Research Article Estimating Compressive Strength of High...

Research ArticleEstimating Compressive Strength of High PerformanceConcrete with Gaussian Process Regression Model

Nhat-Duc Hoang1 Anh-Duc Pham2 Quoc-Lam Nguyen3 and Quang-Nhat Pham3

1 Institute of Research and Development Faculty of Civil Engineering Duy Tan University P809-K725 Quang TrungDanang 550000 Vietnam2Faculty of Project Management The University of Danang University of Science and Technology 54 Nguyen Luong BangDanang 550000 Vietnam3Faculty of Civil Engineering Duy Tan University P809-K725 Quang Trung Danang Vietnam

Correspondence should be addressed to Nhat-Duc Hoang hoangnhatducdtueduvn

Received 3 June 2016 Revised 22 September 2016 Accepted 26 September 2016

Academic Editor Ghassan Chehab

Copyright copy 2016 Nhat-Duc Hoang et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This research carries out a comparative study to investigate a machine learning solution that employs the Gaussian ProcessRegression (GPR) for modeling compressive strength of high-performance concrete (HPC) This machine learning approach isutilized to establish the nonlinear functional mapping between the compressive strength and HPC ingredients To train and verifythe aforementioned prediction model a data set containing 239 HPC experimental tests recorded from an overpass constructionproject in Danang City (Vietnam) has been collected for this study Based on experimental outcomes prediction results of the GPRmodel are superior to those of the Least Squares Support Vector Machine and the Artificial Neural Network Furthermore GPRmodel is strongly recommended for estimating HPC strength because this method demonstrates good learning performance andcan inherently express prediction outputs coupled with prediction intervals

1 Introduction

In construction industry high-performance concrete (HPC)has been widely used in high-rise buildinginfrastructureprojects for its superior strength durability and workabilitywhich exceed those of normal concrete [1 2] Generallyspecial ingredients are employed to make these speciallydesigned concretes to satisfy a combination of performancerequirements Furthermore the compressive strength is oftenconsidered as the most important property of HPC otherconcrete properties such as elastic modulus water tightnessand impermeability appear to have direct relationships withcompressive strength [3] Hence the compressive strengthis commonly utilized as the main criterion in defining therequired quality of concrete [4]

The compressive strength is determined through a stan-dard uniaxial compression test If the test result does notmeetthe designed strength remediation actions must be under-taken Furthermore corrective actions for underground con-crete structures such as concrete piles or foundations can

be very costly As a result an accurate estimation of thecompressive strength before the placement is a practical needof construction engineers

As the relationships between concrete components andcompressive strength are complex and highly nonlinearmathematical modeling of HPC is very challenging andoftentimes inaccurate [5] Consequently traditional statisti-calmethods are inadequate formodeling ofHPCcompressivestrength Herein the main goal is to construct a system thatcan learn from a data set of different HPC mixes and canpredict accurately the compressive strength based on thepattern of concrete components

Accordingly this research extends the body of knowl-edge by evaluating the capability of the Gaussian ProcessRegression (GPR) [6] for modeling compressive strengthof HPC GPR is an efficient and reliable learning approachfor modeling nonlinear and complex functional mappings[7 8] therefore an assessment of this model performance onHPC strength prediction is particularly useful for practicing

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2016 Article ID 2861380 8 pageshttpdxdoiorg10115520162861380

2 Advances in Civil Engineering

engineers Additionally this study can also be viewed asa comparative work since the performance of the GPRis benchmarked against those of other powerful nonlinearmodeling methods including the Artificial Neural Network(ANN) and the Least Squares Support Vector Machine(LSSVM) [9] Moreover a data set of 239 HPC experimentaltests recorded during the construction phase of the Nga BaHue highway overpass project in Danang City (Vietnam) hasbeen collected for this research The subsequent parts of thepaper are organized as follows Section 2 reviews pertinentresearch works in the literature In Section 3 the researchmethod is presented followed by the experimental resultsThe conclusion of this study is stated in the final section

2 Related Works

Due to the importance of the research topic HPC compres-sive strength modeling has been a very active research areaand various artificial intelligence (AI) techniques have beenapplied to tackle the problem of interest Based on previousstudies AI techniques have proved its superior capability overtraditional modeling methods ANN is the most commonmodeling method [10 11] Yeh and Lien [12] applied theGenetic Operation Trees to establish empirical formulaswhich are more accurate than the nonlinear regression butless accurate than ANNmodels Chou et al [13] compare dif-ferent data-mining techniques to identify the fittest method

