Automation in Construction 48 (2014) 88–96

Contents lists available at ScienceDirect

Automation in Construction

j ourna l homepage: www.e lsev ie r .com/ locate /autcon

Hybrid computationalmodel for predicting bridge scour depth near piersand abutments

Jui-Sheng Chou a,⁎, Anh-Duc Pham a,b

a Department of Civil and Construction Engineering, National Taiwan University of Science and Technology, 43, Sec. 4, Keelung Rd., Taipei, Taiwanb Faculty of Project Management, Danang University of Science and Technology, Danang City, Vietnam

⁎ Corresponding author. Tel.: +886 2 2737 6321; fax: +E-mail addresses: jschou@mail.ntust.edu.tw (J.-S. Chou

D9905806@mail.ntust.edu.tw, paduc@dut.udn.vn (A.-D. P

http://dx.doi.org/10.1016/j.autcon.2014.08.0060926-5805/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 28 August 2013Received in revised form 26 July 2014Accepted 20 August 2014Available online xxxx

Keywords:Bridge foundationScour depthSupport vector regressionGenetic algorithmData miningOptimizationArtificial intelligence

Efficient bridge design and maintenance requires a clear understanding of channel bottom scouring near piersand abutment foundations. Bridge scour, a dynamic phenomenon that varies according to numerous factors(e.g., water depth, flow angle and strength, pier and abutment shape and width, material properties of the sed-iment), is a major cause of bridge failure and is critical to the total construction and maintenance costs of bridgebuilding. Accurately estimating the equilibrium depths of local scouring near piers and abutments is vital forbridge design andmanagement. Therefore, an efficient technique that can be used to enhance the estimation ca-pability, safety, and cost reduction when designing and managing bridge projects is required. This study investi-gated the potential use of genetic algorithm (GA)-based support vector regression (SVR)model to predict bridgescour depth near piers and abutments. An SVR model developed by using MATLAB® was optimized using a GA,maximizing generalization performance. Data collected from the literature were used to evaluate the bridgescour depth prediction accuracy of the hybrid model. To demonstrate the capability of the computationalmodel, the GA–SVR modeling results were compared with those obtained using numeric predictive models(i.e., classification and regression tree, chi-squared automatic interaction detector, multiple regression, artificialneural network, and ensemble models) and empirical methods. The proposed hybrid model achieved errorrates that were 81.3% to 96.4% more accurate than those obtained using other methods. The GA–SVR model ef-fectively outperformed existing methods and can be used by civil engineers to efficiently design safer andmore cost-effective bridge substructures.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Bridges are vital structures within a transportation system, con-necting people to economic activities. However, a major problem en-countered when designing bridge structures is estimating scour depthnear piers and abutments. Flow patterns and local scour mechanismsnear piers and abutments are complex phenomena resulting fromsediment removal near the structures by the flow of water. Thus, bridgescour is an outcome of flow energy, sediment-transportation, andbridge substructure characteristics.

Local scour is the removal of bed material near piers, abutments,spurs, and embankments. Because of these factors, developing a meth-odology to predict bridge scour depth is problematic. Bridge failureresulting from severe scouring near bridge piers and abutments is com-mon (Fig. 1). Therefore, estimating a reasonably accurate scour depth is

886 2 2737 6606.),ham).

crucial for appropriately planning, designing, and managing hydraulicstructures.

Shirhole and Holt reported that more than 1000 bridges have col-lapsed over the past 30 years; approximately 60% of the collapses re-sulted from scouring near foundations [33]. Scouring affects the designof pile foundations, because it reduces the friction length of the pilesand increases the risk of pile buckling [12,34]. Thus, scour depth is acritical parameter that must be considered to determine the mini-mum foundation depth when designing a bridge structure. Accu-rately predicting scour depth near piers and abutments is essential forsafe and cost-effective bridge structures, because underestimation maycause bridge failure and overestimation unnecessarily increases con-struction costs.

Moreover, predicting bridge scour depth using available informationduring themaintenance stage is vital for preventing catastrophic bridgefailure that can result in loss of life. Although most prediction formulasused to determine scour depth available in the literature have been de-veloped using conventional regression methods [11,28], these predic-tion formulas do not obtain accurate regression equations. Therefore,to enhance estimation capability, artificial intelligence (AI)-based ap-proaches have been used to develop algorithms that improve modelingaccuracy and speed [5,35]. AI-basedmodels and their hybrid forms [2,6,

Original riverbed

Sediment

Scour hole

near pier

Scour hole

near abutment

Fig. 1. Bridge scour near piers and abutments.

Table 1Empirical methods used to predict scour depth.

Author Empirical model

Melville and Chiew (1999)(scour depth near piers)

ds = KYD Kl Kd (4)where KYD, Kl, and Kd are the flow depth-pierwidth, flow intensity, and sediment sizecoefficients, respectively.

Dey and Barbhuiya (2005)(scour depth near abutments)

ds ¼ 8:689F0:129e h0:103el−0:296

(5)where Fe is the abutment Froude number,

h ¼ h=l,el ¼ l=d50

89J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

9,32,38,39] can potentially be employed to solve civil engineering andmanagement problems.

