Advances in Civil Engineering

Volume 2018, Article ID 6490169, 9 pages

https://doi.org/10.1155/2018/6490169

## Optimizing the Prediction Accuracy of Friction Capacity of Driven Piles in Cohesive Soil Using a Novel Self-Tuning Least Squares Support Vector Machine

^{1}Department of Civil Engineering, Petra Christian University, Jalan Siwalankerto 121-131, Surabaya 60236, Indonesia^{2}PT. Sarana Data Persada, Margorejo Indah XIX/35-Blok D-507, Surabaya, Indonesia

Correspondence should be addressed to Doddy Prayogo; di.ca.artep@ogoyarp

Received 31 August 2017; Accepted 17 December 2017; Published 20 March 2018

Academic Editor: Andrea Benedetto

Copyright © 2018 Doddy Prayogo and Yudas Tadeus Teddy Susanto. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This research presents a novel hybrid prediction technique, namely, self-tuning least squares support vector machine (ST-LSSVM), to accurately model the friction capacity of driven piles in cohesive soil. The hybrid approach uses LS-SVM as a supervised-learning-based predictor to build an accurate input-output relationship of the dataset and SOS method to optimize the *σ* and *γ* parameters of the LS-SVM. Evaluation and investigation of the ST-LSSVM were conducted on 45 training data and 20 testing data of driven pile load tests that were compiled from previous studies. The prediction accuracy of the ST-LSSVM was then compared to other machine learning methods, namely, LS-SVM and BPNN, and was benchmarked with the previous results by neural network (NN) from Goh using coefficient of correlation (*R*), mean absolute error (MAE), and root mean square error (RMSE). The comparison showed that the ST-LSSVM performed better than LS-SVM, BPNN, and NN in terms of *R*, RMSE, and MAE. This comprehensive evaluation confirmed the capability of hybrid approach SOS and LS-SVM to modeling the accurate friction capacity of driven piles in clay. It makes for a reliable and robust assistance tool in helping all geotechnical engineers estimate friction pile capacity.

#### 1. Introduction

Deep foundations built through the past years were made either of concrete, steel, or timber piles, which are either driven and precast or bored and cast-in-situ. Driven piles are frequently used in developing countries with a vast array of suburban and rural areas as foundations to support heavily loaded structures, for example, high-rise buildings and bridges. Recently, a variation of driven piles, jack-in piles, has also successfully used as foundations for high-rise buildings in urban areas due to their lower vibration and noise compared to the conventional-driven piles [1].

Despite all the development in the driven piles method, the design of driven piles still heavily relies on semi-empirical methods to estimate shaft resistance (*f*_{s}) and end resistance (*f*_{b}) [1–3]. The *f*_{b} will be negligible, and the large percentage of pile load will be taken by *f*_{s} if there is no bearing layer, that is, driven piles in cohesive soil. Consequently, *f*_{s} that can be provided by the soil is very important in pile design. Up until now, there is no comprehensive assessment of *f*_{s} prediction methods [3]. Efforts were limited to comparing *f*_{s} prediction from various semiempirical methods with results from pile load tests [3–5]. To overcome this limitation, other efforts were dedicated to predicting *f*_{s} through machine learning techniques [6–8].

In civil engineering, machine learning techniques have developed into an important research area. Several studies reveal the advantages of using machine learning techniques in establishing a better predictive model over traditional methods [9–11]. Recently, least squares support vector machine (LS-SVM) has become one of the widely used machine learning techniques in handling variety of complex problems [12–15]. Although acceptable prediction results have been reported, an improper parameter tuning may lessen the learning process of LS-SVM resulting in a lower accuracy. Building a more accurate predictive model can be achieved by optimizing the LS-SVM parameters. This includes a regularization parameter (*γ*) to deal with the trade-off between minimizing model complexity and training error. Also, it includes a kernel parameter (*σ*) of the radial basis function (RBF) which describes the nonlinear mapping between the input space and high-dimensional feature space.

Identifying the optimal parameters is an optimization issue, therefore, many recent studies combine a machine learning technique with a metaheuristic-based optimizer instead of using a sole machine learning [16–21]. Therefore, this research presents a new hybrid prediction method called self-tuning least squares support vector machine (ST-LSSVM) to accurately model the friction capacity of driven piles. The hybrid approach ST-LSSVM combines the techniques of SOS and LS-SVM. While the SOS is used to optimize the *σ* and *γ* parameters of the LS-SVM, the LS-SVM builds an accurate input-output relationship of the dataset by performing as a supervised-learning-based predictor. The total 45 training data and 20 testing data from Goh [6] have been employed to validate the performance of the proposed method. The ST-LSSVM method is further compared with LS-SVM and BPNN and is benchmarked with the previous results from Goh [6] using the coefficient of correlation (*R*), mean absolute error (MAE), and root mean square error (RMSE).

