Application of Multivariate Adaptive Regression Splines and Classification and Regression Trees to Estimate Wave-Induced Scour Depth Around Pile Groups

Abstract

Pile groups are employed in sea and ocean environments in order to support marine and offshore structures. Estimation of scour depth around pile groups is one of the important factors in the design of coastal and marine structures. The scour phenomenon is a serious hazard that threats the structural stability of piles. Data-driven methods are being used more and more for the prediction of scour depth around pile groups due to the complexity of the process involved. The previous studies have indicated that the M5 model tree (M5MT) was able to provide more accurate results for wave-induced scour around pile groups compared to the empirical equations. Recently, multivariate adaptive regression splines (MARS) approach has been used as a relatively novel technique of data-driven methods for modeling and approximating nonlinear civil engineering problems. In this paper, MARS models are developed and used for estimation of the scour depth around pile groups in terms of the most influential dimensionless parameters using experimental data and field observations. Moreover, the classification and regression trees (CART) algorithm as a well-known decision tree algorithm is also used for prediction of the wave-induced scour depth around pile groups. The main feature of MARS is to provide a simple linear regression equation that calculates quickly and easily scour depth. In addition, CART presents decision rules without the need for any mathematical calculations, and it predicts scour depth straightforwardly. Statistical indices demonstrate that MARS with the root mean square error (RMSE) = 0.24 and correlation coefficient (CC) = 0.95 is more accurate than two well-known decision tree algorithms, namely M5MT (RMSE = 0.34 and CC = 0.92) and CART (RMSE = 0.35 and CC = 0.90). In addition, the sensitivity analysis declares that the Keulegan–Carpenter number (KC) is the most important variable that affects the scour depth.