Sophisticated AI based systems have also been developedto fit particular HPC data sets Słonski [14] combined theANN and the Bayesian evidence framework which helps toconstruct the ANN structure Genetic Weighted PyramidOperation Tree was developed by combining four individualGenetic Operation Trees with adaptive weights [15] themethod appears to be better than the individual tree TheK-nearest neighbor based regression was integrated withDifferential Evolution by Ahmadi-Nedushan [3] this workdemonstrated that despite being simple in certain learningcircumstances the instance-based regression method canoutperform the ANN

Cheng et al [16] proposed a fuzzy Support VectorMachine (SVM) method which can be superior over theoriginal SVM and be comparable to the ANN Pham et al[5] employ LSSVM and Firefly Algorithm to construct ahybrid model for HPC strength estimation The capability ofGenetic Programming based prediction models which fusesthe genetic algorithm and the symbolic programming wasinvestigated by Chen and Wang [17] Mousavi et al [18] andCastelli et al [19] Extensive researches on ensemble learningof Erdal et al [20] and Chou et al [21] found that this formof learning may boost the predictive capability of individualAI models As can be seen in the literature the capability ofGPR has rarely been investigated for the task of HPC strengthmodelingTherefore our study is an attempt to fill this gap inthe literature

3 Research Method

31 Data Set of HPC Experiments This research employsa data set consisting of 239 testing results of HPC concrete

specimens All the experimental tests were performed with 15cm cylindrical specimens of HPC prepared according to theVietnamese standard (TCVN 3105 1993) which is relativelysimilar to the American standard ASTM C39 The amountsof cement (Kgm3) sand (Kgm3) small coarse aggregate(Kgm3)mediumcoarse aggregate (Kgm3) water (literm3)and superplasticizer (literm3) are batch components em-ployed for expressing properties of a concrete sample It isnoted that the concrete age of each sample ismeasured in day

Statistical descriptions ofHPC test are reported in Table 1It is worth noticing that the small coarse aggregate hasdiameter ranging from 5 to 10mm the medium coarseaggregate ranges in diameter from 10 and 20mm In additionthe ratio of water-to-cement of the concrete mixes in the dataset ranges from 027 to 046 Such low water-to-cement rationecessitates the utilization of superplasticizer to enhance theconcrete workabilityTheminimum andmaximum compres-sive strength of concrete specimens are 236 and 852MParespectively

32 Gaussian Process Regression (GPR) GPRpresents a prob-abilistic nonparametric supervised learning approach forgeneralizing nonlinear and complex function mapping hid-den in data sets This approach has recently received hugeattention of researchers in various study disciplines [4 22]GPR is very efficient to handle nonlinear data due to the useof kernel functions Furthermore a significant advantage ofGPR is that the model can provide a reliability response to aninput data [23]

Given a training set119863 = (119909119894 119910119894) | 119894 = 1 119899 the inputdata 119883 isin 119877119863times119899 is called the design matrix and 119910 isin 119877119899 is thevector of desired outputThemain assumption of GPR is thatthe output 119910 is computed as [6 24]

119910 = 119891 (119909) + 120576 (1)

where 120576 sim 119873(0 1205902119899) isin 119877 represents a homoscedastic noise forall sample 119909119894

In GPR methodology the 119899 observations in the data setof interest 119910 = 1199101 119910119899 are considered as a single pointsampled from a multivariate Gaussian distribution More-over it can be assumed that this Gaussian distribution hasthe mean of zeros The covariance function 119896(119909 1199091015840) dictatesthe relation of one observation to another observation Thesquared exponential covariance function is often selected inGPR for the task of function approximation [22 24]

119896 (119909 1199091015840) = 1205902119891 times exp(minus(119909 minus 1199091015840)221198972 ) + 1205902119899120575 (119909 1199091015840) (2)

where the maximum allowable covariance is defined as 1205902119891It is noted that 119896(119909 1199091015840) reaches this maximum allowablecovariance only when 119909 is very closed to 1199091015840 and therefore119891(119909) is almost perfectly correlated with 119891(1199091015840) Meanwhile119897 denotes the length parameter of the kernel function Inaddition 120575(119909 1199091015840) represents a Kronecker delta function 120575119894119895 =1 if 119894 = 119895 and 120575119894119895 = 0 if 119894 = 119895

Advances in Civil Engineering 3

Table 1 Concrete components and statistical descriptions

HPC input factor (IF) Notation Min Mean Std dev MaxCement (Kgm3) IF1 3500 4474 250 4980Fine aggregate (Kgm3) IF2 6660 7289 378 8790Small coarse aggregate (Kgm3) IF3 00 3472 559 4240Medium coarse aggregate (Kgm3) IF4 6260 7213 614 10600Water (literm3) IF5 1340 1788 204 2070Superplasticizer (literm3) IF6 35 51 06 70Concrete age (day) IF7 30 151 109 280Compressive strength (MPam3) CS 236 425 135 852

