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Artificial Neural Networks (ANN) models were developed for predicting pile setup ... Keywords: pile foundation, pile setup, regression, artificial neural network, ...

KSCE Journal of Civil Engineering (2014) 18(4):1018-1027 Copyright ⓒ2014 Korean Society of Civil Engineers DOI 10.1007/s12205-014-0072-7

Geotechnical Engineering

pISSN 1226-7988, eISSN 1976-3808 www.springer.com/12205

TECHNICAL NOTE

Regression versus Artificial Neural Networks: Predicting Pile Setup from Empirical Data Bashar Tarawneh* and Rana Imam** Received February 1, 2013/Revised May 19, 2013/Accepted July 18, 2013

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Abstract Piles have been used as a deep foundation for both inland and offshore structures. After installation, pile capacity may increase with time. This time dependent capacity increase is known as setup, and was first mentioned in the literature in 1900 by Wendel. When accounted for accurately during the design stages, the integration of pile setup can lead to more cost-effective pile design as it will reduce pile length, pile section, and size of driving equipment. In this paper, Both Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN) models were developed for predicting pile setup for three pile types (pipe, concrete, and H-pile) using 169 dynamic load tests obtained from the published literature and the authors' files. In addition, the paper discusses the choice of variables that were examined to obtain the optimum model. Furthermore, the paper compares the predictions obtained by the developed MLR and the ANN models with those given by four traditional empirical formulae. It is concluded that the ANN model outperforms both the MLR model and the examined empirical formulae in predicting the measured pile setup. Finally, static load test data was used to further verify the developed models. It’s noted that the optimal ANN model overestimated pile capacity by 17% to 21% for the H-piles, and underestimated pile capacity by 12% to 17% for the pipe piles. Keywords: pile foundation, pile setup, regression, artificial neural network, empirical data word count (5699) ·································································································································································································································· 1. Introduction

The purpose of a pile foundation is to transfer and distribute load through a material or stratum with inadequate bearing, sliding, or uplift capacity to a firmer stratum that is capable of supporting the load without detrimental displacement. Driving a pile into the ground generates excess pore water pressures, leads to disturbance, and displacement in the soil surrounding the pile. Dissipation of the excess pore water pressures leads to an increase in pile capacity with time. As the soil recovers from the driving disturbance, a time-dependent increase in pile capacity regularly occurs. Setup does not occur in all soil types. In some soils, though not often, a reverse phenomenon termed “relaxation” may occur where the pile loses capacity with time. It is therefore important to understand the setup phenomenon in the context of local geology to take advantage of it. In cohesive and cohesionless soils, it was observed that pile capacity continues to increase with time after complete dissipation of excess pore water pressure. The increase in pile capacity over time that takes place after the dissipation of excess pore water pressure induced from pile driving is termed soil/pile setup which is primarily associated with an increase in shaft capacity (Axelsson, 1998).

Considering pile setup in the axial load capacity of driven pile leads to a more economical pile design; reducing pile length, cross section, and size of driving equipments. To evaluate setup, geotechnical engineers perform dynamic monitoring with a Pile Driving Analyzer (PDA) during initial driving and restrike testing (which takes place several hours to a few weeks after initial driving). For projects with a large number of driven piles, the savings in pile costs significantly exceed the cost of testing needed to characterize setup; however the testing is not justified economically for projects with fewer piles.

2. Evaluation of Pile Setup The mechanisms behind pile setup have been the subject of numerous research works. Simple empirical relations in the literature predict the increase in pile capacity with time from the initial capacity (described as end of driving, EOD) and the elapsed time after driving. Two sets of model constants are suggested for clayey and sandy soils based on limited data sets (Skov and Denver, 1988; Svinkin and Skov, 2000). These constants are specific to the field data from which they were derived; so they can't predict setup reliably for other cases investigated. The most commonly used formulae are:

*Assistant Professor, Dept. of Civil Engineering, The University of Jordan, Amman 11942, Jordan (E-mail: [email protected]) **Assistant Professor, Dept. of Civil Engineering, The University of Jordan, Amman 11942, Jordan (Corresponding Author, E-mail: [email protected]) − 1018 −

Regression versus Artificial Neural Networks: Predicting Pile Setup from Empirical Data

2.1 Skov and Denver (1988) Skov and Denver (1988) presented a formula that is a linear relationship with respect to the log of time. Qt = Qo [A log (t/to) +1]

(1)

where A= Qo = Qt = to =

A constant depending on soil type Axial capacity at time to Axial capacity at time “t” after driving An empirical value measured in days

Qt/QEOD − 1 = B [log10 (t) + 1]

(5)

This equation is similar to Eq. (1) except that the time for End of Driving (EOD) is taken as 0.1 days (2.4 hours). The factor “B” is similar to the factor “A” in Eq.1. The factor “B” ranges from 1.6 to 3.5.

