Predicting shear wave velocity of soil using multiple linear regression …scientiairanica.sharif.edu/article_4263_57852cf72ee... · 2021. 2. 17. · ods, such as simple and multiple

Scientia Iranica A (2018) 25(4), 1943{1955

Sharif University of TechnologyScientia Iranica

Transactions A: Civil Engineeringhttp://scientiairanica.sharif.edu

Predicting shear wave velocity of soil using multiplelinear regression analysis and arti�cial neural networks

O. Ataeea, N. Hafezi Moghaddasa;�, Gh.R. Lashkaripoura, andM. Jabbari Nooghabib

a. Department of Geology, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran.b. Department of Statistics, Faculty of Science, Ferdowsi University of Mashhad, Mashhad, Iran.

Received 16 May 2016; received in revised form 11 October 2016; accepted 28 January 2017

KEYWORDSShear wave velocity;SPT;Depth;Fine-content;Arti�cial neuralnetwork;Multiple linearregression;Mashhad.

Abstract. This paper investigates the correlation between shear wave velocity and some ofthe index parameters of soils, including Standard Penetration Test blow counts (SPT), Fine-Content (FC), soil moisture (W ), Liquid Limit (LL), and Depth (D). The study attemptsto show the application of arti�cial neural networks and multiple regression analysis tothe prediction of the shear wave velocity (VS) value of soils. New prediction equations aresuggested to correlate VS with the mentioned parameters based on a dataset collected fromMashhad city in the north east of Iran. The results suggest that, in the case of ANN methoduse, highly accurate correlations in the estimation of VS are acquired. The predicted valuesusing ANN method are checked against the real values of VS to evaluate the performanceof this method. The minimum correlation coe�cient obtained in ANN method is higherthan the maximum correlation coe�cient obtained from the MLR. In addition, the value ofestimation error in the ANN method is much less than that in the MLR method, indicatingthe role of higher con�dence coe�cient of the ANN in estimating VS of soil.© 2018 Sharif University of Technology. All rights reserved.

1. Introduction

Shear wave velocity (VS) is a fundamental parameterin de�ning the dynamic properties of soils, evaluatingdynamic site response, and characterizing dynamicsite [1,2]. The pro�le of VS in the ground is consid-ered as the most reliable predictor of site-dependentproperties from a seismic action in stable sites [3]. VSis measured often by in-situ methods in low strainlevels; therefore, the measured VS can be employed todetermine the maximum shear modulus (Gmax) of soildeposit in di�erent depths [1]. Gmax is an essential

*. Corresponding author.E-mail addresses: [email protected] (O. Ataee);[email protected] (N. Hafezi Moghaddas);[email protected] (Gh.R. Lashkaripour);[email protected] (M. Jabbari Nooghabi).

doi: 10.24200/sci.2017.4263

input parameter for analyzing the dynamic stability ofslopes, dams, embankments, etc. [4].

Although it is preferable to determining VS di-rectly through �eld tests, conducting these tests ismostly not feasible due to economic considerations,lack of space in urban areas, lack of specialized per-sonnel, and high noise levels in all situations [4-8]. Inthe absence of in-situ dynamic tests data, it is commonworldwide to calculate VS through reported empiricalrelationships between VS and other geotechnical soilproperties such as SPT, CPT, dry density, etc. [4]. SPTis one of the most economical and commonly employedin-situ tests involving very strong relationships withmany of geotechnical soil properties. Many studieshave proposed statistical relationships between VS andSPT blow counts [1,3-6,8-20].

Generally, the relationships between VS and SPTshow considerable dispersion, which is probably due tothe di�erent methods employed in measuring VS and

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1944 O. Ataee et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1943{1955

SPT N value, as well as the geotechnical and geologicalconditions speci�c to any area. Another reason for lowaccuracy of these relationships is the type of regressionanalysis employed [21]. Traditionally, statistical meth-ods, such as simple and multiple regression analyses,are used in geotechnical engineering to create predic-tive models. All of conventional regression methodshave limitations. Besides, empirical methods are notapplicable to complicated and non-linear problems [22].