Given the training data set the ultimate goal of thelearning process is to predict the output value 119910lowast of a newqueried input pattern To achieve such goal it is necessary toestablish three covariance matrices as follows

119870 =[[[[[[[[[

119896 (1199091 1199091) 119896 (1199091 1199092) sdot sdot sdot 119896 (1199091 119909119899)119896 (1199092 1199091) 119896 (1199092 1199092) sdot sdot sdot 119896 (1199092 119909119899)sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdotsdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot119896 (119909119899 1199091) 119896 (119909119899 1199092) sdot sdot sdot 119896 (119909119899 119909119899)

]]]]]]]]]

119870lowast = [119896 (119909lowast 1199091) 119896 (119909lowast 1199092) sdot sdot sdot 119896 (119909lowast 119909119899)] 119870lowastlowast = 119896 (119909lowast 119909lowast)

(3)

Due to the assumption that the data is sampled froma multivariate Gaussian distribution we have the followingexpression

[ 119910119910lowast] sim 119873(0 [119870 119870119879lowast119870lowast 119870lowastlowast]) (4)

Since 119910lowast | 119910 is proved to be generated from amultivariateGaussian distribution with the mean of 119870lowast119870minus1119910 and thevariance of119870lowastlowastminus119870lowast119870minus1119870119879lowast the estimatedmean and varianceof the predicted output 119910lowast are given as follows

119864 (119910lowast) = 119870lowast119870minus1119910var (119910lowast) = 119870lowastlowast minus 119870lowast119870minus1119870119879lowast (5)

When the hyperparameters of the kernel function arespecified the model parameters including 119896 and 120590119899 can bedetermined by Bayesian inference This task boils down tomaximizing a log-posterior function [24] After the trainingphase terminates the GPR model can be employed forpredicting unknown input data sample

4 Experimental Result and Comparison

41 Estimating HPC Compressive Strength with GaussianProcess Regression In this experiment the data set of HPCtesting samples has been divided into two sets the trainingset (90) used for model construction and the testing set

(10) employed for model testing Prior to the trainingprocess it is necessary to specify the hyperparameters ofGPR model These hyperparameters include the initial valuefor the standard deviation of the noise 120590119899 the maximumallowable covariance 120590119891 and the length parameter 119897 of thekernel function Based on recommendations in Mathworks[25] the initial value for the standard deviation of the noiseis set as follows

120590119899 = std (119884Training)radic2 (6)

where std(119884Training) denotes the standard deviation of thedesired output in the training data set

To select the maximum allowable covariance 120590119891 and thelength parameter 119897 of the kernel function we have carried outa model selection process These two parameters are allowedto be varied within the following parameter set (ParSet)

ParSet = 0001 0005 001 005 01 05 15 10 50 100 500 1000 (7)

The training set is further separated into two subsetssubset 1 (90) and subset 2 (10) and a grid searchprocedure described in Algorithm 1 is performed to identifythe most suitable set of 120590119891 and 119897 Subset 1 herein plays the roleof a training set The set of parameters accompanied with themost desirable prediction performance of the model when itis used to predict data in subset 2 is selected To quantify themodel prediction performance the RootMean Squared Error(RMSE) has been used Based on the experiment the valuesof 120590119891 and 119897 are selected to be 01 and 005

With the three aforementioned hyperparameters thetraining process of GPR can be executed Accordingly theconstructed model is utilized to predict the data instances inthe testing set The prediction outcome of the GPR testingphase is illustrated in Figure 1 To express themodel accuracybesides RMSE the Mean Absolute Percentage Error (MAPE)and the Coefficient of Determination (1198772) have also beenemployed The experimental result is reported as followsRMSE = 492 MAPE = 729 and 1198772 = 090These outcomesdemonstrate that GPR has successfully captured the non-linear function that determines the mapping between inputfactors of ingredients and the output of HPC compressivestrength As shown in Figure 1 the GPR modelrsquos outcomes


Establishing Subset1 Subset2Establishing ParSetPM = Performance matrixFor 119894 = 1 119873119875 NP = number of hyper parameters in ParameterSet120590119891 = 119875119886119903119878119890119905(119894)

For 119895 = 1 119873119875119897 = 119875119886119903119878119890119905(119895)Train GPR model with Subset1GPR model prediction with Subset2PM(ij) = RMSE of Subset2 RMSE denotes the Root Mean Squared Error

