Metaheuristic Optimized ANFIS Model for Data Driven Prediction of Scour Depth Downstream of Ski Jump Spillways

Accurate estimation of scour depth downstream of ski‑jump spillways is crucial for dam safety and the cost‑effective design of plunge pools, yet it remains challenging due to the highly nonlinear interactions among hydraulic, geometric, and sediment parameters. This study proposes a hybrid predictive model that integrates an Adaptive Neuro‑Fuzzy Inference System with the Harris Hawks Optimization algorithm (ANFIS–HHO) to estimate the relative scour depth. The model was developed and validated using 95 experimental data points from the literature, incorporating five key dimensionless variables derived from dimensional analysis, including a Froude‑type number, relative energy head, relative bucket radius, relative sediment size, and lip angle. A systematic scenario‑based analysis was conducted to fine‑tune the ANFIS–HHO parameters. The optimal configuration achieved excellent performance during training, with a root mean square error of 0.01794, a mean absolute error of 0.01060, and a coefficient of determination of 0.99234. In the testing phase, the model maintained high accuracy with an RMSE of 0.02698, an MAE of 0.02161, and an R² of 0.98725, while the maximum discrepancy ratio remained low, indicating robust generalization. In comparison, conventional nonlinear regression equations provided acceptable but markedly inferior accuracy, with calibration RMSE of 0.73094 and verification RMSE of 0.52440, along with a considerably higher maximum discrepancy ratio. Although the ANFIS–HHO model clearly outperforms the regression approach in predictive capability, the latter offers the advantage of being a transparent white‑box formulation, enabling direct and interpretable estimation for practical engineering applications. The choice between the two models should therefore balance the need for accuracy against the requirement for simplicity and interpretability, depending on the design stage and available data.