3. Methodology

In the above equation, to is a function of the soil type and pile size and is the time at which the rate of excess pore-water pressure dissipation becomes uniform (linear with respect to the log of time). The value of to is defined as 0.5 for sand and 1.0 for clay. And the value of parameter “A” is a function of soil type, pile material, type, size, and capacity. The “A” value is presented by 0.2 for sand and 0.6 for clay. 2.2 Svinkin (1996) Svinkin (1996) developed a formula for pile setup based on load test data. Qt = 1.4 QEOD t0.1

upper bound

(2)

Qt = 1.025 QEOD t0.1

lower bound

(3)

2.3 Long et al. (1999) Long et al. (1999) presented a formula with to = 0.01 days, which is modified from Eq. (1). Qt = Qo [A log (t/0.01) + 1]

based on Eq. (1).

(4)

2.4 Svinkin and Skov (2000) Svinkin and Skov (2000) proposed a formula for pile setup

In this paper, Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN) models were developed to predict pile setup for three pile types (pipe, concrete, and H-pile). The MLR analysis examines the data statistically whereas the ANN method is based on artificial intelligence. The objectives of this paper are to: • Collect pile setup data from the authors' files and the published literature. • Develop MLR and ANN models that can accurately predict pile setup. • Compare the performance of the developed MLR and ANN models with four traditional methods.

4. Pile Database A database was compiled from the results of 169 pile dynamic tests and CAPWAP analyses for pile capacity. The data were obtained from the authors’ own files and the published literature. Twenty pipe pile setup data were collected from different projects in Ohio (Khan and Decapite, 2011) and 149 were collected from the published literature. The references used to compile the database are listed in Table 1. The collected data included: pile diameter, driven length, time after installation (t), soil type, effective vertical stress at pile tip,

Table 1. Database References Pile Type Pipe Pile Pipe Pile Pipe Pile Pipe Pile Pipe Pile Pipe Pile Concrete Pile Concrete Pile Concrete Pile Concrete Pile Concrete Pile Concrete Pile Concrete Pile Concrete Pile H Pile H Pile H Pile H Pile Vol. 18, No. 4 / May 2014

Reference Antorena and McDaniel (1995) Thompson et al. (2009) Author’s Own files (Khan and Decapite, 2011) Dover and Howard (2002) Holloway and Beddard (1995) Komurka (2004) Skov and Denver (1988) Preim et al. (1989) Svinkin et al. (1994) Svinkin (1995) Axelsson (1998) Chambers and Kingberg (2000) Hussein et al. (2002) Jongkoo (2007) Fellenius et al. (1989) Samson and Authier (1994) Svinkin et al. (1994) Long et al. (2002) − 1019 −

Location of Tests Florida, USA Mississippi, USA Ohio, USA California, USA California, USA Wisconsin, USA Germany Florida, USA Ohio,USA Ohio, USA Stockholm, Sweden Brisbane, Australia Florida, USA North Carolina, USA Wisconsin, USA Canada Ohio, USA New York, USA

No. of Tests 4 58 20 11 5 6 6 1 19 3 11 1 1 3 5 1 4 2

Bashar Tarawneh and Rana Imam

Table 2. Variables Used in Developing the Models Model Variable Mean Soil type 1.66 Pile Type 1.41 Pile diameter (cm) 55.67 Driven length (m) 24.04 Time (days) 17.66 213.20 Effective vertical stress at pile tip (kN/m2) 1925.90 Qo (kN) 3536.49 Qt (kN)* *Obtained from dynamic load tests and CAPWAP analyses.