In this study, a hybrid computational model, genetic algorithm-based support vector regression (GA–SVR), was developed, exploitingthe GA to optimize the internal parameters of SVR and predict scourdepth near bridge piers and abutments. Experimental data collectedfrom laboratory tests and published studies [24,28,29] were used toevaluate the forecasting performance of the proposed hybrid model.

To demonstrate the modeling efficacy, the proposed hybrid algo-rithm was developed using MATLAB® and compared with baselinemodels, such as the classification and regression tree (CART), the chi-squared automatic interaction detector (CHAID), multiple linear regres-sion (MLR), the artificial neural network (ANN), and an ensemblemodel, designed using the IBM SPSS Modeler® and other empiricalmethods described in the literature [11,28]. Performance measures forthe proposed, baseline, and previous models were evaluated by testingthe hypotheses. The last sections in this paper discuss the analytical re-sults and present a conclusion.

2. Literature review

In recent decades, researchers have determined that bridge scour isrelated to numerous factors, including channel geometry, dynamicproperties of hydraulic flow, and the geometry of bridge piers and abut-ment. Predicting bridge scour depth by using available data is essentialfor improving the efficiency of bridge design. The following sectionsreview available empirical methods and AI applications related toscour depth near piers and semicircular abutments.

2.1. Empirical equations used to calculate scour depth

Variables affecting scour depth (ds) near bridge piers include fluidand bed sediment characterization, flow, and pier conditions. Whenthe quantities of incoming sediment equal the quantities of outgoingsediment, dynamic equilibrium occurs and is called equilibrium scourdepth [28]. The relationship between equilibrium scour depth nearpiers and the decision variables [24,28,29] is expressed in Eq. (1):

ds ¼ f μ;V ;VC ; h; g;ρ;D;d50ð Þ ð1Þ

where d50 is the grain size, h is the approach flow depth, g is the gravi-tational acceleration, D is the pier diameter, V is the average velocityof the approach flow, VC is the critical velocity, μ is the dynamic viscosityof fluid, and ρ is the fluid density.

Similarly, the equilibrium depth of local scour near an abutment canbe expressed as

ds ¼ f V ;ρ;ρs; g; l; v; h;d50ð Þ ð2Þ

where ρs is the sediment mass density, l is the abutment length, v is thekinematic viscosity, and ds is the equilibrium scour depth near thesemicircular abutment.

Because ρ, ρs, g, and v are constant for a given sediment and fluid,the relationship between ds and the independent variable [11] can beexpressed as

ds ¼ f V ; l; h; d50ð Þ: ð3Þ

To analyze scour near semicircular abutments, experiments wereperformed in a flume (20 m long, 0.9 m wide, and 0.7 m deep) usinguniform sediments as described by Dey and Barbhuiya [11] and accord-ing to clear water conditions. Table 1 shows the empirical methods [11,28] used to estimate scour depth.

2.2. Artificial intelligence applications

In addition to the aforementioned empirical methods, data mining(DM) and AI-based approaches use computer system programs tosolve problems by emulating human brain processes. The main objec-tive of DM is achieved by combining technological methods fromvarious fields, including computer science, statistics, online analyticalprocessing, information retrieval, machine learning, and expert systems[25]. DM technology is currently employed to predict behavior in nu-merous areas. Therefore, using AI-based and hybrid models can poten-tially solve civil engineering problems [7,19].

GAs, stochastic search algorithms inspired by the mechanics of nat-ural evolution, which include survival of the fittest, reproduction, cross-over, and mutation [14], can be used to effectively solve numerouscomplex optimization problems and are superior to conventional opti-mization methods. In addition, GAs have been increasingly combinedwith other AI techniques [18,23,26]. For example, Feng et al. presenteda hybrid model that integrated the finite element method and GAs toestimate the scour depth near bridge piers [13].

A recently developed AI technique, the support vector machine(SVM), is an alternative tool that can be employed to efficiently model

90 J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

hydrologic processes, such as real time flood stage forecasting [37], lakewater level prediction [21], sediment transport prediction, scour depthprediction near bridge piers [1], and modeling of pier scour using fielddata [31]. Similarly, Hong et al. proposed a method for estimatingtime-dependent scour depth near bridge piers using support vector re-gression (SVR) [16], and determined that the prediction accuracy of theSVR model was superior to that of the ANN model.

However, SVR has several inherent shortcomings. When using SVR,appropriate parameter settings are required to improve regression ac-curacy. In general, identifying the optimal parameters within an SVRmodel is an optimization problem. The mechanism used for determin-ing tuning parameters in AI models is a critical problem that has beenrecognized widely by scholars in various disciplines [5,8,10,18]. SVRparameters that must be optimized include the penalty parameter, thekernel function parameter, and the kernel function.