Arti�cial Neural Network (ANN) is an over-simpli�ed simulation of human brain made up of simpleprocessing units, called neurons. This system is ableto learn and generalize experimental data, even whenthe data are noisy, incomplete with a non-linear na-ture [23,24]. Unlike the conventional statistical models,the main advantage of ANN is that it does not requireany prior knowledge related to the kind of relationshipbetween input and output data. ANNs are also ableto function very well in situations with limited dataaccessibility [25].

In recent years, Arti�cial Intelligent (AI) methodshave been widely used for predicting purposes [26,27].So far, neural networks have been used for estimatingand predicting some of the geotechnical propertiesof soil such as estimation of soil compaction pa-rameters [28,29], compressive and shear strength ofsoils [22,30,31], prediction of soil permeability [29,32],prediction of CBR in �ne-grained soils [33], predictionof compressibility indices of saturated clays [34-36],pile bearing capacity [37,38], prediction of soil settle-ment [39], soil liquefaction [40-43], and analysis of slopestability [44-46]. Researchers have also used neuralnetwork models to predict VS value in oil wells [26,47-50]. In addition, ANNs have been used to estimateand predict VS values of soils using geotechnical soilproperties such as CPT [51-53].

The present study aims to develop an optimalmodel to predict VS of soils in Mashhad city basedon the parameters of SPT, depth, �ne content, liquidlimit, and percentage of soil moisture. In this study, amultilayer perceptron with feed-forward backpropaga-tion is used for modeling VS in soil. The best neuralnetwork model is found and selected through analysisof di�erent models' performances (with di�erent hiddenlayers and neurons in each layer). The purpose of thisstudy is to identify properties of soil that have a moree�cient role in predicting VS of soil; it also attemptsto compare the capabilities of neural networks andmultiple regression technique in predicting VS valueusing the variables mentioned above.

2. Study area

This study was carried out in Mashhad, Iran, which isthe second most populated city in the center of Kho-rasan Razavi province in Iran. Mashhad is located at

36:10�-36:24�N latitude and 59:25�-59:43�E longitudein the northeast of Iran. It is situated on Mashhadplain, which is covered with thick Quaternary alluvialsediments. Kashafrood River is the main drainage sys-tem of Mashhad plain as well as the streams originatingfrom the southern parts of Mashhad (Figure 1).

From the seismotectonical perspective, Mashhadis situated between two folded-thrusted mountains(Koppe-Dagh in northeast and Binalood in south-west). According to Berberian et al. [54], there wereintense earthquake activities in the area in the pastcenturies, especially in the 18th century. The existenceof active faults within a short distance and on the twosides of Mashhad plain indicates that this area has ahigh potential for earthquake. Shandiz, Kashafrood,Toos, south of Mashhad, the north of Neishaboor, andKheirabad faults are the main active faults in thisarea [55].

Mashhad city is an earthquake-prone area andis situated in the high-risk earthquake zone, with0.30-0.35 g maximum acceleration in return period of475 years, according to the Iranian Code of Practicefor Seismic Resistance Design of Buildings (StandardNo. 2800) [56]. These issues indicate the seismicvulnerability of Mashhad city; hence, an accurateestimation of VS for this city is required.

3. Materials and methods

3.1. RegressionRegression analysis is one of the analytical instrumentswidely applied to the investigation of relationshipsbetween a dependent variable and a set of independent(predictor) variables. Regression analysis is eitherlinear or non-linear. In linear regression, data are mod-eled using linear-independent variables or predictivefunctions. In non-linear regression, data are modeledusing a function that is a non-linear combination ofmodel parameters. This type of regression is dependenton one or more independent variables. Regressionanalysis is one of the common methods for creatingpredictive models between VS and soil geotechnicalproperties, including SPT and CPT. In addition toSPT, this paper aims to study the in uence of �necontent, soil moisture, liquid limit, and soil depthon estimating VS value. Therefore, Multiple LinearRegression analysis (MLR) will be employed.