Standard Deviation 0.41 0.59 20.16 7.79 33.20 68.80 1439.73 2229.06

initial axial capacity (described as end of driving, Qo), and the axial capacity at time “t” after driving (Qt). The values associated with soil type are 1 for granular materials, 2 for silt-clay materials; others were calculated by considering the percentage of soil type (granular, silt-clay) up to the pile tip. The variables are summarized in Table 2. Three types of piles are considered in this paper: 1. Steel H-piles which are square beams that provide high axial working capacity, displace little soil and are fairly easy to drive. The major disadvantages of H-piles are the high material costs, and corrosion which occurs unless preventive measures are used. 2. Steel pipe piles which could be driven open- or closed-end and may be filled with concrete or left unfilled. Pipe piles are considered friction piles when most of their resistance is derived from skin friction. 3. Precast Concrete piles which are usually pre-stressed to withstand driving and handling stresses. Concrete piles are usually durable and corrosion-resistant and are often used where the pile must extend above the ground.

5. Development of the Multiple Linear Regression (MLR) Model to Predict Pile Setup A comprehensive statistical analysis was conducted to develop MLR model that better predict the pile setup. MLR analysis is a well-known approach which identifies the relationship between a set of dependent and independent variables using statistical methods. The relations between the dependent variable and number of independent variables are in the form: Yi = a0 + a1X1 + a2X2 + a3X3 + …. + akXk + ei

(6)

where, for a set of “i” successive observations, the predicted variable Y is a linear combination of an offset “a0”, a set of “k” predictor variables “X ” with matching “a” coefficients, and a residual error e. The “a” values are commonly derived via the procedure of ordinary least squares. When the regression equation is used in predictive mode, e (the difference between actual and predicted values not accounted for by the model) is omitted because its expected value is zero. It should be noted that in Eq. (6), “Y” represents the pile capacity after time “t” which is denoted as Qt. While X represents the

Min. 1.00 1.00 23.62 4.57 0.03 41.30 200.17 444.82

Max. 2.00 3.00 106.68 47.24 216.00 427.57 5529.14 8705.17

Range 1.00 2.00 83.06 42.67 215.97 386.27 5328.97 8260.35

independent variables (Qo, effective stress at pile tip, pile length, soil type, diameter of pile, time, and pile type). 144 data points were randomly selected to develop the MLR model while the rest of the data (25 data points) were used to test the MLR model. A stepwise MLR analysis was performed to identify the important independent variables that affect the prediction of the pile setup. A Stepwise Iteration (SI) procedure was used where the termination of the independent variables elimination process is based on the t-test and F-test outcomes. The stepwise regression analysis combines the forward and backward stepwise regression methods. It fits all possible simple linear models and chooses the one with the largest F-test statistic value. At each step, a variable is removed if its significance value falls below the threshold. Elimination of insignificant variables gives more accurate forecasts according to Sonmez and Rowings (1998). The process is completed when no more variables outside the model have the required significance level to enter. However, at each stage of the procedure the deletion of early selected independent variables is permitted. In order to eliminate the insignificant variables, the regression statistics used are significance level (P value less than 0.05) and the coefficient of determination (R2). In the MLR model, all the independent variables were quantitative except pile type which is categorical. Categorical data is included in the regression analysis by using dummy variables. The number of Dummy Variables = No. of categories-1. In this case, two dummy variables were created: concrete Pile and H-pile, to explicitly represent these two types. On the other hand, pipe piles were taken as the reference type being the most common in the data set. For concrete piles, the dummy variable “concrete pile” was set equal to 1 and the dummy variable “H-pile” equal to 0. For H-piles, the dummy variable “H-pile” was set equal to 1 and the dummy variable “concrete pile” equal to 0. For pipe piles, both dummy variables were set to 0. Effectively, the pipe pile becomes the reference or default category. It should be noted that the dummy variable (H-pile) was not statistically significant due to the limited number of H-piles in the data set. As for the variable soil type, the values associated were 1 for granular materials, 2 for silt-clay, and others are calculated by considering the percentage of soil type (granular, silt-clay) up to the pile tip. The adequacy of the developed models was assessed in this study using the coefficient of determination, R2, and the standard error of estimate. The R2 represents the proportion of variation in

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Regression versus Artificial Neural Networks: Predicting Pile Setup from Empirical Data