Therefore, to improve prediction accuracy, the GA [14] is an efficienttechnique for use to avoid the shortcomings of SVR [26,27]. In additionto fulfilling modeling requirements, such a model must also be suffi-ciently robust and must be easily manipulated. However, no studieshave proposed an effective hybrid GA–SVR model that can be used toenhance accuracy when predicting scour depth near bridge piers andabutments. Based on the findings from previous studies [11,24,28,29],two datasets were used in this study to examine the efficacy of the pro-posed hybrid model when predicting the equilibrium scour depth nearpiers and abutments.

3. Data mining methodology and the hybrid computational model

In this study, four data mining techniques, CART, CHAID, MLR, andANN, were used to automatically create baselinemodels. Default valueswere set in numerical predictor nodes using the IBM SPSSModeler®. Anefficient hybrid approach was developed by integrating GA and SVR inMATLAB® to predict scour depth near piers and abutments. The follow-ing sections describe the methodologies and the GA–SVR algorithm.

3.1. Classification and regression trees

The CART is a decision tree method for constructing a classificationor regression tree according to its dependent variable type, which canbe categorical or numerical [4]. The same predictor field can be usedrepeatedly at various tree levels. Surrogate splitting optimizes the useof data with missing values. A CART is adequately flexible to considermisclassification costs as the tree grows and to specify the prior proba-bility distribution in a classification problem. The logic rules used indecision tree methods are superior to those used in other modelingtechniques [33].

Depending on the target field, three impurity measures can beemployed to locate splits within CARTmodels. For example, Gini is typ-ically used for symbolic target fields, whereas the least-squared devia-tion method is applied to automatically select continuous targetswithout explaining the selections. The Gini index g(t) at node t of aCART can be expressed as

g tð Þ ¼Xj≠i

p jjtð Þp ijtð Þ ð6Þ

where i and j are the target field categories.

p jjtð Þ ¼ p j; tð Þp tð Þ ; p jtð Þ ¼ π jð ÞNj tð Þ

N j; andp tð Þ ¼

Xj

p j; tð Þ ð7Þ

where π(j) is the prior probability value for category j, Nj(t) is the num-ber of records in category j of node t, and Nj is the number of records incategory j of the root node. When the Gini index is used to determinethe improvement after a split during tree growth, only the records in

node t and the root node with valid values for the split predictor areused to compute Nj(t) and Nj, respectively.

3.2. Chi-squared automatic interaction detector

Kass developed the CHAID decision tree technique to classifydatasets [20]. The recursive partitioning method in this algorithm,used widely within various domains, tests for independence by usinga chi-square test to assess whether splitting a node significantlyimproves purity. Specifically, for each node, the predictor that has thestrongest association (according to its p value) with the response vari-able is used as a split node. If the tested predictor exhibits statisticallynonsignificant improvement, no split is performed, and the algorithmceases.

The exhaustive CHAID, which classifies the target field, was devel-oped to address the limitations of the CHAID technique [3]. However,the exhaustive CHAID might not optimize the split for a predictor vari-able because categories cease merging when all remaining categoriessignificantly differ. The exhaustive CHAID avoids overfitting the full-grown tree to the training data by continuously merging predictor cat-egories until only two super categories remain. It then identifies thepredictor in the series of merges and computes an adjusted p value forthe set of categories that are most strongly associated with the targetvariable. The exhaustive CHAID determines which predictor to splitbased on the adjusted p values, and then ascertains the optimal splitto use for each predictor [33].

3.3. Multiple linear regression

The multiple linear regression (MLR) model, which is an extensionof the simple regression model, determines the relationship betweentwo or more variables [30]. The most attractive feature of this model isits simplicity. The general formula for the MLR model is

Y ¼ βo þXni¼1

βiXi þ ε ð8Þ

where Y is a concrete compressive strength, βo is a constant, βi is a re-gression coefficient (i = 1, 2,…, n), ε is an error term, and the Xi valuesrepresent predictor attributes. The MLR model involves four MLRmethods using ordinary least squares: enter, stepwise, forward, andbackward.

3.4. Artificial neural networks

The ANN model is a powerful tool used to solve highly complexproblems. Essentially, the processing elements in an NN resemble neu-rons in the human brain, containing numerous simple computationalelements arranged in layers. In a multilayer perception (MLP) NN, theinput layer contains a set of sensory input nodes that represent bridgescour components, one or more hidden layers containing computationnodes, and an output layer containing a computation node that repre-sents bridge scour depth. Similar to any intelligence model, ANNshave learning capability.

The most widely applied and effective learning algorithm used fortraining anMLPneural network is the back-propagation (BP) algorithm.Activation of each neuron in a hidden output layer is expressed as

netk ¼X

wkjoj and yk ¼ f netkð Þ ð9Þ

where netk is the activation of the kth neuron, j is the set of neurons inthe preceding layer,wkj is theweight of the connection between neuron

91J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

k and neuron j, oj is the output of neuron j, and yk is the sigmoid orlogistic transfer function

f netkð Þ ¼ 11þ e−net : ð10Þ

The formula for training and updating weight wkj in each cycle t is

wkj tð Þ ¼ wkj t−1ð Þ þ Δwkj tð Þ: ð11Þ

The change value Δwkj(t) is calculated as

Δwkj tð Þ ¼ ηδpjopj þ αΔwkj t−1ð Þ ð12Þ

where η is the learning rate parameter, δpj is the propagation error, opj isthe output of neuron j for record p, α is the momentum parameter, andΔwkj(t− 1) is the change in wkj during the previous cycle.

