Predicting equilibrium scour depth around non-circular bridge piers with shallow foundations using hybrid explainable machine learning methods

• Hybrid models using metaheuristics and ANNs enhance scour prediction accuracy. • Optimized models show significant error reduction for various pier shapes. • Pier width is identified as the most influential factor in scour depth estimates. Scouring around bridge piers is a critical concern, as the risk of bridge failures poses significant economic and safety threats to the public. Traditional models often struggle to accurately estimate the equilibrium scour depth ( d eq ) at bridge piers due to the complexity of scour processes and their reliance on simple regression methods. This study combines two metaheuristic optimization techniques—Siberian tiger optimization (STO) and brown-bear optimization algorithms (BOA)—with artificial neural networks (ANNs) to enhance d eq prediction accuracy for both round- and sharp-nosed piers using both field and laboratory data. The findings indicate that BOA and STO effectively optimize ANN hyperparameters, resulting in improved prediction accuracy. Furthermore, both BOA–ANN and STO–ANN outperformed empirical equations and other machine learning techniques. An explicit equation was also derived from the BOA–ANN model. The influence of independent variables on d eq was further examined using SHAP, revealing that pier width has the greatest impact on d eq estimates.