End ForEnd ForFinding the best set of 120590119891 119897 based on PM

Algorithm 1 Grid search procedure for GPR hyperparameter determination

35

40

45

50

55

60

65

70

75

80

Pred

icte

d co

mpr

essiv

e stre

ngth

(MPa

)

40 7050 6560 8035 45 7555Actual compressive strength (MPa)

Line of fit R2= 09

Figure 1 GPR prediction result in the testing phase

have obtained a good fit to a straight line Since GPR canexpress uncertainty associated with each predicted outputFigure 2 illustrates the GPR results of prediction intervalwith 95 level of confidence It is noted that all actualcompressive strengths are within the range of the lower andupper boundaries

42 Result Comparison In this section of the article tobetter evaluate the performance of the GPR model theANN [26] and LSSVM [9 27] are employed as benchmarkmethods The reasons for selecting these two benchmarkmodels are that ANN is widely accepted as an effective toolfor nonlinear function approximation and this algorithm hasbeen successfully employed for predicting concrete strength[10 13] LSSVM is also an advancedmachine learningmethodfeatured by high modeling accuracy [28ndash31] and it has beenrecently used formodeling concrete compressive strength [5]

To establish an ANN model number of neurons inthe hidden layer should be determined in advance and

Predicted CSLower bound

Upper boundActual CS

2030405060708090

100110

Com

pres

sive s

treng

th (M

Pa)

2010 15 250 5Testing case

Figure 2 GPR prediction result with prediction interval

this parameter significantly influences the ANN predictioncapability In order to specify an appropriate model structurefor ANN the hidden layer starts with seven neurons (whichis equal to the number of input factors) and then graduallyincreased to the maximum value of 30 neurons The log-sigmoid function is commonly employed as the activationfunction and the Levenberg-Marquardt algorithm is utilizedto train the ANN [26 32 33] Herein the training set isalso separated into two subsets subset 1 (90 or equivalently193 data samples) and subset 2 (10 or equivalently 22data samples) the number of neurons in the hidden layerresults in the best prediction outcome in the testing phase ofANN being chosen On the other hand the hyperparametersof LSSVM (the regularization parameter and the kernelfunction parameter) are automatically tuned by the FireflyAlgorithm as described in [5]

As mentioned earlier the data set is randomly dividedinto 2 sets training set (90) and testing set (10) Accord-ingly the training and testing sets consist of 215 and 24 casesrespectively Nevertheless to avoid the randomness in testingsample selection and to compare the performances of modelsreliably a 10-fold cross validation process is performed [3435] Accordingly the whole data set is randomly divided


40 60 80

Fold 1 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 2 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 3 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 4 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 5 R2= 089

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 6 R2= 094

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Fold 7 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 8 R2= 076

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

Fold 9 R2= 086

CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 10 R2= 092

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Figure 3 GPR prediction result obtained from the 10-fold cross validation

Table 2 Prediction result comparison

Model Criteria Training phase Testing phaseAverage result Standard deviation Average result Standard deviation

GPRRMSE 406 129 404 047MAPE 502 186 514 0891198772 090 007 090 005

LSSVMRMSE 446 058 463 062MAPE 567 092 594 086R2 089 002 087 005

ANNRMSE 507 087 521 185MAPE 656 123 634 2321198772 085 014 081 015

into ten data folds in which each fold in turn serves as atesting set and the performance of the three models (GPRANN and LSSVM) can be quantified by averaging resultsof the ten folds Because all of the subsamples are mutuallyexclusive this cross validation process can reliably assess theGPR model and the other two benchmarking methods

Prediction results of the GPR model and the two bench-mark models obtained from the ten-fold cross validationprocess are reported in Table 2 It can be observed thatthe GPR has achieved the best prediction result in all ofthe performance evaluation criteria followed by LSSVMand ANN Particularly in terms of RMSE GPR achieves a1274 improvement compared with LSSVM and a 2246improvement compared with ANN

The outcomes of the GPR LSSVM and ANN modelsattained from the cross validation process are graphicallyreported in Figures 3 4 and 5 respectively In these figures

the horizontal axis measures the actual compressive strengthnoted as CSA meanwhile the vertical axis measures thepredicted compressive strength (CSP) obtained from theprediction phases of eachmodelTheperformances ofmodelsin these figures can be appraised graphically with the line ofbest fit and quantitatively with 1198772 values it is noted that adata point locating closely to the line of best fit indicates anaccurate prediction outcome Based on experimental resultsthat are visually displayed in Figures 3 4 and 5 it can beconfirmed that the GPRmodel is best suited formodeling thedata set at hand

