Prediction of Scour Hole Geometry Downstream of Ski-Jump Spillways Using Novel Intelligent Computational Machine Learning Models

The ski-jump spillway is an energy-dissipating structure that discharges extra water beyond the dam’s capacity. The scour process occurs below spillways due to the collision of the water jet with high energy. It is critical to acquire information on scour holes to improve the dam’s safety and related components. Machine learning (ML) techniques have successfully demonstrated their effectiveness for modeling scour in hydraulic engineering. The present research considers novel approaches of ML models for estimating the scour hole geometries below ski-jump bucket spillways. This study investigates the capability of two novel feature-engineering approaches, namely Stronger Variable Creator Machine (SVCM) and High Correlated Variables Creator Machine (HCVCM), along with Gene Expression Programming (GEP) and their hybrid forms (SVCM+GEP and HCVCM+GEP), which were employed to predict normalized scour depth, scour length, and scour width below ski-jump spillways. Statistical metrics, graphical analyses, the Rank Mean (RM) method, the cross-validation approach, and U 95 index were used for the evaluation and reliability assessment of the proposed ML models. The results showed that hybrid ML models consistently outperformed individual algorithms. The results indicated that the SVCM+GEP method with R M = 1.83 and 1.50 had the highest performance compared to other methods for the prediction of D s D w and L s D w , respectively. In addition, the HCVCM+GEP method with R M = 1.33 was the best model for the prediction of W s D w . In comparison with the conventional regression-based equations and previously reported ML methods, the proposed hybrid approaches improved the prediction results. In addition, the cross-validation method confirmed the robustness and generalization capability of the suggested hybrid ML models. The superior performance of the hybrid models is attributed to their ability to capture complex nonlinear interactions among hydraulic and geometric variables. The developed SVCM/HCVCM+GEP models provide accurate approaches for predicting scour parameters in hydraulic structures.