BP networks learn by storing nonlinear information between influ-ential factors and the strength of influences. During training, connectionweights are adjusted to match predictions for target values in specificrecords, and the outcomes generated by the network improve as thenetwork learns [33].

3.5. Ensemble model

In the ensemble approach, a set of the aforementioned models isranked according to performance and the optimal performance modelsare combined into an ensemble model. The ensemble approach can beexpressedmathematically as g :ℝd→ℝwith a d-dimensional predictorvariable X and a one-dimensional response Y. In each procedure, aspecified algorithm is employed to derive an estimated function g(·).Estimation using an ensemble-based function gen(·) can be obtainedby linearly combining individual functions as follows:

gen �ð Þ ¼XNj¼1

c j � g �ð Þ ð13Þ

where cj is the linear combination coefficients that are based on averagevalues of various weights.

3.6. Hybrid computational model

Vapnik first introduced SVMs in 2005 [36]. This supervised learningmethod generates SVMs by mapping input–output functions derivedfrom a labeled training dataset. This function can be used to solve bothclassification and regression problems. Typically, the regression modeluses SVR with a quadratic loss function, which corresponds to the con-ventional least squares error criterion, a variation of an SVM for functionestimation to alleviate the burden of computational cost [15]. In thisstudy, the SVR model was used to construct the bridge scour depthinput–output model.

To estimate an SVR function, given a training data set {xk, yk}k= 1N , the

optimization problem is expressed as

minω;b;e

J ω; eð Þ ¼ 12

ωk k2 þ 12γXNk¼1

e2k ; subject to yk

¼ ω;φ xkð Þh i þ bþ ek; k ¼ 1;…N ð14Þ

where ek ∈ R are error variables and γ ≥ 0 is a regulation constant.The resulting SVR model used to estimate functions is expressed as

f xð Þ ¼XNk¼1

αkK x; xkð Þ þ b ð15Þ

where αk and b are the Lagrange multipliers and the bias term,respectively.

Although the SVR can be effectively applied to solve prediction prob-lems, it has notable drawbacks. The accuracy of the SVRmodel dependson the SVR architecture. The kernel function in the SVR is used as aradial basis function (RBF) kernel (i.e.,K(x, xk) = exp(−‖x − xk‖

2/2σ2)) because it can analyze highly dimensional data and requiresonly two parameters [15,17]. To enhance prediction accuracy, parame-ter optimization in the SVR should include the regularization parameter(γ) and the sigma (σ) of the RBF kernel.

To automate the optimization process, the GA was employed to en-able simultaneous optimization of SVR parameters. The SVMs aremain-ly used to address learning and curve fitting, whereas the GA is appliedto optimize parameters σ and γ, minimizing the prediction error. TheGA functionswere implemented usingGAOPTIMSET andGA in the glob-al optimization toolbox that is included in the MATLAB® commercialsoftware. The proposed algorithm (Appendix A) was coded usingMATLAB® R2012a on a Pentium CORE 2 Quad that had 2 GB of RAMand operated on Window 7. The fitness function of the GA was asfollows:

f ¼ RMSETraining−data þ RMSETest−data þMin sv ð16Þ

where RMSE represents root mean squared error, and Min_sv is theminimal number of support vectors.

Fig. 2 depicts the structure of the hybrid AI model, in which the SVRcalls the GA as a subroutine to optimize its structure parameters. Thismodel was designed to use the fittest SVR shapes with the minimalnumber of support vectors (Min_sv) and optimal SVR parameters, en-suring acceptable estimation when solving optimization problems.Historical data were classified as training data and test data. The testdata were used to evaluate the performance of the trained SVR modelafter the SVR model was optimized.

4. Experimental setting

In this study, a hybrid method featuring a GA-based approach wasemployed to optimize the SVR structure parameters and increase accu-racy when predicting bridge scour depth near piers and abutments. Re-searchers frequently apply the k-fold cross-validation algorithm tominimize bias associated with the random sampling of the trainingand holdout data samples. Kohavi indicated that 10 folds are optimalfor acceptable generalization capability [22]. In each round, one foldwas used to test the performance of the prediction models, and theremaining nine folds were used for training. The testing fold was thenused to evaluate the model of each approach. The procedure wasrepeatedly performed using various folds as the testing fold until allfolds were tested (Fig. 3).

The complete dataset used to investigate scour near piers, containing151 samples [24,28,29],was divided into twoparts, using a 10-fold crossvalidation algorithm: a training dataset containing 136 samples anda testing dataset containing the remaining data (15 samples). Thecomplete dataset used to determine scour near abutments, which com-prised 99 samples [11], was divided into a training dataset (89 samples)and testing dataset (10 samples). Table 2 summarizes the statistical pa-rameters. The response was the scour depth (ds) and the predictor var-iables were the remaining attributes.