5 Conclusion

This research has investigated the capability of theGPRmodelfor the task of HPC compressive strength prediction Toconstruct and verify the machine learning model a data set


Fold 1 R2= 092 Fold 2 R2

= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Figure 4 LSSVM prediction result obtained from the 10-fold cross validation


= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

Figure 5 ANN prediction result obtained from the 10-fold cross validation

of actual HPC compressive tests has been collected for thisstudy Based on experimental results the GPR model hasachieved the most desirable performance with comparativelylow prediction errors (RMSE = 404 MAPE = 515) anda high coefficient of determination 1198772 = 090 These are

very desirable because the modeling HPC strength is widelyknown to be a highly complex task

One significant advantage of GPR over other benchmarkmethods is that the GPR can deliver estimated compressivestrength coupled with prediction interval This property is


also of great usefulness for construction engineers to reliablyassess the strength of HPC concrete mixtures Therefore theGPR model is recommended as a promising alternative toassist construction engineers in concrete mixture design

Despite the aforementioned advantages of GPR onelimitation of the study is that the employed approach is ablack-box prediction model hence this may impose certainhindrance for civil engineers to understand the model struc-ture In addition the size of the current data set should beexpanded by collecting more testing results of HPC samplesto further enhance the generalization of the predictionmodel

Therefore future extensions of this research may includeapplications of GPR for solving other predictionmodelingtasks in civil engineering investigation on the effects of novelcovariance functions on the GPR model performance anddiscovering new techniques to improve the model learningcapability On the other hand studying the potentiality ofother machine learning techniques with transparent modelstructures such as instance-based learning or regressiontrees to meliorate the model interpretation is also a worth-investigating research direction

Competing Interests

The authors (Nhat-Duc Hoang Anh-Duc Pham Quoc-LamNguyen and Quang-Nhat Pham) declare that there is noconflict of interests regarding the publication of this article

References

[1] B-I Bae H-K Choi and C-S Choi ldquoFlexural strengthevaluation of reinforced concrete members with ultra highperformance concreterdquo Advances in Materials Science andEngineering vol 2016 Article ID 2815247 10 pages 2016

[2] O Gunes S Yesilmen B Gunes and F-J Ulm ldquoUse of UHPCin bridge structuresmaterialmodeling anddesignrdquoAdvances inMaterials Science and Engineering vol 2012 Article ID 31928512 pages 2012

[3] B Ahmadi-Nedushan ldquoAn optimized instance based learningalgorithm for estimation of compressive strength of concreterdquoEngineering Applications of Artificial Intelligence vol 25 no 5pp 1073ndash1081 2012

[4] B A Omran Q Chen and R Jin ldquoComparison of datamining techniques for predicting compressive strength of envi-ronmentally friendly concreterdquo Journal of Computing in CivilEngineering 2016

[5] A Pham N Hoang and Q Nguyen ldquoPredicting compressivestrength of high-performance concrete using metaheuristic-optimized least squares support vector regressionrdquo Journalof Computing in Civil Engineering vol 30 no 3 Article ID06015002 2016

[6] C E Rasmussen and C K Williams Gaussian Processesfor Machine Learning Adaptive Computation and MachineLearning The MIT Press Cambridge Mass USA 2006

[7] J Hu and J Wang ldquoShort-term wind speed prediction usingempirical wavelet transform and Gaussian process regressionrdquoEnergy vol 93 part 2 pp 1456ndash1466 2015

[8] L Zhou J Chen and Z Song ldquoRecursive gaussian processregression model for adaptive quality monitoring in batch

processesrdquo Mathematical Problems in Engineering vol 2015Article ID 761280 9 pages 2015

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

[10] S Chithra S R R S Kumar K Chinnaraju and F AlfinAshmita ldquoA comparative study on the compressive strengthprediction models for High Performance Concrete containingnano silica and copper slag using regression analysis and Artifi-cial Neural NetworksrdquoConstruction and BuildingMaterials vol114 pp 528ndash535 2016

[11] R Gupta M A Kewalramani and A Goel ldquoPrediction of con-crete strength using neural-expert systemrdquo Journal of Materialsin Civil Engineering vol 18 no 3 pp 462ndash466 2006

[12] I-C Yeh and L-C Lien ldquoKnowledge discovery of concretematerial using Genetic Operation Treesrdquo Expert Systems withApplications vol 36 no 3 pp 5807ndash5812 2009

