Advancements in predicting scour depth induced by turbulent wall jets: A comparative analysis of mathematical formulations and machine learning models

Abstract

This study examines the scour depth induced by turbulent wall jets and proposes novel mathematical formulations to predict the depth of scouring. Through a comprehensive gamma test, key parameters influencing the scour depth are identified, including the apron length, densimetric Froude number, median sediment size, tailwater level, Reynolds number, and Froude number of the jet. Regression analysis is subsequently conducted to establish relationships between the dependent parameter and the aforementioned independent variables. A comparative analysis is then undertaken between the measured scour depths and those predicted by existing equations from previous studies. Furthermore, predictive models leveraging the support vector machine, artificial neural network with particle swarm optimization, M5 tree algorithm, gene expression programming, and adaptive neuro-fuzzy inference system (ANFIS) are developed using the collected data. Statistical metrics are employed to evaluate the performance of each model and the regression equation. The effectiveness of each model in predicting scour depth is demonstrated. Notably, ANFIS yields a coefficient of determination of 0.809 and a root mean square error (RMSE) of 1.585. Multi-nonlinear regression analysis exhibits a coefficient of determination of 0.752 and an RMSE of 0.421, while the M5 tree achieves a coefficient of determination of 0.739 and an RMSE of 1.874, demonstrating superior performance compared to other machine learning techniques and regression equations employed in this study.