Enhancing Prediction of Equilibrium Scour Depth Around Bridge Piers Using Staking Machine Learning Models

Scouring is a natural phenomenon in water bodies that exposes an inevitable risk to hydraulic structures. This study proposes a stacking method for estimating equilibrium scour depth around bridge piers for enhancing sustainable and safety design. It consists of 16 machine learning (ML) models, including advanced ensemble methods, with the top-performing ML model as the meta-learner. The comparative analysis also entails 9 commonly used empirical equations over a dataset consisting of 859 field samples. Moreover, reliability assessments and interpretability techniques were conducted to provide deeper insights into the key factors affecting scour depth. Among individual ML models, ensemble boosting techniques, like CatBoost Regressor (CBR), Gradient Boosting Regressor, and Histogram Gradient Boosting Regressor, performed as the most robust ones, yielding a ranking index higher than 0.91. Furthermore, Gaussian Process Regression and K-Nearest Neighbors (KNN) exhibited similarly high accuracy, coupled with the highest reliability percentages, with training reliabilities both higher than 96% and testing reliabilities of 62.02% and 55.81%, respectively. The results revealed that ML models consistently outperformed empirical methods in predictive performance. Given that CatBoost Regressor outperformed other individual ML models, it was chosen as the foundation for the stacking approach. The results of the stacked CBR model demonstrated superior performance, achieving the best overall results in both training and testing phases. Additionally, the SHapley Additive exPlanations analysis identified the shape correction coefficient and the upstream flow depth divided by the width of the pier as the most effective key factors influencing scour depth, providing actionable insights for infrastructure design. Furthermore, it indicated that KNN and CBR predictions are the most influential components contributing to the accuracy of the staking predictions. The findings suggest that ML-based stacking models, particularly the ensemble boosting methods, offer a reliable and versatile approach for estimating scour depth, thereby contributing significantly to practical applications by offering a reliable methodology to enhance the design, cost-efficiency and safety of bridge structures.