To establish a baseline for validation, modeling parameters were setto the default values when various DM techniques were compared(Table 3), ensuring that themodels were constructed to facilitate objec-tive, simple, and efficient use and accuracy.

Fig. 4 illustrates themodeling stream obtained from the experimen-tal data. Analyses were performed using a cross-validation algorithm. Ineach experimentalmodel, one fold of the original datasetwas employedto identify and evaluate the optimal model of each DM method.The training dataset (remaining folds) was applied to train the modelsin each DM method. The ensemble models were constructed by

Initialization

GA operation:SelectionCrossoverMutation

Stopping criteria

Y

N

MATLAB

Evaluate fitness values

Train SVR model with (σ, γ)

Build optimal SVR model

Initial parameter (σ, γ)

SVR modelGA

optimization

Historical data

Ten-fold cross-validation

The results of bridge scour depth prediction

Cross-fold

Cross-fold

Fig. 2. Flow chart of SVR optimized using GA.

92 J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

combining the optimal individual predictive models with the outputensemble scores.

In the GA–SVR model, the input and output variables were normal-ized within the range from 0 to 1, using Eq. (17).

xN ¼ x−xminð Þxmax−xmin

ð17Þ

where xN is the normalization value of x, xmax is the maximal value, andxmin is the minimal value of each variable from the original data.This normalization step is essential for training the SVR model and

improving performance. Table 4 lists the performance measures forthe proposed model during the training and testing stages.

5. Analysis and results

To verify the applicability and efficiency of the proposed hybridmodel in predicting bridge scour depth near piers and abutments, theperformance of the model was compared with the results obtainedfrom individual models (i.e., CART, CHAID, MLR, and ANN), ensemblemodels, and empirical methods. Laboratory data reported in the litera-ture [24,28,29] were used for comparisons. Unlike in previous studies,k-fold cross validation was employed to ensure efficient generalization

Fig. 3. Ten-fold cross-validation method.

Table 3Default model parameter settings.

Model Parameter Setting

CART Level below root 5Mode SimpleMaximum surrogates 5Minimum change in impurity 0.0001Impurity measure for categorical targets GiniMinimum records in parent branch (%) 2Minimum records in child branch (%) 1

93J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

capability. The performance of the proposed prediction modelwas validated in terms of the linear correlation coefficient (R), RMSE,and the mean average percentage error (MAPE). A high R value andlow RMSE and MAPE values indicated efficient model performance.Among the four individual models built to predict scour depth, CART,CHAID, and ANN showed the optimal performance. The most efficienttest models were then combined to develop an ensemble model.

Table 5 shows the performance results obtained by the GA–SVR andother predictive approaches. A comparison confirmed that the GA–SVRmodel was superior. Regarding scour near abutment, the average RMSEvalues derived by CART (15.09), CHAID (16.34), MLR (19.45), ANN(16.34), and the CART + CHAID + ANN ensemble model (10.05)

Table 2Statistical parameters applied for each scour dataset.

Parameter Unit Min Average Max Variable

Pier dataPier diameter (D) mm 16.00 84.20 16.00 InputGrain diameter mean (d50) mm 0.26 1.52 7.80 InputApproach flow depth (h) mm 20.00 256.27 600.00 InputFlow velocity (V) m/s 0.17 0.56 1.29 InputCritical velocity (VC) m/s 0.30 0.48 1.27 InputEquilibrium pier scour (ds) mm 4.00 132.52 615.38 Output

Abutment dataFlow velocity (U) m/s 0.22 0.35 0.67 InputAbutment length (l) mm 40.00 81.52 130.00 InputApproach flow depth (h) mm 50.00 163.89 250.00 InputGrain diameter mean (d50) mm 0.26 0.93 3.10 InputEquilibrium abutment scour (ds) mm 55.00 125.31 280.00 Output

CHAID Mode SimpleAlpha for splitting 0.05Alpha for Merging 0.05Chi-square method PearsonMinimum records in parent branch (%) 2Minimum records in child branch (%) 1Epsilon for convergence 0.001Maximum iterations for convergence 100Allow splitting of merged categories FalseUse Bonferroni adjustment True

MR Singularity tolerance 1.0E−4Probability entry 0.05Probability removal 0.1F value entry 3.84F value removal 2.71

ANNs Alpha 0.9Initial eta 0.3High eta 0.1Low eta 0.01Eta decay 30Hidden layers Three (20,15,10)Persistence 200

Fig. 4. Individual and ensemble modeling streams.

Table 5Comparison of predicted and observed scour depths according to training and testing sets.

Models Training data Testing data

94 J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

were worse than that obtained by the GA–SVR (1.53) from the testingset. In both datasets, the GA–SVR had aMAPE that was below 5%.More-over, the average correlation coefficients obtained by GA–SVR from thetesting sets exceeded 99.9%, indicating that the hybridmodels fit closelywith the experimental data. Figs. 5 and 6 compare the predicted valuesand the values obtained by the GA–SVR model for scour depths nearpiers and abutments, respectively.

To ensure accurate and reliable evaluation, the GA–SVR model wascompared with empirical methods reported in previous studies [11,

Table 4Performance measures.

