and superplasticizer within the concretemix respectively

The ANN model structure which contains the inputhidden and output layers is illustrated in Figure 6 It isnoted that 1198821 and 1198822 are the weight matrices of the hiddenlayer and the output layer respectively Θ = 6 denotes thenumber of neurons in the hidden layer 1198871 = [11988711 11988712 1198871Θ]

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8

10

12

14

16

18

20

Con

cret

e slu

mp

(cm

)


Figure 5 The CSP-LSSVR testing results

represents the bias vector of the hidden layer 1198872 denotes thebias vector of the output layer 119899119894 is the output of the 119894thneuron in the hidden layer 119865 is the tan-sigmoid activationfunctionwhich is commonly used in the hidden layer [29 30]

119891119860 (V) = 11 + exp (minusV) (8)

where V denotes an input for the functionIt is noted that the weight matrices (1198821 and1198822) and the

bias vectors (1198871 and 1198872) of the ANNmodel for concrete slumpestimation are learnt via a training process with the errorbackpropagation algorithm [31] After the training phaseresults of the ANN parameters are shown as follows

1198821

=[[[[[[[[[[[[

minus14769 07164 minus12991 minus24781 minus01608 minus17888minus24336 minus05163 00260 33005 minus25351 minus03737minus26319 02066 29821 minus20341 minus42239 0173710796 01646 minus06626 minus18433 minus00726 minus5073027421 minus11328 00858 minus37346 34695 17114minus08771 03779 05195 minus25811 minus07168 minus32345

]]]]]]]]]]]]

1198822 = [19870 05667 13222 24838 05420 minus35485] 1198871 = [minus26084 14889 minus03951 02309 minus11501 03311] 1198872 = 07132

(9)

Table 3 provides the result comparison between theproposed method and other benchmark models The resultof the MLR in the testing process is very poor (RMSE =028 MAPE = 1208 1198772 = 028) this indicates that thelinearmodel is insufficient to explain the behavior of concreteslump

The ANN and CSP-LSSVR models achieve much betterperformances both models have the 1198772 values which are


1

1

1

F

F

F

1

y

Input layer Hidden layer Output layerANN parametersANN structure

x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2

w11 X = [x1 x2 middot middot middot x6]

W1 =

[[[[[[[[

w11 w12 middot middot middot w16


wΘ1 wΘ2 middot middot middot wΘ6

]]]]]]]]

W2 = [1205791 1205792 middot middot middot 120579Θ]

Figure 6 The ANNmodel structure

Table 3 Result comparison

MLR ANN CSP-LSSVRTrainingRMSE 123 094 046MAPE () 962 363 3071198772 082 091 097TestingRMSE 154 105 054MAPE () 1208 596 3681198772 028 083 096

greater than 08 According to Smith [32] such high valuesof 1198772 imply strong correlations between the predicted andmeasured concrete slumps Furthermore theCSP-LSSVRhasachieved the lowest prediction error (MAPE = 368 andRMSE = 054) Thus benchmarked with the ANN the newmethod has attained 38 and 49 reductions in terms ofMAPE and RMSE

Moreover to avoid the randomness in selecting testingsamples the second experiment carries out a 10-fold cross-validation process Using the cross-validation process thewhole dataset is randomly divided into 10 data folds inwhich each fold in turn serves as a testing set and theperformance of the model can be assessed by averagingresults of the 10 folds Because all of the subsamples aremutually exclusive this experiment can evaluate the CSP-LSSVR more accurately

Table 4 summarizes the result of the cross-validationprocess Observably the proposed approach has attained thelowest prediction error in both training and testing processesThe average RMSE and MAPE for testing data of the CSP-LSSVR are 050 and 281 respectively These predictionerrors are significantly lower than the ANN (RMSE = 062

and 444) and the MLR (RMSE = 136 and 1064) Theproposed approach also yields the highest 1198772 (090) whenpredicting the slump of testing concrete mixes Hence theexperimental results have strongly demonstrated the superiorpredictive capability of the CSP-LSSVR model

5 Conclusion

This study has established a new method for predictingconcrete workability quantified by the slump values Theresearch extends the body of knowledge by investigatingthe capability of LS-SVR for concrete slump prediction Toestablish the proposed CSP-LSSVR a dataset consisting ofactual concrete slump tests has been collected From theexperiments the proposed model has achieved the mostaccurate prediction results

The average MAPE of the method obtained from thecross-validation process is less than 3 which is verydesirable because modeling concrete slump is known to bevery complex and highly nonlinear Since the tenfold cross-validation process is a very reliable way for model perfor-mance evaluation [33] it is expected that the proposed CSP-LSSVR can predict the flow of concrete based on the similarconditioning factors with the same accuracy Accordingly thenewly established method can be a very useful tool to assistthe engineers in the task of concrete mix design