3.2. Multiple Linear Regression analysis(MLR)

Simple linear regression is a useful technique to predicta response based on a single predictor variable. How-ever, in practice, it often occurs that there is more thanone predictor. MLR is used when there are more thanone explanatory variable in a model, which can helpexplain or predict the response variable; therefore, all

O. Ataee et al./Scientia Iranica, Transactions A: Civil Engineering 25 (2018) 1943{1955 1945

Figure 1. Geological map of study area with location of boreholes and faults.


of these explanatory variables are put into the model tocarry out a multiple linear regression analysis. Then,the MLR equation is given as follows:

Y = �0 + �1X1 + �2X2 + � � �+ �pXp + "; (1)

where Xp represents the pth predictor, and �p quan-ti�es the relation between the variable and response.�p is interpreted as the mean e�ect on Y of a one-unit increase in Xp, holding all other predictors �xed.Regression coe�cients, �0; �1 � � ��p, in Eq. (1) areunknown and must be estimated using the least squaresapproach as is the case in simple linear regression [57].

3.3. Arti�cial Neural Network (ANN)ANN is a massively parallel-distributed informationprocessing system with certain performance character-istics, simulating the biological neural networks of thehuman brain [58]. A neuron is the basic componentof the neural networks that accepts and sums upinputs, applies a transfer function, which is normallynonlinear, and gives the result that is as either a modelprediction or input into other neurons. An arti�cialneural network is a combination of many such neuronsconnected in a systematic way. Neurons with the sameproperties in an ANN are ordered in groups, calledlayers [33]. One-layer neurons are connected to theneurons of the adjacent layers (not to the neurons of thesame layer). The strength of connection between thetwo neurons in adjacent layers is recognized throughthe strength of connection or weight.

Usually, an ANN has three layers: one inputlayer, one hidden layer, and one output layer. SinceANNs have an error tolerance and the ability to workwith incomplete data, they can easily produce modelsfor complicated problems. In particular, for semi-structural or non-structural problems, neural networkmodels can provide very successful results. Further-more, they are faster and more reliable than thetraditional methods are [23].

3.4. Multi-Layer Perceptron (MLP)MLPs, also known as feed-forward neural networks,typically trained with back propagation algorithm, areusually used for prediction. Neurons in such networksare arranged in di�erent layers (typically one inputlayer, one or more hidden layers, and one output layer)each of which is interconnected to its preceding andfollowing layers. Figure 2 depicts a feed-forward three-layer ANN with the description of input and outputlayers employed in the current study. Connectionsbetween neurons have weights associated with them.These weights determine the strength of in uence thatone neuron can have on another. From the input layerand through the processing layer(s), information owsto the output layer to generate predictions. Duringtraining, the network learns to generate predictions

Figure 2. Architecture of multilayer neural network forthis study.

that are more accurate through adjusting the connec-tion weights so that predictions can be matched withtarget values for speci�c records.

Determining the network architecture requires theoptimum number of hidden layers between input andoutput layers and the optimum number of neurons ineach hidden layer. That is one of the most importantand most complicated parts of designing neural net-works, as there is no single theory or accepted rulefor determining the optimal network architecture [59-61]. The number of hidden layers and their neurons ismostly determined by trial and error [62,63].

3.5. Data preparation and normalizationThe dataset used in this study was collected fromgeotechnical and geophysical reports from civil engi-neering projects done across Mashhad city by con-sulting engineering companies. Data related to 85drilled boreholes were employed in data analysis. Acomplete dataset of six variables was required for thisstudy; �nally, 185 soil samples were used for regres-sion analysis, neural network design, and its accuracyevaluation. The model input variables selected for thepresent study are SPT, LL, W , FC, and D; the targetor output variable is VS of the soil.

In most of the datasets, there is a lot of variabilityin the scale of range �elds. Therefore, to nullify thee�ect of scale, range �elds are transformed to havethe same scale for all. In this situation, normalizationcan speed up the training process and improve theaccuracy of the output model. Range �elds are rescaledin Clementine to have values between 0 and 1. In thisstudy, before inserting data into ANN, the input andoutput datasets were normalized through the followingformula [64]:

xnormalized =xactual � xmin

xmax � xmin; (2)

where xnormalized is the normalized value of the ob-served variable, xactual is the real value of the observedvariable, and xmax and xmin are the maximum andminimum values of observed variable in the dataset,


respectively. When the function of the network iscomplete, network outputs are post-processed so thatdata can be converted into non-normalized units [28].For ANN modeling, data are divided randomly intothree categories of training, testing, and validation [60].The network is trained by the �rst category of data.The training set is also used for adjusting the weightsof the connections. The validation set is used to testthe performance of the network in di�erent stages oftraining. When the training is successful, the testingset is used to evaluate the performance of the model.

