Application of Multivariate Adaptive Regression Splines and Classification and Regression Trees to Estimate Wave-Induced
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RESEARCH PAPER
Application of Multivariate Adaptive Regression Splines and Classification and Regression Trees to Estimate Wave‑Induced Scour Depth Around Pile Groups Mehrshad Samadi1 · Mohammad Hadi Afshar1 · Ebrahim Jabbari1 · Hamed Sarkardeh2 Received: 8 April 2019 / Accepted: 24 February 2020 © Shiraz University 2020
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 waveinduced 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. Keywords Regression trees · Multivariate adaptive regression splines · Pile groups · Scour depth · Waves
1 Introduction
* Ebrahim Jabbari [email protected] Mehrshad Samadi [email protected]
Mohammad Hadi Afshar [email protected]; [email protected]
Hamed Sarkardeh [email protected] 1
School of Civil Engineering, Iran University of Science and Technology (IUST), Narmak, P.O. Box 16765‑163, Tehran, Iran
Department of Civil Engineering, Hakim Sabzevari University, Sabzevar, Iran
2
Piles are generally used as supports for structures placed on top of them. When an obstacle such as pile is exposed to waves, currents, or a combination of both in marine and ocean environments, it changes the flow pattern (Sumer et al. 2001). Generally, scour occurs due to the interac
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