Table 3. Significance of Variables in Each MLR Model Unstandardized Coefficients

Model 1

2

3

4

5

6

Constant Qo Constant Qo Effective Stress Constant Qo Effective Stress Soil Type Constant Qo Effective Stress Soil Type Diameter Constant Qo Effective Stress Soil Type Diameter Time Constant Qo Effective Stress Soil Type Diameter Time Concrete Pile

a 927.986 1.274 -64.759 1.199 5.191 -1887.378 1.318 5.572 945.661 -2238.786 1.162 5.338 783.079 17.750 -2346.144 1.133 4.864 680.359 22.778 9.465 -1825.518 1.068 3.914 586.616 24.717 10.682 -504.421

Std. Error 154.213 0.064 270.358 0.063 1.192 471.759 0.064 1.119 206.580 466.453 0.077 1.081 204.838 5.216 445.984 0.074 1.039 197.295 5.147 2.472 469.971 0.075 1.064 194.878 5.058 2.445 173.690

Standardized Coefficients Beta 0.858 0.808 0.184 0.888 0.197 0.193 0.783 0.189 0.160 0.158 0.763 0.172 0.139 0.203 0.140 0.719 0.139 0.120 0.221 0.158 -0.112

t

P-value (Significance)

6.018 19.915 -0.240 19.133 4.354 -4.001 20.549 4.980 4.578 -4.800 15.105 4.937 3.823 3.403 -5.261 15.354 4.682 3.448 4.425 3.828 -3.884 14.174 3.680 3.010 4.886 4.370 -2.904

0.000 0.000 0.811 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.003 0.000 0.000 0.004

Table 4. MLR Models Summary Model

R

R2

Adjusted R2

Std. Error of the Estimate

R2 Change

0.736 0.735 1089.32648 0.736 1 0.858a 0.768 0.764 1026.35445 0.031 2 0.876b 0.798 0.794 960.62589 0.030 3 0.893c 0.813 0.808 926.25714 0.016 4 0.902d 0.831 0.825 883.85983 0.018 5 0.912e 0.841 0.834 860.97377 0.010 6 0.917f Predictors: (Constant), Qo Predictors: (Constant), Qo, Effective Stress Predictors: (Constant), Qo, Effective Stress, Soil Type Predictors: (Constant), Qo, Effective Stress, Soil Type, Diameter Predictors: (Constant), Qo, Effective Stress, Soil Type, Diameter, Time Predictors: (Constant), Qo, Effective Stress, Soil Type, Diameter, Time, Concrete Pile

the dependent variable that is accounted for by the regression model and has values from zero to one. If it is equal to one, the entire observed points lie on the suggested least square line, which means a perfect correlation exists. In addition, the mean standard square error of estimate measures the accuracy in the predicted values. It was found that pile length and the effective vertical stress at Vol. 18, No. 4 / May 2014

F Change 396.608 18.959 20.955 11.582 14.655 8.434

Change Statistics Degree of Degree of Freedom 1 Freedom 2 1 142 1 141 1 140 1 139 1 138 1 137

Sig. F Change 0.000 0.000 0.000 0.001 0.000 0.004

pile tip are highly correlated with R = 0.97. Therefore, only the effective vertical stress at pile tip was statistically significant in the regression model. Six regression models were developed as shown in Tables 3 and 4. Table 3 provides the standardized and the unstandardized regression coefficients resulting from the stepwise procedure, these coefficients are the weights used for the independent

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6. Development of ANN Model to Predict Pile Setup

Fig. 1. Correlation between Predicted and Measured Qt using the MLR Model-6

variables in the prediction model. Model 6 has the highest adjusted R2 value equal to 0.834 and the least standard error of estimate (860.97). This model included the variables: initial axial capacity (Qo), effective vertical stress at pile tip, soil type, pile diameter, time after installation, and concrete pile type. As summarized in Table 3, MLR Model 6 is presented in Eq. (7) as follows: Qt = – 1825.52 + 1.068Qo + 3.914σ′ + 586.616St + 24.717d + 10682t – 504.421CP where CP = d= Qt = Qo = St = t= σ' =

(7)

Concrete pile type Pile diameter Axial capacity at time “t” after driving Axial capacity at time to Soil type Time after installation Effective stress

Table 4 shows the change in the unadjusted R2 values for all the MLR models. The unadjusted R2 value increases with the addition of terms to the regression model. The amount of change in R2 is a measure of the increase in predictive power of a particular independent variable or variables, given the independent variable or variables already in the model. For example, the effect of soil type on pile setup increases the unadjusted R2 value by 0.031 while the effect of the time increases the unadjusted R2 value by 0.018. It can be noted that the concrete pile type has the least effect on the adjusted R2 value. The MLR model-6 was tested using randomly selected 25 data point. Fig. 1 shows the correlation between the predicted and measured Qt using the developed MLR model-6. It can be noted that the R2 value (0.8) is acceptable to predict the pile setup.

