Estimation of Scour Downstream of a Ski-Jump Bucket Using Support Vector and M5 Model Tree

Abstract

Estimation of scour downstream of a ski-jump bucket has been a topic of research among hydraulic engineers. For estimation of scour downstream of ski jump bucket, several empirical models are in use. In recent years, there has been emphasis to develop models which are capable of producing scour with high accuracy. Use of Artificial Neural Network (ANN) approach to model depth, width and length of scour hole indicates that performance of ANN models is far better than existing empirical models. At present, use of Support Vector Machines (SVMs) and M5 Pruned Model Tree are being considered in different disciplines to further improve upon the performance of ANN models as a potential alternate. With this in view, the present study deals with the development of regression models for computing various parameters of scour hole using SVMs and M5 Model Tree. A comparative evaluation of the performance of ANN versus SVMs and M5 Model Tree clearly shows that SVMs and M5 Model Tree can prove more useful than ANN models in estimation of scour downstream of a ski jump bucket. Further, M5 model tree offers explicit expressions for use by design engineers. Notation dsMaximum depth of scour below tail water level (m); dwTail water depth (m); d50Mean sediment size (m); H1 Head between upper reservoir water level and tail water level (m);

Estimation of scour downstream of a ski-jump bucket using the multivariate adaptive regression splines

“…nique implemented for predicting the scouring depth at downstream of ski-jump bucket. Goyal and Ojha [27] developed the ANN, SVM, and M5 Model Tree for predicting the scour depth at downstream of ski-jump bucket. They considered various scenarios with regard to the a ective parameters during the development of mentioned soft computing techniques.…”

“…In the eld of mathematical modeling, using both of CFD and soft computing techniques was reported by Xiao et al [11].Nowadays, by advancing the soft computing techniques in the most areas related to hydraulic engineering, investigators have tried to use these techniques for predicting the scouring phenomena [12][13][14][15][16][17][18][19], speci cally scour depth at downstream of ip bucket. In this regard, using the Arti cial Neural Networks (ANNs), Genetic Programming (GP), Support Vector machine and M5 Model Tree, Group Method of Data Handling (GMDH), and Adaptive Neuro Fuzzy Inference System (ANFIS) can be mentioned [20][21][22][23][24][25][26][27][28][29][30][31][32]. Based on the reports, the precision of all the soft computing techniques was much more than the empirical formulas.…”

Predicting time-dependent pier scour depth with support vector regression

“…which is most commonly used to nonlinearly map the samples into a high-dimensional space to handle nonlinear problems (Goyal and Ojha, 2011). Moreover, the optimum values of the regularization cost parameter (C), which controls the model's tolerance to error and the size of error insensitive zone (e), need to be determined.…”

“…In the last decade, several studies reported the use of support vector regression (SVR) in civil and water resources engineering related applications (Dibike et al, 2001;Cigizoglu, 2005;Pal and Goel, 2006;Firat and Gungor, 2009;Goel and Pal, 2009;Goyal and Ojha, 2011). The results obtained from these studies showed that the SVR provided better results compared with the neural network approach.…”

Estimation of scour depth below free overfall spillways using multivariate adaptive regression splines and artificial neural networks

“…In order to model scouring, a variety of soft computing schemes have been used in recent years, such as an artificial neural network (ANN) to predict scour below a ski-jump bucket spillway (Azmathullah, Deo, & Deolalikar, 2005) and culvert outlets (Azamathulla & Haque, 2012), classification and regression trees to estimate wave-induced scour around a circular pile (Ayoubloo, Etemad-Shahidi, & Mahjoobi, 2010), an M5 model tree to estimate scour downstream of a ski-jump bucket spillway (Goyal & Ojha, 2011), an adaptive network based on fuzzy systems to determine scour around an arch-shaped bed sill (Keshavarzi, Gazni, & Homayoon, 2012), linear genetic programming to predict scour around a circular pile (Guven, Azamathulla, & Zakaria, 2009), and the group method of data handling to predict scour downstream of a ski-jump bucket spillway (Najafzadeh, Barani, & Hessami Kermani, 2014).…”