Integrating machine learning and empirical approaches for scour depth estimation at sluice gates: evaluating tree-based models, hyperparameter tuning, and proposing new formulas

Abstract Abstract: Accurate prediction of maximum scour depth (MSD) at sluice gates is critical for guaranteeing the stability and safety of hydraulic systems. Traditional empirical formulas often fail to capture the non-linear interactions between flow dynamics, sediment characteristics, and structural configurations. This study addresses these limitations by leveraging advanced machine learning (ML) techniques, specifically tree-based models, to enhance predictive accuracy. The performance of three tree-based models–Extra Trees (ERT), CatBoost (CAT), and Histogram-Based Gradient Boosting (HGB)–was examined using two hyperparameter tuning methods: Tree-Structured Parzen Estimator (TPE) and Particle Swarm Optimization (PSO). The models underwent 100 simulations to quantify uncertainty and variability in performance metrics. The results indicate that CAT_PSO (optimized with PSO) exhibits superior predictive performance compared to empirical formulas and other ML techniques. CAT_PSO achieved the highest mean CORR (correlation coefficient) of 0.9644 and mean NSE (Nash-Sutcliffe Efficiency) of 0.9272. HGB models demonstrated slightly lower performance compared to CAT and ERT, with higher variability in predictions. Further analysis explored the influence of individual input factors on model performance. The inclusion of more variables, such as tailwater depth and sediment size, generally enhanced model performance. The study also developed new empirical equations for MSD estimation by considering both multiplicative and additive models, progressively incorporating additional input features. These new formulas show improved predictive accuracy over empirical methods, though they still fall short of the performance achieved by the ML models.