The introduction of Artificial Neural Networks (ANN) was first made by McCulloch and Pitts (1943). Bendana et al. (2008) describe ANN as “massively parallel distributed processor” which can store information taken from a data set that is supplied out of the network. The ANN system consists of three or more layers. The first layer has the input neurons (parameters), while the last layer contains the output. In between are one or more hidden layers, which are for delineating and learning the patterns governing the network’s data. The development of an ANN model requires the determination of model inputs and outputs, division and pre-processing of the available data, the determination of appropriate network architecture, stopping, and model validations. Previous research in the field of pile foundations made use of ANN models. Nejad et al. (2009) developed an ANN model to predict pile settlement based on standard penetration test data. Abu-Kiefa (1998) introduced three neural network models to predict the capacity of driven piles in cohesionless soils. Lee and Lee (1996) utilized neural networks to predict the ultimate bearing capacity of piles. Chan et al. (1995) developed a neural network as an alternative to pile driving formula. Goh (1994, 1995) presented a neural network model to predict the friction capacity of piles in clays. In this study, Neuro-Solutions 6.0 Software was used in creating the neural network models. This software combines a modular design interface with advanced learning procedures, giving the power and flexibility needed to design the neural network that produces the best solution. The same dataset described in the MLR analysis was used to develop and validate the neural network model. The ANN model input variables are: Qo, pile diameter, pile length, soil type, effective vertical stress at pile tip, H-pile type, concrete pile type, and the time after installation. The ANN model output is: Pile capacity after period of time t (Qt) due to pile setup. The data was divided into three sets: training, cross validation, and testing. Seventy percent of the data points were selected for training, 15% were selected for cross validation, and 15% were used for testing the network. The training data points were used to train the network and compute the weights of the inputs. The cross validation computes the error in a test set at the same time that the network is being trained with the training set. The test data points were used to measure the performance of the selected ANN model. It is important that the data used for training, cross validation, and testing represent the same population and the statistical properties (e.g., mean, standard deviation and range) of the data subsets need to be similar (Shahin et al., 2004). Also, ANNs perform best when they do not extrapolate beyond the range of their training data (Flood and Kartam, 1994; Tokar and Johnson, 1999). Accordingly, in order to develop the best possible model, all patterns that are contained in the data need to be included in the training set. Similarly, since the test set is used to determine

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Regression versus Artificial Neural Networks: Predicting Pile Setup from Empirical Data

Table 5. ANN Models with a Single Hidden Layer Model No.

Input Nodes

1 2 3 4

8 8 8 8

Hidden Layer-1 Processing Transfer Elements Function 4 sig 4 tanh 5 tanh 7 tanh

Output Layer Processing Transfer Elements Function 1 sig 1 tanh 1 tanh 1 tanh

Testing Data RMSE

R

846.78 874.23 1000.1 929.2

0.93 0.93 0.91 0.92

Table 6. ANN Models with Two Hidden Layers Model No. 5 6 7

Input Nodes 8 8 8

Hidden Layer-1 Processing Transfer Elements Function 4 tanh 5 tanh 4 Sig

Hidden Layer-2 Processing Transfer Elements Function 4 tanh 4 tanh 4 Sig.