The dataset collected from the Mashhad cityregion was �rst analyzed for possible relationshipsbetween the parameters, and those variables whichseemed likely to be in uential in predicting VS wereseparated. Finally, �ve main parameters, includingSPT, LL, W , FC, and D, were considered as inputparameters in MLR and ANN models. In designinga neural network, data were divided into training,testing, and validation sets. From 185 datasets usedin this study, 80% (137 samples) were employed fortraining the model, 10% (19 samples) for testing themodel, and 10% (29 samples) for validation of ANNanalysis. All data were employed in regression analysis.Table 1 shows descriptive statistics related to the inputand output parameters for all sets.

3.6. Performance evaluation criteriaFor the assessment of methods, the obtained results

from each model (MLR and ANN) were evaluatedbased on di�erent criteria. There are many criteria forassessing the performance of models. In this section,the e�ciency criteria used in this study are presentedand evaluated. There are four criteria herein: thecorrelation coe�cient (R), coe�cient of determination(R2), Root Mean Square Error (RMSE), and MeanAbsolute Error (MAE). Each of the above criteriaused in this study was computed through the followingequations:

3.6.1. Pearson Correlation Coe�cient (R)R can be used to estimate the correlation betweenmodel and observations:

R =Pni=1(mi � �m) � (pi � �p)qPn

i=1(mi � �m) �Pni=1 (pi � �p)2

; (3)

where mi is the measured value, Pi is the predictedvalue, �m is the mean of measured values, and �P is themean of predicted values.

3.6.2. Coe�cient of determination or the square ofthe Pearson correlation coe�cient (R2)

R2 describes how much of the variance between the twovariables is described by the linear �t.

3.6.3. Root Mean Square Error (RMSE)The RMSE of a model prediction is de�ned as thesquare root of the mean squared error:

Table 1. Descriptive statistics of input and output data.

Partition Statistics D SPT FC W LL VS (m/s)

All

data

set Mean 16.20 43 31.41 6.56 21.46 515

Std. Deviation 10.40 21 28.21 5.18 5.97 157Minimum 0.50 10 1.80 1.60 2.00 202Maximum 49.00 97 99.00 26.10 55.00 850

Tra

inin

gse

t Mean 15.94 44 30.50 6.18 21.48 516Std. Deviation 10.11 21 26.77 4.48 6.38 148Minimum 0.50 10 1.80 1.60 2.00 202Maximum 49.00 97 97.00 21.95 55.00 850

Tes

ting

set Mean 19.00 42 37.97 9.22 21.74 524

Std. Deviation 12.25 20 36.34 8.54 5.60 175Minimum 1.50 16 6.00 2.10 15.00 204Maximum 41.00 91 99.00 26.10 35.00 773

Val

idat

ion

set

Mean 15.59 40 31.42 6.63 21.18 504Std. Deviation 10.53 22 29.45 5.12 4.06 186Minimum 1.50 11 7.30 2.00 15.00 210Maximum 41.50 91 98.50 26.00 32.70 790


RMSE =

rPni=1(mi � pi)2

n; (4)

where n is the number of data presented in thedatabase.

3.6.4. Mean Absolute Error (MAE)The Mean Absolute Error (MAE) is a quantity usedto measure how close predictions are to the eventualoutcomes. The mean absolute error is given by:

MAE =Pni=1 jmi � pij

n: (5)

4. Results and discussion

4.1. Regression analysisAs previously mentioned, �ve independent variables formultiple regression analysis were selected. At �rst, therelationships between VS and each of the independentvariables were studied. The relationship between VSand SPT as well as VS and depth has a power-lawform [1-20]. Therefore, the most preferred functionalform of relation between SPT and VS proposed inliterature (VS = a � N b) has been used as the mainformat for MLR analysis. This equation is given below:

VS = a �N b �Dc � FCd �W e � LLf : (6)

In this equation, N , D, FC, W , and LL represent SPT,depth, �ne-content, moisture content, and liquid limit,respectively, and a to f are coe�cients that should bedetermined by regression. The power-law form of thismodel allows us to write it as follows:

log VS = log a+ b logN + c logD + d log FC

+ e logW + f log LL: (7)

In this case, the linear regression can be used todetermine the constant values. MLR analysis wasperformed on 31 possible combinations of independentvariables. After comparing the results, nine combina-tions whose coe�cient of determination exceeded 0.5were selected to obtain the best model to govern VS .The combination of input variables in di�erent modelsin this study is given in Table 2. The MLR regressionanalysis was performed using SPSS software, and thecriteria for performance evaluation were calculated foreach combination, as shown in Table 3.

