Precise forecasting of scour depth downstream of flip bucket spillway through data-driven models

Abstract

Flip-bucket spillways are utilized in hydraulic engineering to diminish the kinetic energy of flowing water by redirecting the flow jet into the air. In the downstream stailing basin with low tail-water, sediment particles movement results in scour hole formation, posing a threat to spillway stability. The accurate prediction of scour hole depth is a crucial area of the present research work. This study endeavors to employ four data-driven models (DDMs), namely Support Vector Machine (SVM), Gene Expression Programming (GEP), Multilayer Perceptron (MLP), and Multivariate Adaptive Regression Splines (MARS), in combination with five selected empirical equations. The objective is to accurately predict scour depth utilizing field-collected data from site number 84. Relative scour depth, dsH1, was simulated based on the readily extracted parameter i.e. Froude number, Fr=qgH13. The evaluation of model performance was conducted using fundamental metrics, including root mean square error (RMSE), coefficient of determination (R2), mean average error (MAE), and the maximum value of the developed discrepancy ratio (DDRmax). Among the DDMs, the MARS model demonstrated superior performance in both the training and testing phases. In the training phase, it yielded metrics (RMSE = 0.08665, MAE = 0.05714, R2 = 0.99169, DDRmax = 4.519), and in the testing phase, it produced metrics (RMSE = 0.0252, MAE = 0.0170, R2 = 0.09933, DDRmax = 9.144). This exceptional performance of the MARS model surpassed the initially selected (Wu, 1973) [1] experimental model, which exhibited metrics (RMSE = 0.39667, MAE = 0.17463, R2 = 0.96172, DDR = 1.428). The evaluation indices conclusively establish the MARS method's absolute superiority over the experimental approach proposed by Wu (1973) [1].