when to stop training, it needs to be representative of the training set and should contain all of the patterns that are present in the available data (Shahin et al., 2002). To accomplish this, several random combinations of the training, cross validation and testing sets were tried until a statistically consistent data set was obtained. The statistical parameters considered include the mean, standard deviation, minimum, maximum and range, as suggested by Shahin et al. (2004). 6.1 ANN Model Architecture A total of eight input variables were included in the ANN model. The output layer has a single node representing the measured value of the pile capacity (Qt) after a period of time (t). Several network structures, with different numbers of hidden layers and nodes in the hidden layer, were trained and tested to find the model with best performing network architecture. Although it has been shown that a network with one hidden layer can approximate any continuous function (Hornik et al., 1989), in this research one and two hidden layers were employed. In order to determine the optimum network geometry, first ANNs with a single hidden layer and different number of nodes in the hidden layer were trained with sigmoid (Sig.) and hyperbolic tangent (tanh) transfer functions for the hidden and output layers. Combinations of number of elements in the hidden layer and types of transfer function that yielded the most accurate predictions of pile setup are shown in Table 5. Then ANNs with two hidden layers with different number of nodes in the hidden layers were trained. The models were trained with sigmoid (Sig.) and hyperbolic tangent (tanh) transfer functions for the hidden and output layers. Combinations of the number of elements in the hidden layers and type of transfer function that yielded the most accurate predictions of pile setup are shown in Table 6. 6.2 Model Optimization Backpropagation neural network algorithms were adopted in this study to develop ANN models that can accurately predict Vol. 18, No. 4 / May 2014

Output Layer Processing Transfer Elements Function 1 tanh 1 tanh 1 Sig.

Testing Data RMSE

R

640.6 950.088 989

0.97 0.92 0.94

pile setup. The weights of the network are adjusted during the training phase to minimize error. In each iteration, the error propagates backward to minimize the error to a desired level. The back-propagation algorithm is used for optimizing the connection weights in this study, whereas the LevenbergMarquardt (LM) algorithm was used as a learning rule. It is one of the most appropriate higher-order adaptive algorithms known for minimizing the Mean Square Error (MSE) of a neural network (Principe et al., 1999). The cross-validation technique was adopted in this study as the stopping criteria, as it is ensures over-fitting does not occur. It was considered that sufficient data was available to create training, testing and validation sets. The training set was used to adjust the connection weights, whereas the testing set measured the ability of the model to generalize. 6.3 Model Validation The performance of the trained model should be validated using data sets that have not been used as part of the learning process. This data set is known as the testing set. The purpose of the model validation phase is to ensure that the model has the ability to generalize the input-output relationships that are contained in the training data (Shahin et al., 2002). The coefficient of correlation, R; the root mean squared error, RMSE; and the mean absolute error, MAE, are the main criteria that are used to evaluate the prediction performance of ANN models. 6.4 ANN Results For the one hidden layer models, Table 5 shows the results of the top performing models. The RMSE values ranged between 846.78 and 1000.1, while the coefficient of correlation, R, values were between 0.91 and 0.93 for the testing data set. Model 1 (with four processing elements in the hidden layer and sigmoid as transfer function for both hidden and output layer) was the best performing among all models. Model 1 had the lowest RMSE value (846.78) and the highest R value (0.93) for the testing data set. Table 6 shows the results of the top performing ANN models with two hidden layers. The RMSE values ranged between 640.6

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Bashar Tarawneh and Rana Imam

Table 7. Amplitude and Offset for the Input Layer Number of Nodes Amplitude ain 1.800 1.800 1.800 0.022 0.042 0.008 0.005 0.000

8 Offset Ofin -2.700 -0.900 -0.900 -1.412 -1.093 -0.900 -1.092 -0.968

capacity increase due to setup.

Fig. 2. Correlation between Predicted and Measured Qt using ANN Model-5

and 989, while the coefficient of correlation, R, values were between 0.92 and 0.97 for the testing data set. On the other hand, Model 5 (with four processing elements in each hidden layer, tanh as transfer function for both hidden layers and the output layer) had the lowest RMSE (640.6); R value for this model was 0.97 for the testing data set. Using the 25 training data points, Fig. 2 shows the correlation between the predicted Qt and measured Qt for Model 5. To summarize, Model 5 was the best performing thus optimal model among all the ANN models. Based on the available data and results, Model 5 was recommended to predict the pile

6.5 ANN Model 5 Figure 3 presents the structure of the developed ANN for Model 5. In this model I1, I2, I3, I4, I5, I6, I7, and I8 represent soil type, concrete pile, H-pile, diameter of pile, pile length, time, effective stress at pile tip, and Qo, respectively. This model has two hidden layers with four nodes in each layer. Tables 7-9, and 10 provide the numerical values of the ANN amplitude, offset, weights and biases. In order to use the developed ANN Model 5 to calculate Qt, below is a four step procedure to calculate Qt: 1. The first step is to calculate the normalized inputs (IN) for the inputs I1 through I8 by using the amplitude (ain) and the offset (ofin) values provided in Table 7 (IN = ain In + ofin). Each sample of data is multiplied by the amplitude and shifted by an offset. The amplitude and offset are often referred to as normalization coefficients. 2. The second step is to calculate inputs and outputs at each node in the first hidden layer (H1, H2, H3, and H4).