Nevertheless in addition to the currently used six con-ditioning factors of concrete slump other factors (eg thetype size absorption and the water amount of the fine andcoarse aggregates) can be relevant and should be consideredby the model Furthermore another limitation of the currentstudy is that the employed dataset only consists of 95 datapointsThus this dataset should be expanded in a future studyto further enhance the generalization of the current modeland better ensure the predictive accuracy of the model whendealing with new concrete mixes


Table 4 The result of the 10-fold cross-validation process

Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR

TrainingRMSE 046 032 024 030 025 029 029 026 069 029 034MAPE 315 137 065 113 068 090 088 096 521 092 1591198772 097 099 099 099 099 099 099 099 094 099 098TestingRMSE 068 033 064 046 058 039 038 067 049 037 050MAPE 450 229 222 260 269 170 216 351 392 252 2811198772 099 083 100 058 098 099 099 097 097 072 090

ANN


MLR


Note Avg denotes the average result

Competing Interests

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

References

[1] I-C Yeh ldquoModeling slump flow of concrete using second-order regressions and artificial neural networksrdquo Cement andConcrete Composites vol 29 no 6 pp 474ndash480 2007

[2] A Oztas M Pala E Ozbay E Kanca N Caglar and MA Bhatti ldquoPredicting the compressive strength and slump ofhigh strength concrete using neural networkrdquoConstruction andBuilding Materials vol 20 no 9 pp 769ndash775 2006

[3] I-C Yeh ldquoExploring concrete slump model using artificialneural networksrdquo Journal of Computing in Civil Engineering vol20 no 3 pp 217ndash221 2006

[4] Y Li J Wang and Z Xu ldquoDesign optimization of a concreteface rock-fill dam by using genetic algorithmrdquo MathematicalProblems in Engineering vol 2016 Article ID 4971048 11 pages2016

[5] P KMehta andP JMMonteiroConcrete-Structure Propertiesand Materials Prentice Hall Inc Englewood Cliffs NJ USA1993

[6] Y Peng H Chu and J Pu ldquoNumerical simulation of recycledconcrete using convex aggregate model and base force element

methodrdquo Advances in Materials Science and Engineering vol2016 Article ID 5075109 10 pages 2016

[7] J Kasperkiewicz J Racz andADubrawski ldquoHPC strength pre-diction using artificial neural networkrdquo Journal of Computing inCivil Engineering vol 9 no 4 pp 279ndash284 1995

[8] I-C Yeh ldquoModeling of strength of high-performance concreteusing artificial neural networksrdquoCement andConcrete Researchvol 28 no 12 pp 1797ndash1808 1998

[9] S U Khan M F Nuruddin T Ayub and N Shafiq ldquoEffectsof different mineral admixtures on the properties of freshconcreterdquo The Scientific World Journal vol 2014 Article ID986567 11 pages 2014

[10] J-S Chou C-F Tsai A-D Pham and Y-H Lu ldquoMachinelearning in concrete strength simulations multi-nation dataanalyticsrdquo Construction and Building Materials vol 73 pp 771ndash780 2014

[11] N Hoang A Pham Q Nguyen and Q Pham ldquoEstimatingcompressive strength of high performance concrete with gaus-sian process regression modelrdquo Advances in Civil Engineeringvol 2016 Article ID 2861380 8 pages 2016

[12] W-H Chine H-H Hsu L Chen T-S Wang and C-HChiu ldquoModeling slump of concrete using the artificial neuralnetworksrdquo in Proceedings of the International Conference onArtificial Intelligence and Computational Intelligence (AICI rsquo10)pp 236ndash239 Sanya China October 2010

[13] A Bilgil ldquoEstimation of slump value and Bingham parametersof fresh concrete mixture composition with artificial neural


network modellingrdquo Scientific Research and Essays vol 6 no8 pp 1753ndash1765 2011

[14] A Baykasoglu A Oztas and E Ozbay ldquoPrediction and multi-objective optimization of high-strength concrete parameters viasoft computing approachesrdquo Expert Systems with Applicationsvol 36 no 3 pp 6145ndash6155 2009

[15] L Chen C-H Kou and S-W Ma ldquoPrediction of slump flowof high-performance concrete via parallel hyper-cubic gene-expression programmingrdquo Engineering Applications of ArtificialIntelligence vol 34 pp 66ndash74 2014