A comparison of the above results demonstratesthat C�3 with a higher correlation coe�cient and coef-�cient of determination (0.856 and 0.733, respectively)and smaller values of RMSE and MAE is the bestmodel for predicting the value of VS of soil. It can beobserved that the combination of the three parameters,including D, SPT, and FC (silt and clay), shows thebetter correlation with VS . Figure 3 shows the scatterplot of VS values predicted by MLR and its measuredvalues in the �eld.

Table 2. Input and output for the di�erent combinations.

Combinationno.

Input Output

C � 1 D, SPT, LL

VS

C � 2 D, SPT, WC � 3 D, SPT, FCC � 4 D, FC, WC � 5 D, SPTC � 6 D, LLC � 7 D, WC � 8 D, FCC � 9 SPT

Table 3. Performance evaluation criteria for the di�erentcombinations obtained by MLR analysis.

Combinationno.

R2 R RMSE(m/s)

MAE(m/s)

C � 1 0.719 0.848 84.28 70.84C � 2 0.729 0.854 83.34 69.89C � 3 0.733 0.856 82.29 68.81C � 4 0.588 0.767 100.74 82.02C � 5 0.711 0.843 85.7 71.34C � 6 0.506 0.711 111.37 90.27C � 7 0.560 0.748 106.45 87.73C � 8 0.573 0.757 102.09 83.77C � 9 0.599 0.774 99.52 85.44

4.2. Arti�cial neural network developmentIn this study, a FFBP-based ANN solver (Clementinedata mining system) was used for designing and testingANN models. Clementine is a preeminent data-miningtoolkit widely used in academic researches and indus-trial applications. To apply Clementine ANN solver,like other FFBP-based software products, diverse net-work architectures should be examined to obtain thebest result. The �rst step in this process is to selectinput and output variables for this study, selected inprior sections.

In the next step, the number of hidden layers andneurons in each layer is de�ned for the model. Thereis no obvious solution for determining hidden layersand neurons for the ANN network. Although Zhang etal. [65] suggested that the optimum number of hiddenlayers in FFBP architecture is mostly one or two, someresearchers have also suggested that, between n and2n, hidden neuron is enough for FFBP models [66].

Generally, there are two fundamental approachesto constructing a FFBP network [67]. In a methodcalled additive or constructive, the model starts witha minimal network consisting of a single hidden layer,and, gradually, hidden layers and neurons are added


Figure 3. Scatter plot of measured VS versus predictedVS for the best model by MLR analysis.

and the e�ectiveness of the obtained model is evalu-ated using the evaluation instruments. In the secondapproach, the model starts with a very large network;moreover, pruning algorithm is used to reduce the sizeof the model [68].

Clementine provides both approaches: The dy-namic method uses the additive approach. In this state,the network topology changes during the training phaseby the neurons that are added so that the network canobtain an optimum performance, while the system alsomonitors lack of improvement and overtraining. Thisprocess continues until no improvement can be achievedfrom the future model expansion. Conceptually, theprune method is di�erent from the dynamic method.The prune method starts with a large network and,then, gradually prunes it by removing the unhelpfulneurons from the input and hidden layers. There aretwo stages for pruning: pruning the hidden neuronsand the input neurons. The two-stage process iteratescontinuously until the overall stopping criteria are met.These two stages are described below. The trainingprocess in this approach discards the weakest hiddenneurons and selects the optimal size of the hiddenlayers. When one hidden layer is obviously enough,another option called Quick can be used where a simplemode creates a network with one hidden layer and at-tempts to determine the number of hidden neurons giv-ing the best results. The stopping rules in Clementineinclude a measure of desirable accuracy, the number ofcycles on which the model is run, and the real amountof time in which the model is allowed to run.