Fig. 3. The ANN Structure of Model-5 − 1024 −

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Regression versus Artificial Neural Networks: Predicting Pile Setup from Empirical Data

Table 8. Weight of Inputs to Hidden Layer-1 (winm)* and Bias of Hidden Node (bh1, bh2, bh3, and bh4) wi11 -1.05998 wi21 -0.07875 -0.97818 wi22 -0.36307 wi12 0.53000 wi23 0.58266 wi13 -1.48868 wi24 1.41723 wi14 -1.53115 wi71 1.38235 wi61 0.74676 wi72 0.52149 wi62 -0.76553 wi73 0.65230 wi63 -0.59154 wi74 -0.45018 wi64 winm represents the weight from input n to hidden node m

wi31 wi32 wi33 wi34 wi81 wi82 wi83 wi84

-1.03908 0.66518 0.60286 -0.18830 -0.87905 -1.16152 -0.30891 0.51903

wi41 wi42 wi43 wi44 bh1 bh2 bh3 bh4

0.14078 -1.81114 -0.47063 0.36107 -1.90618 0.48651 -0.00089 -1.08215

wi51 wi52 wi53 wi54

-1.09478 -0.60038 -1.45489 -0.35243

Table 9. Weight of Hidden Layer-1 to Hidden Layer-2 (whnm)* and Bias of Hidden Node (bh5, bh6, bh7, and bh8) wh15 -0.76024 wh25 -0.12555 1.58898 w -0.25653 wh16 h26 -0.87752 wh27 -1.47939 wh17 0.81976 wh28 -0.90719 wh18 whnm represents the weight from hidden n to hidden node m

wh35 wh36 wh37 wh38

-0.78917 1.04953 0.62465 0.34528

wh45 wh46 wh47 wh48

-0.89640 -0.58204 0.76657 -0.32703

bh5 bh6 bh7 bh8

0.86527 -0.78080 0.45322 0.26680

Table 10. Weights of Hidden layer-2 to Output Layer (wo) and Bias of Output Node (bo) wo1 wo2 wo3 wo4 Bo

-0.45505 -1.43763 -0.53964 1.46179 -0.77440

Input at each node in the first hidden layer = Σwinm.IN+bhm (8) Output at each node in the first hidden layer = tanh (Swinm.IN+bhm) (9) 3. The third step is to calculate inputs and outputs at each node in the second hidden layer (H5, H6, H7, and H8). Input at each node in the second hidden layer = Swhnm.HN+bo (10)

Fig. 4. Measured Qt vs. Predicted Qt using Skov and Denver (1988), Svinkin (1996), Svinkin and Skov (2000), and Long et al. (1999) Table 11. Coefficient of Determination for Measured Qt vs. Predicted Qt Prediction Method ANN-Model-5 MLR Svinkin-Upper Svinkin-Lower Skov and Denver Svinkin and Skov Long

Output at each node in the second hidden layer = tanh (Swhnm.HN+bo) (11) 4. The last step is to calculate the inputs and outputs at the node in the output layer (O). Input at the Output layer = Swoi.HN+bhm

(12)

Output = tanh (Swoi.HN+bhm )

(13)

Coefficient of Determination, R2 0.94 0.8 0.75 0.75 0.69 0.69 0.65

7. Numerical Model In this section, the testing data set was used to compare the measured Qt against the predicted Qt from both the optimal ANN model (Model 5), and the MLR model, as well as the empirical formulae presented in this paper. As mentioned earlier, this data set was neither included in the training data of the ANN nor in the development of the MLR model. Plots of measured versus predicted Qt are shown in Fig. 4 for the optimal ANN Model 5, Vol. 18, No. 4 / May 2014