[16] V Chandwani V Agrawal and R Nagar ldquoModeling slump ofreadymix concrete using genetic algorithms assisted training ofArtificial Neural Networksrdquo Expert Systems with Applicationsvol 42 no 2 pp 885ndash893 2015

[17] J Suykens J V Gestel J D Brabanter B D Moor andJ Vandewalle Least Square Support Vector Machines WorldScientific Singapore 2002

[18] J Ji C Zhang Y Gui Q Lu and J Kodikara ldquoNew observationson the application of LS-SVM in slope system reliabilityanalysisrdquo Journal of Computing in Civil Engineering 2016

[19] D Yao J Yang X Li and C Zhao ldquoA hybrid approach forfault diagnosis of railway rolling bearings using STWD-EMD-GA-LSSVMrdquo Mathematical Problems in Engineering vol 2016Article ID 8702970 7 pages 2016

[20] J-S Chou and A-D Pham ldquoSmart artificial firefly colonyalgorithm-based support vector regression for enhanced fore-casting in civil engineeringrdquo Computer-Aided Civil and Infras-tructure Engineering vol 30 no 9 pp 715ndash732 2015

[21] D Tien Bui B T Pham Q P Nguyen and N HoangldquoSpatial prediction of rainfall-induced shallow landslides usinghybrid integration approach of Least-Squares Support VectorMachines and differential evolution optimization a case studyin Central Vietnamrdquo International Journal of Digital Earth vol9 no 11 pp 1077ndash1097 2016

[22] D-T Vu andN-DHoang ldquoPunching shear capacity estimationof FRP-reinforced concrete slabs using a hybrid machinelearning approachrdquo Structure and Infrastructure Engineeringvol 12 no 9 pp 1153ndash1161 2016

[23] V Chandwani V Agrawal and R Nagar ldquoModeling slump ofready mix concrete using genetically evolved artificial neuralnetworksrdquo Advances in Artificial Neural Systems vol 2014Article ID 629137 9 pages 2014

[24] M-Y Cheng and N-D Hoang ldquoInterval estimation of con-struction cost at completion using least squares support vectormachinerdquo Journal of Civil Engineering andManagement vol 20no 2 pp 223ndash236 2014

[25] C W Hsu C C Chang and C J Lin ldquoA practical guideto support vector classificationrdquo Tech Rep Department ofComputer Science National Taiwan University Taipei Taiwan2010

[26] J-S Chou C-K Chiu M Farfoura and I Al-TaharwaldquoOptimizing the prediction accuracy of concrete compressivestrength based on a comparison of data-mining techniquesrdquoJournal of Computing in Civil Engineering vol 25 no 3 pp 242ndash253 2011

[27] M THagan andM BMenhaj ldquoTraining feedforward networkswith the Marquardt algorithmrdquo IEEE Transactions on NeuralNetworks vol 5 no 6 pp 989ndash993 1994

[28] N R Draper and H Smith Applied Regression Analysis Wiley-Interscience 1998

[29] M T Hagan H B Demuth and M H Beale Neural NetworkDesign PWS Publishing Boston Mass USA 1996

[30] T Tran and N Hoang ldquoPredicting colonization growth ofalgae on mortar surface with artificial neural networkrdquo Journalof Computing in Civil Engineering vol 30 no 6 Article ID04016030 2016

[31] D E Rumelhart G E Hinton and R J Williams ldquoLearningrepresentations by back-propagating errorsrdquo Nature vol 323no 6088 pp 533ndash536 1986

[32] G N Smith Probability and Statistics in Civil EngineeringCollins London UK 1986

[33] S Arlot andA Celisse ldquoA survey of cross-validation proceduresfor model selectionrdquo Statistics Surveys vol 4 pp 40ndash79 2010

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Figure 1 Concrete slump test (image source httpxaydungth-anhvinhvn)

models to estimate concrete slump the common finding isthat ANN is an effective nonlinear modeling method andits results are more accurate than the models based on thetraditional regression analysis approach

Baykasoglu et al [14] utilized the gene expression pro-gramming (GEP) to model high-strength concrete slumpChen et al [15] constructed a parallel hypercubic GEPto forecast the slump of high-performance concrete thisresearch showed that the improved method is better than theGEP and similar to the performance of ANN Chandwaniet al [16] proposed a Genetic Algorithm assisted ANN thestudy showed that the integrated approach can enhance theconvergence speed of ANN and its prediction accuracy

