Estimating equilibrium scour depth around non-circular bridge piers using interpretable hybrid machine learning models

Scouring at bridge piers is a crucial issue that risks bridge collapses, causing economic losses and endangering public safety. Classic models struggle to accurately estimate equilibrium scour depth (d_se) due to the complex scouring mechanism. This study combines Bayesian optimization (BO) with support vector machine (SVM) and extreme gradient boosting (XGBoost) to improve d_se estimates. These models predict d_se around round-nosed, square, and sharp-nosed bridge piers using field and laboratory data. The results demonstrate that the BO algorithm can effectively optimize the hyperparameters of SVM and XGBoost and ameliorate their d_se estimates. For the square, sharp-nosed, and round-nosed piers, BO–XGBoost achieves the lowest mean absolute error (MAE) of 0.37 m, 0.35 m, and 0.36 m, the lowest root mean square error (RMSE) of 0.52 m, 0.60 m, and 0.56 m, and the highest coefficient of determination (R²) of 0.85, 0.80, and 0.84, respectively. Accurate estimation of d_se is essential to balance safety and affordability of the bridge designs. Underestimating d_se can lead to bridge failure, posing significant safety risks. Conversely, overestimating d_se can result in unnecessary construction expenses. Finally, the impact of independent variables on d_se estimates is analyzed using Shapley additive explanations (SHAP).