#### 2. The Proposed Self-Optimized Machine Learning Framework

The objective of this proposed hybrid method is to improve the learning abilities of LS-SVM by searching for optimized set of LS-SVM parameters automatically. The collaborative integration between LS-SVM-based regression and SOS facilitates the LS-SVM to accurately determine the complicated relationship behavior between input variables and the output variable of the given historical data. The LS-SVM and SOS are briefly described below.

##### 2.1. Machine Learning Technique: Least Squares Support Vector Machine (LS-SVM)

LS-SVM is first introduced by Suykens and Vandewalle [12] as a modification of the conventional support vector machine (SVM). LS-SVM is used with a least squares loss function which allows for function estimation while reducing computational costs. Where highly nonlinear spaces occur, RBF kernel is chosen as the kernel function in LS-SVM which brings more promising results than other kernels [12, 22]. The following model of interest underlies the functional relationship between one or more independent variables along with a response variable [12, 23]:where , , and is the mapping to the high-dimensional feature space. In LS-SVM for regression analysis, given a training dataset , the optimization problem is formulated as follows:

where are the error variables and denotes the regularization constant.

In the previous optimization problem, a regularization term and a sum of squared fitting errors make for the objective function. For the cost function, this will be similar to the standard procedure with training feedforward neural networks and this is closely related to a ridge regression. However, the primal problem becomes somewhat impossible to solve when becomes infinite dimensional. In this case, the dual problem should be derived after constructing the Lagrangian [12].

The Lagrangian is given bywhere are the Lagrange multipliers. The conditions for optimality are given by

After elimination of *e* and , the following linear system is obtained:where , , and . And the kernel function is applied as follows:

The resulting LS-SVM model for function estimation is expressed aswhere and *b* are the solution to the linear system (5).

The kernel function that is often utilized is RBF kernel. Description of RBF kernel is given as follows:where is the kernel function parameter.

With the *γ* parameter, the imposed penalty (to data points that move away from the regression function) can be controlled. For the *σ* parameter, this will have a direct impact on the smoothness of the regression function. To ensure the best performance of the predictive model, it should be noted that proper setting of these tuning hyperparameters is required.

##### 2.2. Metaheuristic Optimization Algorithm: Symbiotic Organisms Search (SOS)

Developed by Cheng and Prayogo, SOS is a recently developed metaheuristic algorithm that took inspiration from dependency-based interaction normally found among natural organisms and symbiosis [24]. Just like many other metaheuristic solutions, SOS guides the searching process using special operators that use candidate solutions; it looks for organisms containing candidate solutions to find the global solution in the search space; it requires a maximum number of evaluations and other common control parameters; and it preserves the better solutions by using a selection mechanism.

Nevertheless, there are some key differences because SOS does not need algorithm-specific parameters; for example, particle swarm optimization (PSO) relies upon the social factor, inertia weight, and cognitive factor. To tune the parameters, SOS requires no extra work, and this is a huge advantage. With improper tuning of the parameters, there is a possibility that the obtained solutions are found in local optima regions. Since the first development in 2014, SOS has been successfully utilized in solving many optimization problems in various research areas [25–31].

At the beginning, SOS will create a random ecosystem matrix (population) with each problem having a viable candidate solution. For the user, the number of organisms can be entered within the ecosystem, and this is called the ecosystem size. In each row of the matrix, this represents organisms which are the same as individuals in many other solutions. With each virtual organism, a candidate solution is represented alongside the corresponding objective. Once the ecosystem has been generated, the search then begins.

With three clear phases, the idea comes from the most well-known symbioses. In the long term, organisms use them to improve their survival advantage and fitness (Figure 1). Throughout this searching process, there are three ways in which the organisms benefit from interacting with one another. The SOS algorithm adopts greedy selection scheme. Therefore, the updated organisms can replace the current organisms only if their fitness is better. Once one organism has finished all three phases, the best organism can then be updated. All things considered, the phases will form a continual cycle until the stopping criterion has been reached.