Genetic algorithm based support vector machine regression in predicting wave transmission of horizontally interlaced multi-layer moored floating pipe breakwater

https://doi.org/10.1016/j.advengsoft.2011.09.026Get rights and content

Abstract

Planning and design of coastal protection works like floating pipe breakwater require information about the performance characteristics of the structure in reducing the wave energy. Several researchers have carried out analytical and numerical studies on floating breakwaters in the past but failed to give a simple mathematical model to predict the wave transmission through floating breakwaters by considering all the boundary conditions. Computational intelligence techniques, such as, Artificial Neural Networks (ANN), fuzzy logic, genetic programming and Support Vector Machine (SVM) are successfully used to solve complex problems. In the present paper, a hybrid Genetic Algorithm Tuned Support Vector Machine Regression (GA-SVMR) model is developed to predict wave transmission of horizontally interlaced multilayer moored floating pipe breakwater (HIMMFPB). Furthermore, optimal SVM and kernel parameters of GA-SVMR models are determined by genetic algorithm. The GA-SVMR model is trained on the data set obtained from experimental wave transmission of HIMMFPB using regular wave flume at Marine Structure Laboratory, National Institute of Technology, Karnataka, Surathkal, Mangalore, India. The results are compared with ANN and Adaptive Neuro-Fuzzy Inference System (ANFIS) models in terms of correlation coefficient, root mean square error and scatter index. Performance of GA-SVMR is found to be reliably superior. b-spline kernel function performs better than other kernel functions for the given set of data.

Highlights

► In the present study GA-SVMR model is developed. ► This model predicts Kt of HIMMFPB. ► The performance of GA-SVMR models is compared with ANN and ANFIS models. ► GA-SVMR model with b-spline kernel function perform better than ANN and ANFIS models. ► It can be used to provide a fast and reliable solution in predicting Kt of HIMMFPB.

Introduction

Floating breakwaters are well accepted in recent years because of their basic advantages, such as, flexibility, easy mobilization, installation, and retrieval. The system can be fabricated in land, towed to the site, and installed along any desired alignment with ease. In addition, they have several desirable characteristics, such as, comparatively small capital cost, adoption to varying harbour shapes and sizes, short construction time and freedom from silting and scouring. Floating breakwaters could also be utilized to meet location changes, extent of protection required or seasonal demand. They can be used as a temporary protection for offshore activities in hostile environment during construction, drilling works, salvage operation, etc. Hence, it is necessary to study a detailed investigation of proposed floating breakwater.

Several researchers in the past have carried out experimental and numerical investigations on different types of floating breakwaters, such as, Horizontal, sloping, A-type, Y-type, Cage, Pontoon, Tires, Pipes [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11]. However, there is a lack of a simple mathematical model to predict breakwater performance characteristics, such as the transmission coefficient, which is defined as the ratio of the transmitted wave height past the breakwater to the incident wave height on the breakwater. It is also found that most of the numerical methods have been attempted on simple box-type rectangular floating breakwaters or spar buoy floating breakwaters. These studies are carried out considering a floating breakwater in basic form with some assumptions common in hydrodynamics, which shows less improvement. Till now, there has not been available a simple mathematical model to predict a wave transmission through floating breakwaters by considering all the boundary conditions. Also, for floating pipe breakwaters the energy dissipation process depends on various other factors like pipe interference effect, the spacing between the pipes and number of layers. As the effect of all these factors on transmission and forces in the moorings is not clearly understood, it will be extremely difficult to quantify them mathematically. Still it is a complex problem.

Computational intelligence techniques, such as, Artificial Neural Networks (ANN), Fuzzy logic (FL), Genetic Programming (GP), Support Vector Machines (SVMs) or combinations of these techniques are successfully used to solve complex problems associated with coastal/ocean engineering. Among these techniques, ANN is widely used in coastal/ocean engineering to predict ocean wave parameters like wave height, wave period, impact wave force [12], [13], [14], [15]. The most significant features of neural networks are the extreme flexibility due to learning ability and the capability of non-linear function approximations. This has made ANN very popular in recent years, and further this technique has provided promising results in prediction of tidal levels [16], damages to coastal structures [17], depth of eroded caves in a seawall [18], seabed liquefaction [19], storm surges [20], etc. According to Shahidi and Mahjoobi [21] ANNs are not as, transparent as, semi-empirical regression based models. In addition, neural network approach needs to find network parameters, such as, number of hidden layers and neurons by trial and error, which is time consuming. To overcome the problems inherent in ANN training procedures Jeng et al. [19] adopted the concept of genetic algorithm based training of ANN models, which provided accurate results for determining maximum liquefaction depth in a real world application. It is also noticed that apart from improving the performance of ANN, computational effort and time needed for training and testing the model is significantly reduced compared to traditional methods [17].

When the performance of ANN alone is poor in mapping input–output relation, many researchers developed hybrid models by combining ANN with fuzzy system, ANN with numerical wave modeling [22], [23], [24], adaptive neuro-fuzzy inference system by Sylaios et al. [23] for wind wave modeling, model trees by Shahidi and Mahjoobi [21] for prediction of significant wave height, etc., for example. ANN is a low level computational structure that performs well when dealing with raw data. The pure feed-forward back propagation learning process could easily be trapped into the local minima.