[13] 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

[14] M Słonski ldquoA comparison of model selection methods forcompressive strength prediction of high-performance concreteusing neural networksrdquo Computers and Structures vol 88 no21-22 pp 1248ndash1253 2010

[15] M-Y Cheng P M Firdausi and D Prayogo ldquoHigh-perform-ance concrete compressive strength prediction using GeneticWeighted Pyramid Operation Tree (GWPOT)rdquo EngineeringApplications of Artificial Intelligence vol 29 pp 104ndash113 2014

[16] M-Y Cheng J-S Chou A F V Roy and Y-W Wu ldquoHigh-performance concrete compressive strength prediction usingtime-weighted evolutionary fuzzy support vector machinesinference modelrdquo Automation in Construction vol 28 pp 106ndash115 2012

[17] L Chen and T-S Wang ldquoModeling strength of high-performance concrete using an improved grammatical evolu-tion combined with macrogenetic algorithmrdquo ASCE Journal ofComputing in Civil Engineering vol 24 no 3 pp 281ndash288 2010

[18] S M Mousavi P Aminian A H Gandomi A H Alavi andH Bolandi ldquoA new predictive model for compressive strengthof HPC using gene expression programmingrdquo Advances inEngineering Software vol 45 no 1 pp 105ndash114 2012

[19] M Castelli L Vanneschi and S Silva ldquoPrediction of highperformance concrete strength using Genetic Programmingwith geometric semantic genetic operatorsrdquoExpert SystemswithApplications vol 40 no 17 pp 6856ndash6862 2013

[20] H I Erdal O Karakurt and E Namli ldquoHigh performance con-crete compressive strength forecasting using ensemble modelsbased on discrete wavelet transformrdquo Engineering Applicationsof Artificial Intelligence vol 26 no 4 pp 1246ndash1254 2013

[21] 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

[22] M-Y Cheng C-C Huang and A F V Roy ldquoPredicting projectsuccess in construction using an evolutionary gaussian processinferencemodelrdquo Journal of Civil Engineering andManagementvol 19 supplement 1 pp S202ndashS211 2013

[23] M Pal and S Deswal ldquoModelling pile capacity using Gaussianprocess regressionrdquo Computers and Geotechnics vol 37 no 7-8pp 942ndash947 2010


[24] M Ebden ldquoGaussian processes a quick introductionrdquo httpsarxivorgabs150502965

[25] Mathworks Statistics andMachine Learning ToolboxTheMath-Works 2016

[26] M H Beale M T Hagan and H B Demuth Neural NetworkToolbox Userrsquos Guide The MathWorks 2012

[27] K De Brabanter P Karsmakers F Ojeda et al ldquoLS-SVMlabtoolbox userrsquos guide version 18rdquo Internal Report 10-146 ESAT-SISTA KU Leuven Leuven Belgium 2010

[28] 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 2016

[29] W Sun and M Liu ldquoPrediction and analysis of the three majorindustries and residential consumption CO2 emissions basedon least squares support vector machine in Chinardquo Journal ofCleaner Production vol 122 pp 144ndash153 2016

[30] M-Y Cheng N-D Hoang and Y-W Wu ldquoCash flow pre-diction for construction project using a novel adaptive time-dependent least squares support vector machine inferencemodelrdquo Journal of Civil Engineering and Management vol 21no 6 pp 679ndash688 2015

[31] MCheng andNHoang ldquoA self-adaptive fuzzy inferencemodelbased on least squares SVM for estimating compressive strengthof rubberized concreterdquo International Journal of InformationTechnology amp Decision Making vol 15 no 3 pp 603ndash619 2016

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

[33] T-H Tran and N-D Hoang ldquoPredicting colonization growthof algae on mortar surface with artificial neural networkrdquoJournal of Computing in Civil Engineering 2016

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

[35] P Zhang ldquoModel selection via multifold cross validationrdquo TheAnnals of Statistics vol 21 no 1 pp 299ndash313 1993

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



engineers Additionally this study can also be viewed asa comparative work since the performance of the GPRis benchmarked against those of other powerful nonlinearmodeling methods including the Artificial Neural Network(ANN) and the Least Squares Support Vector Machine(LSSVM) [9] Moreover a data set of 239 HPC experimentaltests recorded during the construction phase of the Nga BaHue highway overpass project in Danang City (Vietnam) hasbeen collected for this research The subsequent parts of thepaper are organized as follows Section 2 reviews pertinentresearch works in the literature In Section 3 the researchmethod is presented followed by the experimental resultsThe conclusion of this study is stated in the final section

