Predicting equilibrium scour depth around circular bridge piers using hybrid machine learning models

Abstract

Accurate prediction of scour depth is essential to bridge design in terms of safety, planning, and cost. Existing empirical methods for predicting scour depth are limited by their reliance on specific datasets and linear assumptions. As a result, these formulas fail to capture the complexities in real-world scour processes. Using a diverse dataset of 841 measurements sourced from 35 laboratory and field studies, this research applies hyperparameter tuning and hybrid machine learning models to predict equilibrium scour depth around circular bridge piers. Grid search (GS), grey wolf optimizer (GWO), and whale optimization algorithm (WOA) are leveraged to optimize support vector regression (SVR) hyperparameters. These optimization techniques are particularly effective in handling nonlinear data patterns typical of pier scour. By applying them in this study, improved model accuracy and adaptability to a complex scour process is achieved. Model performance is evaluated using RMSE, R², and MAE. WOA–SVR demonstrates the highest predictive accuracy, achieving RMSE = 0.03547 m, R² = 0.9267, and MAE = 0.02336 m. All three hyperparameter optimization techniques prove to significantly improve the SVR model in both training and testing phases. A 5-fold cross-validation analysis further confirms the stability and generalization capacity of the enhanced SVR models. Additionally, comparison with established methodologies validates the superior performance of the proposed models over well-known empirical equations.