Due to the popularity of concrete in the constructionindustry better alternatives for concrete slump prediction areof practical need for construction engineers in concrete mixdesign This research contributes to the body of knowledgeby proposing a new approach for improving the accuracyof concrete slump prediction which is based on the LeastSquares Support Vector Regression (LS-SVR) LS-SVR is anadvanced machine learning method which is designed fornonlinear modeling [17] the superiority of the approach hasbeen illustrated in recent applications [18ndash22]

Furthermore a dataset that contains slump test recordscollected from a hydroelectric dam construction project incentral Vietnam is used to establish and verify the proposedapproach The rest of the article is organized as follows thesecond section presents the research method The proposedslump prediction model is described in the third sectionThenext section reports the experimental results The conclusionof this study is stated in the final section

2 Research Method

21 The Concrete Slump Test Dataset This research recordedtesting results of 95 concrete mixes during the constructionprogress of the Song Bung 2 hydroelectric dam constructionproject in central Vietnam (httpwwwsb2vn) The test isin conformity with the Vietnamese standard (TCVN-3106)for slump test which is equivalent to the ASTM-C-143 Theequipment for the slump test includes a hollow frustum ofa cone and a ruler as the measuring device (see Figure 1)

Table 1 Statistical description

Factors Notation Min Mean Std dev MaxCement (kgm3) 1199091 2010 3386 623 4463Natural sand (kgm3) 1199092 3840 6901 1542 8270Crushed sand (kgm3) 1199093 00 816 1590 3990Coarse aggregate (kgm3) 1199094 11070 11557 330 12180Water (literm3) 1199095 1640 1742 64 1860Superplasticizer (literm3) 1199096 10 31 09 45Concrete slump (cm) 119910 80 102 29 190

Table 2 The dataset of concrete slump test

Mix 1199091 1199092 1199093 1199094 1199095 1199096 1199101 2610 3970 3970 12000 1760 13 802 2480 3990 3990 12080 1760 12 803 3200 3880 3880 11540 1790 32 904 3040 3910 3910 11620 1790 30 905 3360 3850 3850 11480 1780 34 956 3560 7690 00 11540 1700 32 100 90 3390 7650 00 11540 1770 34 8591 3750 7700 00 11440 1670 34 10092 3930 7570 00 11440 1660 35 11093 4040 7670 00 11240 1660 40 9094 3780 7510 00 11080 1860 38 18095 3591 7650 00 11110 1860 36 190

The height of the cone is 30 cm The diameter of the top andbottom of the cone is 10 cm and 20 cm respectivelyThe coneis filled with fresh concrete and then lifted vertically Theheight difference between the concrete and the cone is theslump value

In this study the concrete slump conditioning factors areselected based on reviewing previous works [1 12 16 23]on slump flow modeling and the availability of measuringequipment The amounts of cement (kgm3) natural sand(kgm3) crushed sand (kgm3) coarse aggregate (kgm3)water (literm3) and superplasticizer (literm3) are mixingredients For each mix design the slump value obtainedfrom the actual slump test experiment is recorded Statisticaldescriptions of all specimens are shown in Table 1 The wholedataset is partially described in Table 2 It is noted that theamounts of cement (1199091) natural sand (1199092) crushed sand (1199093)coarse aggregate (1199094) water (1199095) and superplasticizer (1199096)are used as input factors to predict the outputs which are theconcrete slump (119910)22 Least Squares Support Vector Regression (LS-SVR) LS-SVR proposed by Suykens et al [17] is an advancedmachinelearning algorithm which is constructed on the principalof structural risk minimization This approach has beenproved to be very efficient in nonlinear modeling Notably



y

(Concrete slump)y


Input space

Feature space

y(x) =N

sumk=1

120572kK(xk xl) + b120601(x)

120601(x)

120601(xu)






Minimize 119869119901 (119908 119890) = 12119908119879119908 + 12057412119873sum119896=1

1198902119896Subjected to 119910119896 = 119908119879120601 (119909119896) + 119887 + 119890119896 119896 = 1 119873

(1)



119871 (119908 119887 119890 120572) = 119869119901 (119908 119890)minus 119873sum119896=1

120572119896 119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 (2)



120597119871120597119908 = 0 997888rarr119908 = 119873sum119896=1

120572119896120601 (119909119896) 120597119871120597119887 = 0 997888rarr119873sum119896=1

120572119896 = 0120597119871120597119890119896 = 0 997888rarr120572119896 = 120574119890119896 119896 = 1 119873120597119871120597120572119896 = 0 997888rarr

119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 = 0 119896 = 1 119873

(3)


119910 (119909) = 119873sum119896=1

120572119896119870(119909119896 119909119897) + 119887 (4)