In the present study, combinations of these ap-proaches were used to reach the best results. Duringthe construction of these models, the prevent over-training parameter is always in the selection mode

to prevent the overtraining of the model. Input andoutput data were normalized before being inserted inthe network. To design the neural network, the datasetwas randomly divided into three discrete sets calledtraining, testing, and validation (80%, 10%, and 10%,respectively). Only those data concerning the trainingset are used by neural network to learn the existingpatterns in the data and optimize model parameters.During network training, the optimum numbers ofneurons in the hidden layer and the learning rate arecalculated. The training phase stops when the varia-tion of error becomes su�ciently small. After buildinga model using the training set, the performance of thetrained model must be validated using new data. Toget a more realistic estimation of how the model wouldperform with unseen data, we must allocate a part ofthe data not trained during the training process to thispurpose. This set of data is known as the ValidationSet. The testing set includes the unseen data forevaluating the performances of various candidate modelstructures and testing the network's generalization.

In this study, data analysis with neural networkswas performed using the SPSS Clementine software.The ANN analysis was also carried out on nine selectedcombinations of independent variables in the previoussections. Di�erent network methods were employedfor each combination. In addition, the method wasselected capable of estimating the value of the targetparameter with higher accuracy and the least numberof hidden layers and hidden neurons.

The performance criteria required for evaluatingthe accuracy of the designed models were computed forthe training, testing, and validation stages (Table 4).Based on the model performance in validation stage,the best ANN model was determined. By comparingthe evaluation criteria in Table 4, compared with othercombinations, the combination (C � 3) involving astructure of 3-2-3-1, which has the highest value ofcorrelation and coe�cient of determination and thelowest values of RMSE and MAE, was selected asthe optimal model in neural network analysis. Withrespect to this combination, it was observed that thevalues of RMSE and MAE were obtained as 63.42 and52.64 m/s for testing set and as 66.92 and 57.34 m/sfor validation set, respectively. Therefore, concerningcertain �ndings through regression analysis, it can beconcluded that VS correlates well with SPT, FC, andD. Results showed that high correlation coe�cient andlow RMSE values were also obtained for C�2 and C�5in both ANN and MLR methods, implying that thecomposition of two parameters SPT and depth of soilcould be good estimators for predicting VS ; however,joining parameters, such as FC and W , would improvethe prediction accuracy.

Furthermore, the coe�cient of determination forboth of the testing and validation data shows that the


Table 4. Performance criteria for di�erent models in testing and validation stage by ANN method.

Combinationno.

R2 R RMSE MAE

Test Validation Test Validation Test Validation Test Validation

C � 1 0.856 0.869 0.926 0.932 64.27 69.41 53.7 61.84

C � 2 0.854 0.885 0.924 0.941 70.95 67.32 58.4 57.37

C � 3 0.878 0.887 0.931 0.942 63.42 66.92 52.64 57.34

C � 4 0.681 0.817 0.825 0.904 101.07 86.29 77.96 73.52

C � 5 0.863 0.870 0.929 0.933 76.86 69.32 60.71 60.2

C � 6 0.748 0.839 0.865 0.916 88.97 82.93 70.52 67.58

C � 7 0.760 0.759 0.872 0.871 90.46 96.65 75.5 83.1

C � 8 0.741 0.812 0.861 0.901 90.39 87.53 76.19 71.47

C � 9 0.669 0.803 0.818 0.896 104.05 89.99 88.07 74.19

Figure 4. Relationship between measured and predicted shear wave velocity by ANN analysis in (a) testing and (b)validation phase.

predicted values of VS , using ANN method, show areasonably good correlation with actual values. Fig-ure 4 shows the relationship between the actual andpredicted values of VS using the ANN in testing andvalidation phases for the optimal model.

4.3. Comparison between ANN predictionsand results of MLR

Combinations 1 to 9 were analyzed using both ANNand MLR methods. The predicted VS by the ANNmodels for the testing and validation sets was comparedwith the estimated VS by multiple regression analysismodels. The MAE, RMSE, and R2 values extractedfrom ANN and MLR methods for di�erent combina-tions are depicted in Figures 5, 6, and 7. Figures 5 and6 show that the values of RMSE and MAE obtainedfrom regression analysis are greater than the ANNmethod for all of the above combinations in bothtesting and validation sets. It is also obvious accordingto Figure 7 that the correlation coe�cient obtained

from ANN models is more than that from the MLRmodels, re ecting the higher ability of ANN models foraccurate prediction of VS value.