Performance measure Equation

Linear correlation coefficient (R)R ¼ n∑y:y0− ∑yð Þ ∑y0ð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

n ∑y2� �

− ∑y� �2

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffin ∑y02� �

− ∑y0� �2q

(18)Mean absolute percentage error(MAPE) MAPE ¼ 1

n∑n

i¼1

y−y0y

���� ���� (19)Root mean squared error (RMSE)

RMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n∑

n

i¼1y0−yð Þ2

s(20)

Note: y ′ is the predicted value; y is the actual value; and n is the number of data samples.

28]. Eqs. (4) and (5) were used to estimate scour depth. Melville andChiew [28] and Dey and Barbhuiya [11] obtained R values of 92.76%and 96.34%, respectively. The values for R, RMSE, and MAPE obtainedusing theGA–SVRmodelwere better than those obtained using existingformulae (Table 6).

R (%) RMSE (mm) MAPE (%) R (%) RMSE (mm) MAPE (%)

Scour near pierCART 94.75 27.12 15.33 93.00 42.02 29.68CHAID 88.02 39.82 27.85 95.79 43.28 39.79MR 86.61 42.14 47.83 92.85 42.89 50.44ANN 85.45 44.45 57.14 94.04 44.52 58.53Ensemble 92.66 32.48 30.06 89.21 37.99 38.97GA–SVR 97.75 18.21 5.27 99.91 7.10 4.66

Scour near abutmentCART 99.19 6.74 4.23 86.00 15.09 10.60CHAID 98.62 8.77 3.91 85.52 16.34 10.49MR 94.56 17.28 12.36 85.60 19.45 13.53ANN 95.59 15.66 9.92 84.86 16.34 10.30Ensemble 99.27 6.65 4.15 97.87 10.05 6.35GA–SVR 99.98 1.37 0.76 99.99 1.53 0.74

Training phase Test phase

Fig. 5. Actual and predicted scour depths near piers obtained by GA–SVR in training and testing stages for the best testing fold.

Training phase Test phase

Fig. 6. Actual and predicted scour depth near abutments obtained by GA–SVR in training and testing stages for the optimal testing fold.

95J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

Furthermore, the consistency and reliability of GA–SVR modelingperformance were evaluated by comparing the tested hypothesis re-sults derived by the empirical methods, the ensemble model, and themost efficient individual models (Tables 6). For example, according tonull hypothesis H0, the prediction accuracy of the GA–SVR model (μ)was less than or equal to that of the optimal individualmodel or ensem-ble model or empirical method (μo) in the R test case. The rejection re-gion must be in the form of {μ ≤ μ0}, such that P = (μ ≤ μ0|H0) = αreaches the desired significance level in the test. In other test cases(RMSE andMAPE), the null hypothesis indicated that themean averageerror (μ) in the GA–SVR model equals or exceeds that in the optimal

Table 6Tested hypothesis results of improvement rates obtained by GA–SVR model.

Optimal individual model andempirical methods

Performance measure % improved by GA–SVR

R RMSE MAPE R RMSE MAPE

(%) (mm) (%)

Scour near pierMelville and Chiew (1999) 92.76 167.5 51.45 7.7*** 95.8*** 90.9***CART 93.00 42.02 29.68 7.4*** 83.1*** 84.3***Ensemble 89.21 37.99 38.97 12.0*** 81.3*** 88.0***GA–SVR 99.91 7.10 4.66 – – –

Scour near abutmentDey and Barbhuiya (2005) 96.34 24.40 20.70 3.8*** 93.7*** 96.4***CART 86.00 15.09 10.60 16.3*** 89.9*** 93.0***Ensemble 97.87 10.05 6.35 2.2*** 84.8*** 88.4***GA–SVR 99.99 1.53 0.74 – – –

Note: The improvement and hypothesis tests were calculated using average performancemeasures.*** indicates significance level exceeding 1%.

individual model/ensemble model/empirical method (μo); the alterna-tive hypothesis was the rejection of H0.

Table 6 indicates that for predicting scour depth, the improved errorrate obtained by the proposedmodel was 81.3% to 96.4% better than theimproved error rates obtained by other prediction models. All testsyielded statistically significant results at 1% of the α level according totheir p values, thereby rejecting the null hypothesis (i.e., modeling per-formance of the GA–SVR model equaled or exceeded the results of theoptimal individual model/ensemble model/empirical method). Thus,the hypothesis tests confirmed that the performance measures for theproposed hybrid model were superior for all experimental datasets;in other words, the accurate and reliable prediction of bridge scourdepth was superior to those of other predictive methods.

6. Conclusion

In this study, a hybrid computational model was developed usingGA-based SVR to predict bridge scour near piers and abutments in anequilibrium state. A cross-fold validation algorithm was used to ensureoptimal generalization capability. To predict the equilibrium scourdepth, the SVR parameters were optimized. The results from thetraining and testing stages indicated that the GA–SVRmodelmore accu-rately predicted scour depth near piers and abutments than did othermethods.