Data normalization

LS-SVR training

Grid search

LS-SVR training

Hyperparameters

LS-SVR predicting

LS-SVR predicting


Prediction process


Dataset

Training data

Testing data




119870(119909119896 119909119897) = exp(minus1003817100381710038171003817119909119896 minus 1199091198971003817100381710038171003817221205902 ) (5)












0 10 20 30 40 50 60 70

8

10

12

14

16

18

20

22

Con

cret

e slu

mp

(cm

)











0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8

10

12

14

16

18

20

Con

cret

e slu

mp

(cm

)




119891119860 (V) = 11 + exp (minusV) (8)



1198821

=[[[[[[[[[[[[


]]]]]]]]]]]]


(9)




1

1

1

F

F

F

1

y


x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2


W1 =

[[[[[[[[




]]]]]]]]









5 Conclusion






Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











y

(Concrete slump)y


Input space

Feature space

y(x) =N

sumk=1

120572kK(xk xl) + b120601(x)

120601(x)

120601(xu)






Minimize 119869119901 (119908 119890) = 12119908119879119908 + 12057412119873sum119896=1

1198902119896Subjected to 119910119896 = 119908119879120601 (119909119896) + 119887 + 119890119896 119896 = 1 119873

(1)



119871 (119908 119887 119890 120572) = 119869119901 (119908 119890)minus 119873sum119896=1

120572119896 119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 (2)



120597119871120597119908 = 0 997888rarr119908 = 119873sum119896=1

120572119896120601 (119909119896) 120597119871120597119887 = 0 997888rarr119873sum119896=1

120572119896 = 0120597119871120597119890119896 = 0 997888rarr120572119896 = 120574119890119896 119896 = 1 119873120597119871120597120572119896 = 0 997888rarr

119908119879120601 (119909119896) + 119887 + 119890119896 minus 119910119896 = 0 119896 = 1 119873

(3)


119910 (119909) = 119873sum119896=1

120572119896119870(119909119896 119909119897) + 119887 (4)



Data normalization

LS-SVR training

Grid search

LS-SVR training

Hyperparameters

LS-SVR predicting

LS-SVR predicting


Prediction process


Dataset

Training data

Testing data




119870(119909119896 119909119897) = exp(minus1003817100381710038171003817119909119896 minus 1199091198971003817100381710038171003817221205902 ) (5)












0 10 20 30 40 50 60 70

8

10

12

14

16

18

20

22

Con

cret

e slu

mp

(cm

)











0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8

10

12

14

16

18

20

Con

cret

e slu

mp

(cm

)




119891119860 (V) = 11 + exp (minusV) (8)



1198821

=[[[[[[[[[[[[


]]]]]]]]]]]]


(9)




1

1

1

F

F

F

1

y


x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2


W1 =

[[[[[[[[




]]]]]]]]









5 Conclusion






Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Data normalization

LS-SVR training

Grid search

LS-SVR training

Hyperparameters

LS-SVR predicting

LS-SVR predicting


Prediction process


Dataset

Training data

Testing data




119870(119909119896 119909119897) = exp(minus1003817100381710038171003817119909119896 minus 1199091198971003817100381710038171003817221205902 ) (5)












0 10 20 30 40 50 60 70

8

10

12

14

16

18

20

22

Con

cret

e slu

mp

(cm

)











0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8

10

12

14

16

18

20

Con

cret

e slu

mp

(cm

)




119891119860 (V) = 11 + exp (minusV) (8)



1198821

=[[[[[[[[[[[[


]]]]]]]]]]]]


(9)




1

1

1

F

F

F

1

y


x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2


W1 =

[[[[[[[[




]]]]]]]]









5 Conclusion






Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 10 20 30 40 50 60 70

8

10

12

14

16

18

20

22

Con

cret

e slu

mp

(cm

)











0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

8

10

12

14

16

18

20

Con

cret

e slu

mp

(cm

)




119891119860 (V) = 11 + exp (minusV) (8)



1198821

=[[[[[[[[[[[[


]]]]]]]]]]]]


(9)




1

1

1

F

F

F

1

y


x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2


W1 =

[[[[[[[[




]]]]]]]]









5 Conclusion






Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










1

1

1

F

F

F

1

y


x1

x2

x6

wΘ6

b12

b11

b1Θ

nΘ

n1

n2

1205791

1205792

120579Θ

sum

sum

sum

sum

b2


W1 =

[[[[[[[[




]]]]]]]]









5 Conclusion






Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Data fold 1 2 3 4 5 6 7 8 9 10 Avg

CSP-LSSVR


ANN


MLR



Competing Interests


References







































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation

































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article estimating concrete workability based on...

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