MLR model, the Skov and Denver (1988), Svinkin (1996), Svinkin and Skov (2000), and Long et al. (1999) formulae. It can be seen that the optimal ANN model satisfactorily predicted the measured data and significantly outperformed the examined empirical formulae. Table 11 shows the coefficient of determination, R2 for the measured Qt versus the optimal ANN model, MLR model, the Skov and Denver, Svinkin, Svinkin and Skov, and Long et al.,

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Bashar Tarawneh and Rana Imam

Table 12. Reliability of the Developed Models using Static Load Test Data Static Load Test Data

ISU4 1.70 0.00 1.00 25.00 17.00 16.00 324.00 422.00 685.00

Ng (2011) ISU5 2.00 0.00 1.00 25.00 16.77 9.00 288.25 632.00 1081.00

Soil Type Concrete Pile H-Pile Diameter (cm) Length (m) Period (days) Effective Stress (kPa) Qo (kN) Qt (kN)* Predicted Qt (kN) 829.00 1298.00 Qt using ANN model-5 1679.40 1864.97 Qt using MLR (Estimated/Measured) Qt Ratio for: (ANN model-5/SLT) 1.21 1.20 (MLR/SLT) 2.45 1.73 *Qt obtained from static load test is based on the Davisson’s criterion

formulae. It can be seen that the optimal ANN model has the highest R2 value.

8. Verification of the Developed Models using Static Load Test Data To secure a higher reliability of the developed models, Static Load Tests (SLT) data were used to predict Qt using the ANN and MLR models. The static load test is considered an expensive and time-consuming approach for testing piles. A total of six static load tests (three pipe piles and three H-piles) with setup data were collected from the literature, Ng (2011) and the authors’ own files as shown in Table 12. The six static load tests were performed following the ASTM D 1143: Quick Load Test Method. It is noted that the ANN Model 5 overestimated Qt by 17% to 21% for the H-piles and underestimated Qt by 12% to 17% for the pipe piles. However, the MLR model over predicted Qt for the H-piles by 73% to 145% and by 5% to 54% for the pipe piles. It can be concluded that the ANN model outperformed the MLR model and can be used to predict pile setup satisfactorily.

Authors Own Files

ISU8 1.65 0.00 1.00 25.00 16.00 15.00 305.00 557.00 721.00

2.00 0.00 0.00 35.66 16.76 5.60 250.00 591.61 1230.34

1.75 0.00 0.00 40.54 40.00 4.00 567.00 1080.92 1598.00

1.65 0.00 0.00 30.48 4.57 2.10 85.00 907.44 1160.99

842.00 1709.20

1085.00 1899.32

1333.00 3619.43

970.70 1220.04

1.17 2.37

0.88 1.54

0.83 2.26

0.84 1.05

A back-propagation neural network was used to evaluate the feasibility of ANNs to predict the pile axial capacity increase due to setup. A database containing 169 case records of field measurements of pile setup was used to develop and verify the model. The results indicated that back-propagation neural networks have the ability to predict the pile setup with an acceptable degree of accuracy (R2 = 0.94, RMSE = 640.6). The result of this study indicated that ANNs yielded more accurate pile setup predictions than those obtained from the traditional methods examined: Skov and Denver (1998), Svinkin (1996), Svinkin and Skov (2000), and Long et al.’s (1999) formulae. Six Static Load Tests (SLT) data were used to predict Qt using the ANN and MLR models. The ANN Model 5 overestimated Qt by 17% to 21% for the H-piles and underestimated Qt by 12% to 17% for the pipe piles. However, the MLR model over predicted Qt for the H-piles by 73% to 145% and by 5% to 54% for the pipe piles. It can be concluded that the ANN Model 5 outperformed the MLR model and can be used to predict pile setup satisfactorily.

References 9. Conclusions This paper presented the results of a study that was conducted to evaluate the use of MLR and ANNs to develop models that are able to accurately estimate pile setup. A comprehensive statistical analysis was conducted to develop MLR model that better predict pile setup. Pile diameter, driven length, time after installation (t), soil type, the effective vertical stress at pile tip, the initial axial capacity (described as end of driving, Qo) and the axial capacity at time “t” after driving (Qt) appeared as significant independent variables (model predictors) to predict pile setup.

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