The results of this study indicated that using a hybrid approach im-plemented in theMATLAB environment to predict scour depth in bridgedesign and maintenance projects is efficient. Compared with conven-tional DM models and empirical methods, the hybrid GA–SVR modelprovided error rates that were 81.3% to 96.4% more accurate than thoseobtained by other models when predicting scour depth. Therefore, civil

96 J.-S. Chou, A.-D. Pham / Automation in Construction 48 (2014) 88–96

engineers can use the proposed model to obtain fast and reliable solu-tions when designing safe, economical, and technically sound bridgesubstructures.

The present study has several implications for the constructionphase of bridge projects. The proposed hybrid computational modelcan be used as an alternative tool to verify the scour loss of riverbedsor sea beds caused by flow change. In addition to conventional fluiddynamics methods, AI techniques can be integrated into an automaticsystem to compute scour depth without overburdening the construc-tion management personnel. When bridge construction is completed,an in situ scour monitoring system can be installed to collect real-timedata that can be used to update a developed dynamic scour depth pre-diction model.

Future research is required to investigate the effectiveness of theGA–SVR and other advanced intelligence models when predictingbridge scour depth based on field data and estimating time-dependentscour depth. Additionally, further studies can consider the effect ofpier and abutment scour on the length of piles in the bridge foundations.

Appendix A. The pseudocodes for the GA–SVR model

1. Initialization stageNormalize the datasetSubdivide the data into k subsets as training data, and test dataInitialize search parameterSet the number of initial population, number of generations in each stage,boundary of optimized parameters, rate of crossover, and rate of mutation

2. Perform k folds such that for each fold2.1 Optimization stage using GA optimization toolbox

Genetic operations: perform genetic operation as selection, crossover, andmutation, and form a new population

2.2 SVR functionSet the kernel (rbf) and loss-function (quadratic) parametersTrain model using (σ, γ)Evaluate the fitness function

2.3 Stop condition: stopping criteria are fulfilled3. Choose optimal parameters

Calculate the average accuracy among the k folds4. Plot stage

Use the optimal parameters to create a hybrid model

References

[1] H. Azamathulla, A. Ghani, N. Zakaria, A. Guven, Genetic Programming to PredictBridge Pier Scour, J. Hydraul. Eng. 136 (3) (2010) 165–169.

[2] H.M. Azamathulla, Gene expression programming for prediction of scour depthdownstream of sills, J. Hydrol. 460–461 (2012) 156–159.

[3] D. Biggs, B. De Ville, E. Suen, A method of choosing multiway partitions for classifi-cation and decision trees, J. Appl. Stat. 18 (1) (1991) 49–62.

[4] L. Breiman, J. Friedman, R. Olshen, C. Stone, Classification and Regression Trees,Chapman & Hall/CRC, New York, 1984.

[5] J.-S. Chou, M.-Y. Cheng, Y.-W. Wu, Improving classification accuracy of project dis-pute resolution using hybrid artificial intelligence and support vector machinemodels, Expert Syst. Appl. 40 (6) (2013) 2263–2274.

[6] J.-S. Chou, M.-Y. Cheng, Y.-W. Wu, C.-C. Wu, Forecasting enterprise resource plan-ning software effort using evolutionary support vector machine inference model,Int. J. Proj. Manag. 30 (8) (2012) 967–977.

[7] J.-S. Chou, C. Chiu, M. Farfoura, I. Al-Taharwa, Optimizing the Prediction Accuracy ofConcrete Compressive Strength Based on a Comparison of Data-Mining Techniques,J. Comput. Civ. Eng. 25 (3) (2011) 242–253.

[8] J.-S. Chou, C. Lin, Predicting Disputes in Public–Private Partnership Projects: Classifi-cation and Ensemble Models, J. Comput. Civ. Eng. 27 (1) (2013) 51–60.

[9] J.-S. Chou, A.-D. Pham, Applying Smart Meter and DataMining Techniques to PredictRefrigeration System Performance, in: P. Meesad, H. Unger, S. Boonkrong (Eds.), The9th International Conference on Computing and InformationTechnology(IC2IT2013), vol. 209, Springer, Berlin Heidelberg, 2013, pp. 249–257.

[10] J.-S. Chou, C.-F. Tsai, Preliminary cost estimates for thin-film transistor liquid-crystaldisplay inspection and repair equipment: A hybrid hierarchical approach, Comput.Ind. Eng. 62 (2) (2012) 661–669.

[11] S. Dey, A. Barbhuiya, Time Variation of Scour at Abutments, J. Hydraul. Eng. 131 (1)(2005) 11–23.

[12] R. Ettema, G. Constantinescu, B. Melville, Final Report for NCHRP Project Web-OnlyDocument 175: Pier Scour Processes and Predictions, Evaluation of Bridge ScourResearch, Transportation Research Board, Washington DC, 2012.

[13] C.-W. Feng, S.-H. Ju, H.-Y. Huang, Hybridizing Finite Element Method and GeneticAlgorithms to Estimate Bridge Scour Depths, in: M.H.H.S. Al Zahir, J. Cheng (Eds.),The 23rd IASTED International Conference on Modelling and Simulation, ACTAPress, Canada, 2012.

