Computational Intelligence in Prediction of Wave Transmission for Horizontally Interlaced Multi-layer Moored Floating Pipe Breakwater

Abstract

Energy dissipation process of Horizontally Interlaced Multi-layer Moored Floating Pipe Breakwater (HIMMFPB) depends on various factors like pipe interference effect, the spacing between the pipes and number of layers. As the effect of all these factors on transmission is not clearly understood, it will be extremely difficult to quantify them mathematically. Furthermore, it is a complex problem, and till now there has not been available a simple mathematical model to predict the wave transmission through HIMMFPB by considering all the boundary conditions, and hence one has to depend on physical model studies which are expensive and time consuming. Computational Intelligence (CI) techniques, such as, Artificial Neural Network (ANN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Machine Regression (SVMR), Genetic Programming (GP) and Genetic Algorithm (GA) have been efficaciously proposed as an efficient tool for modelling and predictions in coastal/ocean engineering problems. For developing CI models in prediction of wave transmission for HIMMFPB, data set were obtained from experimental wave transmission of HIMMFPB using regular wave flume at Marine Structure Laboratory, National Institute of Technology, Karnataka, Surathkal, Mangalore, India. These data sets are divided into two groups, one for training and other for testing. The input parameters that influence the wave transmission Kt  of floating breakwater, such as, relative spacing to pipesS D, relative breakwater widthW L, ratio of incident wave height to water depthHi d, incident wave steepness Hi L are considered in developing CI models for prediction of wave transmission past HIMMFPB. In the present work, five layer pipes with S / D of 2, 3, 4 and 5 are considered. The ANN model is developed for prediction of wave transmission for HIMMFPB. Two network models, ANN1 and ANN2 are constructed based on the parameters which influence the wave transmission of floating breakwater. The input parameters of ANN1 model areW / L , Hi / d and Hi / L . To study over a range of spacing of pipesiv S / D on Kt , an input parameter, S / D is added to form ANN2 model. Training and testing of the network models are carried out for different hidden nodes and epochs. It is observed that the correlation (above 90%) between predicted wave transmission values by the network models and measured values are in good agreement. Furthermore, to improve the result of prediction of wave transmission of HIMMFPB, recently developed technique such as SVMR is used. This technique 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. Support vector machines (SVMs) are 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. Six SVMR models are constructed using kernel functions. In order to study the performance of each kernel in predicting wave transmission of HIMMFPB, SVMR is trained by applying these kernel functions. Performance of SVMR is based on the best setting of SVMR and kernel parameters. Correlation Coefficient (CC) of SVMR (b-spline) model (CC Train = 0.9779 and CC Test = 0.9685) is considerably better than other SVMR models. However, it is noticed that ANN model in isolation cannot capture all data patterns easily. Adaptive neuro-fuzzy inference system (ANFIS) uses hybrid learning algorithm, which is more effective than the pure gradient decent approach used in ANN. ANFIS models are developed to predict wave transmission of HIMMFPB. The performance of the ANFIS models in the prediction of Kt is compared with the measured values using statistical measures, such as, CC, Root mean Square Error ( RMSE ) and Scatter Index ( SI ). All the ANFIS models have shown CCs higher than or equal to 0.9510, with RMSE less than or equal to 0.051074 and SI less than or equal to 0.102296. ANFIS5 model predictions are very realistic when compared with the measured values (CC Train = 0.9723, CC Test = 0.9635). It is also observed that an S D plays an important role to train ANFIS5 model to map an input-output relation. Furthermore influence of input parameters is assessed using Principalv Component Analysis (PCA). It is observed that Hi / L is the least influential parameter Based on the PCA study discarding the least influential parameters, ANFIS6 model is developed. It is observed that the ANFIS models yield higher CCs as compared to that of ANN models. To improve the performance of SVMR and better selection of SVMR and kernel parameters, hybrid genetic algorithm tuned support vector machine regression (GASVMR) model is developed to predict wave transmission through HIMMFPB. Furthermore, parameters of both linear and nonlinear SVM models are determined by GA. The results are compared with ANN, SVMR and ANFIS models in terms of CC, RMSE and SI . Performance of GA-SVMR is found to be reliably superior. CI models can be utilized to provide a fast and reliable solution in prediction of the wave transmission for HIMMFPB, thereby making GA-SVMR as an alternate approach to map the wave structure interactions of HIMMFPB.