2 Related Works

Due to the importance of the research topic HPC compres-sive strength modeling has been a very active research areaand various artificial intelligence (AI) techniques have beenapplied to tackle the problem of interest Based on previousstudies AI techniques have proved its superior capability overtraditional modeling methods ANN is the most commonmodeling method [10 11] Yeh and Lien [12] applied theGenetic Operation Trees to establish empirical formulaswhich are more accurate than the nonlinear regression butless accurate than ANNmodels Chou et al [13] compare dif-ferent data-mining techniques to identify the fittest method

Sophisticated AI based systems have also been developedto fit particular HPC data sets Słonski [14] combined theANN and the Bayesian evidence framework which helps toconstruct the ANN structure Genetic Weighted PyramidOperation Tree was developed by combining four individualGenetic Operation Trees with adaptive weights [15] themethod appears to be better than the individual tree TheK-nearest neighbor based regression was integrated withDifferential Evolution by Ahmadi-Nedushan [3] this workdemonstrated that despite being simple in certain learningcircumstances the instance-based regression method canoutperform the ANN

Cheng et al [16] proposed a fuzzy Support VectorMachine (SVM) method which can be superior over theoriginal SVM and be comparable to the ANN Pham et al[5] employ LSSVM and Firefly Algorithm to construct ahybrid model for HPC strength estimation The capability ofGenetic Programming based prediction models which fusesthe genetic algorithm and the symbolic programming wasinvestigated by Chen and Wang [17] Mousavi et al [18] andCastelli et al [19] Extensive researches on ensemble learningof Erdal et al [20] and Chou et al [21] found that this formof learning may boost the predictive capability of individualAI models As can be seen in the literature the capability ofGPR has rarely been investigated for the task of HPC strengthmodelingTherefore our study is an attempt to fill this gap inthe literature

3 Research Method

31 Data Set of HPC Experiments This research employsa data set consisting of 239 testing results of HPC concrete

specimens All the experimental tests were performed with 15cm cylindrical specimens of HPC prepared according to theVietnamese standard (TCVN 3105 1993) which is relativelysimilar to the American standard ASTM C39 The amountsof cement (Kgm3) sand (Kgm3) small coarse aggregate(Kgm3)mediumcoarse aggregate (Kgm3) water (literm3)and superplasticizer (literm3) are batch components em-ployed for expressing properties of a concrete sample It isnoted that the concrete age of each sample ismeasured in day

Statistical descriptions ofHPC test are reported in Table 1It is worth noticing that the small coarse aggregate hasdiameter ranging from 5 to 10mm the medium coarseaggregate ranges in diameter from 10 and 20mm In additionthe ratio of water-to-cement of the concrete mixes in the dataset ranges from 027 to 046 Such low water-to-cement rationecessitates the utilization of superplasticizer to enhance theconcrete workabilityTheminimum andmaximum compres-sive strength of concrete specimens are 236 and 852MParespectively

32 Gaussian Process Regression (GPR) GPRpresents a prob-abilistic nonparametric supervised learning approach forgeneralizing nonlinear and complex function mapping hid-den in data sets This approach has recently received hugeattention of researchers in various study disciplines [4 22]GPR is very efficient to handle nonlinear data due to the useof kernel functions Furthermore a significant advantage ofGPR is that the model can provide a reliability response to aninput data [23]

Given a training set119863 = (119909119894 119910119894) | 119894 = 1 119899 the inputdata 119883 isin 119877119863times119899 is called the design matrix and 119910 isin 119877119899 is thevector of desired outputThemain assumption of GPR is thatthe output 119910 is computed as [6 24]

119910 = 119891 (119909) + 120576 (1)

where 120576 sim 119873(0 1205902119899) isin 119877 represents a homoscedastic noise forall sample 119909119894

In GPR methodology the 119899 observations in the data setof interest 119910 = 1199101 119910119899 are considered as a single pointsampled from a multivariate Gaussian distribution More-over it can be assumed that this Gaussian distribution hasthe mean of zeros The covariance function 119896(119909 1199091015840) dictatesthe relation of one observation to another observation Thesquared exponential covariance function is often selected inGPR for the task of function approximation [22 24]

119896 (119909 1199091015840) = 1205902119891 times exp(minus(119909 minus 1199091015840)221198972 ) + 1205902119899120575 (119909 1199091015840) (2)

where the maximum allowable covariance is defined as 1205902119891It is noted that 119896(119909 1199091015840) reaches this maximum allowablecovariance only when 119909 is very closed to 1199091015840 and therefore119891(119909) is almost perfectly correlated with 119891(1199091015840) Meanwhile119897 denotes the length parameter of the kernel function Inaddition 120575(119909 1199091015840) represents a Kronecker delta function 120575119894119895 =1 if 119894 = 119895 and 120575119894119895 = 0 if 119894 = 119895