Recently fuzzy inference systems have become popular in solving complex engineering problems and are widely used in coastal/ocean engineering. However, fuzzy systems lack the ability to learn and cannot adjust themselves. Inspired by the idea of basing the fuzzy logic inference procedure on a feed forward network structure, Jang [25] proposed a fuzzy neural network model – the Adaptive Neuro-Fuzzy Inference System (ANFIS), which is a five-layer feed-forward neural network, which includes fuzzification layer, rule layer, normalization layer, defuzzification layer and a single summation neuron. It is a hybrid neuro-fuzzy technique that brings learning capabilities of neural networks to fuzzy inference system. An ANFIS uses a hybrid learning algorithm that combines the least-squares method and gradient descent principle [25], [26]. This hybrid model attracted many researchers to solve complex problems associated with coastal/ocean engineering [22], [27], [28], [29]. Ozger and Sen [30] have adopted dynamic fuzzy approach to identify the effect of wind speed on wave characteristics variations in ocean wave generating system. Bakhtyar et al. [31] have concluded that the ANFIS model is more flexible than the FIS model, with more options for incorporating the fuzzy nature of the real world system. Sylaios et al. [23] have used Takagi–Sugeno [32] rule based fuzzy inference system for forecasting wave parameters based on the wind speed, direction and the lagged wave characteristics. They used subtractive clustering method to identify the initial and final antecedent fuzzy membership functions. Yagci et al. [33] have used fuzzy logic method in breakwater damage ratio estimation. Erdik [34] has applied fuzzy logic approach in design of conventional rubble mound structures. Apart from above computational intelligence techniques, many authors have used various new approaches to solve complex coastal engineering problems like genetic programming by Gaur and Deo [35] for real time wave forecasting, Guven et al. [36] for prediction of circular pile scour.

SVMs are the recently developed learning techniques that have gained enormous popularity in the field of classification, pattern recognition and regression. SVM works on structural risk minimization principle that has greater generalization ability and is superior to the empirical risk minimization principle as adopted in conventional neural network models. Han et al. [37] applied SVM for flood forecasting, Radhika and Shashi [38] for prediction of atmospheric temperature, Msiza et al. [39] used ANN and SVR for water demand prediction, Rajasekaran et al. [40] developed a Support Vector Machine Regression (SVMR) model for forecasting storm surges. They compared these results with numerical methods and ANN, which indicated that storm surges and surge deviations are efficiently predicted using SVMR. According to Mahjoobi and Mosabbeb [41], SVM creates a more reliable model with better generalization error, in comparison to ANN, they also reveal that SVMs do not over-fit, while ANNs may face such problem and need to deal with it.

Soft computing tools are used for other applications as discussed above. However, it is observed that there are hardly any applications of SVMs on wave transmission of floating breakwater. This fact leads us to use SVM models in this work. In the present paper, the performance of GA-SVMR models for predicting wave transmission coefficient of HIMMFPB is investigated. GAs are used to optimize the SVMR and kernel parameters. Results of GA-SVMR models are compared with that of ANN and ANFIS models.

The paper is organized as follows: Section 1 starts with literature associated with floating breakwaters and applications of soft computing techniques in coastal engineering. Section 2 details wave transmission of floating breakwater and experimental HIMMFPB. Fundamentals of SVMR, GAs for parameter selection and proposed GA-SVMR are detailed in Section 3. Results and discussion are described in Section 4. Conclusions is presented in Section 5.

Section snippets

Wave transmission of floating breakwater

The design of floating breakwater is based on the principle that the wave energy is concentrated at the surface in deep water and the same energy is concentrated at below the surface in shallow water, which is to be dissipated. Therefore different types of floating breakwaters like Box, Pontoon, Mat, Tethered float and Pipe are becoming popular. The basic concept by which floating breakwater reduces wave energy include reflection, dissipation, interference and conversion of the energy into

Fundamentals of Support Vector Machine Regression (SVMR)

Vapnik [46] proposed the Support Vector Machines (SVMs), which is based on statistical learning theory. The basic idea of support vector machines is to map the original data x into a feature space with high dimensionality through a non-linear mapping function and construct an optimal hyper-plane in new space. Hence, given a set of data S={(xi,di)}i=1N, where xi is the input data set, di is the desired result, and N corresponds to the size of the data set. Then, according to Smola and Scholkopf

Results and discussion

To study the effectiveness of the approach, statistical comparison of measured and predicted values of Kt, correlation coefficient (CC) is used, which is defined asCC=i=1N(Ktmi-Ktm¯)(Ktpi-Ktp¯)i=1N(Ktmi-Ktm¯)2×i=1N(Ktpi-Ktp¯)2where Ktmi and Ktpi represents the measured and predicted wave transmission coefficient, respectively, Ktm¯ and Ktp¯ are the mean value of measured and predicted observations, N is the number of observations. Higher the CC value better is the agreement between the

Conclusions

An application of hybrid genetic algorithm tuned support vector machine regression for prediction of wave transmission for HIMMFPB is presented in this paper. Our proposed model optimizes SVMs and kernel parameters simultaneously. The performance of GA-SVMR models is compared with ANN and ANFIS models. The results obtained shows that GA-SVMR with b-spline kernel functions performs better than ANN and ANFIS models.

The forecasting performance of GA-SVMR appears to be highly influenced by the

Acknowledgements

The authors are grateful to the Director, and Head, Department of Applied Mechanics and Hydraulics, NITK, Surathkal, India for support and encouragement provided to them and for permission to publish the paper. Thanks are also due to Ministry of Earth Sciences, GOI for sponsoring the project on HIMMFPB at NITK, Surathkal, India.

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