Finally, to compare the ANN and MLR methodsand evaluate their performances, the predicted VSvalues by these two methods for the optimal model(C � 3) and for 20 random soil samples are presentedin Figure 8. As the �gure shows, the neural networkspredict VS values closer to the actual (measured VS)values for most of the samples.

5. Conclusions

The goal of this study is to evaluate the feed-forwardneural networks as a possible tool for predicting VSin Mashhad city. Five important input variables wereused for predicting VS value. Di�erent combinations ofthese inputs have been studied. Nine combinations ofthese variables, which achieved the highest correlationcoe�cient in regression analysis, were selected for


Figure 5. Comparison of RMSE values obtained by ANN and MLR: (a) Testing set and (b) validation set.

Figure 6. Comparison of MAE values obtained by ANN and MLR: (a) Testing set and (b) validation set.

Figure 7. Coe�cient of determination (R2) obtained by ANN and MLR: (a) Testing set and (b) validation set.

comparing the ANN and MLR methods. The neuralnetworks were trained for nine mentioned combinationsby the feed-forward backpropagation algorithm; itseems that it correlated the static properties of soil wellwith VS . To validate the neural network models, new

observation data were introduced to the networks andthe forecasted VS were compared with actual values ofVS in the study area. Good agreement exists betweenreal and calculated data.

Both of the methods showed that the combina-


Figure 8. Measured VS versus predicted VS by ANN and MLR methods for the best model (C � 3): (a) Testing set and(b) validation set.

tions of the three parameters including D, SPT Nvalue, and FC give the best estimation of VS of soil.The value of correlation coe�cient and coe�cient ofdetermination obtained from the ANN method washigher than that of the MLR method. It should bementioned that the error values computed throughRMSE and MAE obtained from the MLR method weremore than those extracted from the ANN method forall combinations under study. Therefore, it can beconcluded that in comparison with MLR models, ANNmodels give more reliable prediction of VS . In otherwords, ANN models have a better performance and canbe used with a higher con�dence coe�cient to predictVS value of soil.

Acknowledgment

The authors appreciate cooperation from consultingengineering companies and soil mechanics laboratoriesin Mashhad city for providing their geotechnical re-porting for use in this paper. They also acknowledgethe kind cooperation from the Zamin Physics PooyaConsulting Engineering Company for giving permissionto use measured shear wave velocity.

Geolocation Information: Mashhad is the secondmost populated city in the center of the KhorasanRazavi province. It is located 850 km North East ofTehran, the capital of Iran, at 36:20� north latitude and

59:35� east longitudes in the valley of the KashafroodRiver near Turkmenistan, between the two mountainranges of Binalood and Hezar-Masjid, which are closeto the borders of Afghanistan, and Turkmenistan.

Role of funding sources: The work was not �nan-cially supported by any funding sources.

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Biographies

Omolbanin Ataee is a PhD Student at the Depart-ment of Geology at Ferdowsi University of Mashhad,Iran. Her main areas of research interest are soilmechanics, geostatistics and environmental geology.

Naser Hafezi Moghaddas is currently a Professor ofEngineering Geology at Ferdowsi University of Mash-had. His research interests focus on the landslide, sitee�ect and micro zonation of earthquake, slop stability.

Gholam Reza Lashkaripour is a Professor of Engi-neering Geology at Ferdowsi University of Mashhad.He teaches courses such as environmental geology,hydrology, advanced engineering geology, rock mechan-ics, groundwater and geotechnical problems, geologicalhazards, site investigation, and soils improvement atgraduate and postgraduate levels.

Mehdi Jabbari Nooghabi is an Assistant Professorat the Department of Statistics at Ferdowsi Universityof Mashhad. He taught di�erent courses such as sta-tistical applications in management, statistical qualitycontrol, time series, research method and statisticalconsulting, statistics for managers, business mathemat-ics and statistics, statistical analysis, special topics, ad-vanced applied statistics, statistics meteorology, linearmodels and their application in genetic improvementof farm animals, advanced methods of statistical in-ference, industrial statistics, and multivariate discreteand continuous analysis at graduate and postgraduatelevels.

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