119870 =[[[[[[[[[


]]]]]]]]]


(3)












ParSet = 0001 0005 001 005 01 05 15 10 50 100 500 1000 (7)








35

40

45

50

55

60

65

70

75

80

Pred

icte

d co

mpr

essiv

e stre

ngth

(MPa

)


Line of fit R2= 09







2030405060708090

100110

Com

pres

sive s

treng

th (M

Pa)






40 60 80

Fold 1 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 2 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 3 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 4 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 5 R2= 089

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 6 R2= 094

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Fold 7 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 8 R2= 076

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

Fold 9 R2= 086

CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 10 R2= 092

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)




GPRRMSE 406 129 404 047MAPE 502 186 514 0891198772 090 007 090 005

LSSVMRMSE 446 058 463 062MAPE 567 092 594 086R2 089 002 087 005

ANNRMSE 507 087 521 185MAPE 656 123 634 2321198772 085 014 081 015





5 Conclusion




= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)



= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)









Competing Interests


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













119870 =[[[[[[[[[


]]]]]]]]]


(3)












ParSet = 0001 0005 001 005 01 05 15 10 50 100 500 1000 (7)








35

40

45

50

55

60

65

70

75

80

Pred

icte

d co

mpr

essiv

e stre

ngth

(MPa

)


Line of fit R2= 09







2030405060708090

100110

Com

pres

sive s

treng

th (M

Pa)






40 60 80

Fold 1 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 2 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 3 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 4 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 5 R2= 089

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 6 R2= 094

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Fold 7 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 8 R2= 076

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

Fold 9 R2= 086

CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 10 R2= 092

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)




GPRRMSE 406 129 404 047MAPE 502 186 514 0891198772 090 007 090 005

LSSVMRMSE 446 058 463 062MAPE 567 092 594 086R2 089 002 087 005

ANNRMSE 507 087 521 185MAPE 656 123 634 2321198772 085 014 081 015





5 Conclusion




= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)



= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)









Competing Interests


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














35

40

45

50

55

60

65

70

75

80

Pred

icte

d co

mpr

essiv

e stre

ngth

(MPa

)


Line of fit R2= 09







2030405060708090

100110

Com

pres

sive s

treng

th (M

Pa)






40 60 80

Fold 1 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 2 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 3 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 4 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 5 R2= 089

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 6 R2= 094

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Fold 7 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 8 R2= 076

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

Fold 9 R2= 086

CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 10 R2= 092

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)




GPRRMSE 406 129 404 047MAPE 502 186 514 0891198772 090 007 090 005

LSSVMRMSE 446 058 463 062MAPE 567 092 594 086R2 089 002 087 005

ANNRMSE 507 087 521 185MAPE 656 123 634 2321198772 085 014 081 015





5 Conclusion




= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)



= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)









Competing Interests


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










40 60 80

Fold 1 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 2 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 3 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 4 R2= 09

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

Fold 5 R2= 089

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 6 R2= 094

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)

Fold 7 R2= 093

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 8 R2= 076

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

Fold 9 R2= 086

CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

Fold 10 R2= 092

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)




GPRRMSE 406 129 404 047MAPE 502 186 514 0891198772 090 007 090 005

LSSVMRMSE 446 058 463 062MAPE 567 092 594 086R2 089 002 087 005

ANNRMSE 507 087 521 185MAPE 656 123 634 2321198772 085 014 081 015





5 Conclusion




= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)



= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)









Competing Interests


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











= 091 Fold 3 R2= 093 Fold 4 R2

= 086 Fold 5 R2= 083


= 089 Fold 8 R2= 076 Fold 9 R2

= 082 Fold 10 R2= 086

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 7050CSA (MPa)

50

55

60

65

70

75

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)

50

60

70

80

CSP

(MPa

)



= 092 Fold 3 R2= 091 Fold 4 R2

= 066 Fold 5 R2= 081


= 085Fold 8 R2

= 088 Fold 9 R2= 091 Fold 10 R2

= 096

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

30

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

60

80

CSP

(MPa

)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

6040CSA (MPa)

40

50

60

70

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

60 8040CSA (MPa)

40

50

60

70

80

CSP

(MPa

)

50

60

70

80

CSP

(MPa

)

8060CSA (MPa)









Competing Interests


References








































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation













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 Compressive Strength of High...

Documents

Transcript of Research Article Estimating Compressive Strength of High...