[14] D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning,Addison-Wesley, Boston, MA, USA, 1989.

[15] W. Haifeng, H. Dejin, Comparison of SVM and LS-SVM for Regression, InternationalConference on Neural Networks and Brain, 2005, ICNN&B '05, vol. 1, 2005, pp.279–283.

[16] J.-H. Hong, M.K. Goyal, Y.-M. Chiew, L.H.C. Chua, Predicting time-dependent pierscour depth with support vector regression, J. Hydrol. 468–469 (2012) 241–248.

[17] C.-W. Hsu, C.-J. Lin, A Simple Decomposition Method for Support Vector Machines,Mach. Learn. 46 (1–3) (2002) 291–314.

[18] J. Huang, X. Hu, F. Yang, Support vector machine with genetic algorithm for machin-ery fault diagnosis of high voltage circuit breaker, Measurement 44 (6) (2011)1018–1027.

[19] W.-K. Kao, H.-M. Chen, J.-S. Chou, Aseismic ability estimation of school building usingpredictive data mining models, Expert Syst. Appl. 38 (8) (2011) 10252–10263.

[20] G.V. Kass, An Exploratory Technique for Investigating Large Quantities of CategoricalData, J. R. Stat. Soc.: Ser. C: Appl. Stat. 29 (2) (1980) 119–127.

[21] M. Khan, P. Coulibaly, Application of Support Vector Machine in Lake Water LevelPrediction, J. Hydrol. Eng. 11 (3) (2006) 199–205.

[22] R. Kohavi, A Study of Cross-Validation and Bootstrap for Accuracy Estimation andModel Selection Paper presented at the International Joint Conference on ArtificialIntelligence, 1995.

[23] I. Kucuk,N.Derebasi, Predictionof power losses in transformer coresusing feed forwardneural network and genetic algorithm, Measurement 39 (7) (2006) 605–611.

[24] C. Lauchlan, B. Melville, Riprap Protection at Bridge Piers, J. Hydraul. Eng. 127 (5)(2001) 412–418.

[25] S.-H. Liao, P.-H. Chu, P.-Y. Hsiao, Data mining techniques and applications— A decadereview from 2000 to 2011, Expert Syst. Appl. 39 (12) (2012) 11303–11311.

[26] H.-B. Lui, Y.-B. Jiao, Application of Genetic Algorithm–Support Vector Machine(GA–SVM) for Damage Identification of Bridge, Int. J. Comput. Intell. Appl. 10 (04)(2011) 383–397.

[27] S. Martino, F. Ferrucci, C. Gravino, F. Sarro, A Genetic Algorithm to Configure SupportVector Machines for Predicting Fault-Prone Components, in: D. Caivano, M. Oivo, M.Baldassarre, G. Visaggio (Eds.), Product-Focused Software Process Improvement,vol. 6759, Springer, Berlin Heidelberg, 2011, pp. 247–261.

[28] B. Melville, Y. Chiew, Time Scale for Local Scour at Bridge Piers, J. Hydraul. Eng. 125(1) (1999) 59–65.

[29] M. Mia, H. Nago, Design Method of Time-Dependent Local Scour at Circular BridgePier, J. Hydraul. Eng. 129 (6) (2003) 420–427.

[30] J. Neter, M.H. Kutner, C.J. Nachtsheim, W. Wasserman, Applied Linear StatisticalModels, Fourth ed. McGraw-Hill/Irwin, 1996.

[31] M. Pal, N.K. Singh, N.K. Tiwari, Support vector regression based modeling of pierscour using field data, Eng. Appl. Artif. Intell. 24 (5) (2011) 911–916.

[32] L. Ren, X. Xiang, J. Ni, Forecast Modeling of Monthly Runoff with Adaptive NeuralFuzzy Inference System and Wavelet Analysis, J. Hydrol. Eng. 18 (9) (2013)1133–1139.

[33] SPSS, Clementine 12.0 Algorithms Guide, Integral Solutions Limited, Chicago, USA,2007.

[34] T.W. Sturm, R. Ettema, B.W. Melville, Final Report for NCHRP Web-Only Document181: Abutment and Contraction Scour Processes and Prediction, Evaluation ofBridge-Scour Research, Transportation Research Board, Washington DC, 2012.

[35] X.-h. Tan, W.-h. Bi, X.-l. Hou, W.Wang, Reliability analysis using radial basis functionnetworks and support vector machines, Comput. Geotech. 38 (2) (2011) 178–186.

[36] V. Vapnik, Universal learning technology: Support Vector Machines, NEC J. Adv.Technol. 2 (2) (2005) 137–144.

[37] P.-S. Yu, S.-T. Chen, I.F. Chang, Support vector regression for real-time flood stageforecasting, J. Hydrol. 328 (3–4) (2006) 704–716.

[38] W.G. Zhang, A.T.C. Goh, Multivariate adaptive regression splines for analysis ofgeotechnical engineering systems, Comput. Geotech. 48 (2013) 82–95.

[39] H.-b. Zhao, Slope reliability analysis using a support vector machine, Comput.Geotech. 35 (3) (2008) 459–467.