Comparison of hybrid deep learning models for estimation of the time-dependent scour depth downstream of river training structures

Submerged weirs, mainly positioned downstream of bridges, play a key role in safeguarding against floods and long-term scour damage. However, the structural stability of these structures could be threatened by local scour holes. This study evaluates five deep learning algorithms—Deep Neural Networks, Convolutional Neural Networks (CNNs), Convolutional Extreme Gradient Boosting (CXGB), convolutional extremely randomized trees regression, and Self-Attention-based Convolutional Neural Network (SA-CNN) in predicting the evolution of scour depth. Using Hyperband and Bayesian optimization, the models were fine-tuned for maximum accuracy. Additionally, this study investigates the impact of two data splitting methods, including random pointwise sampling and case-wise sampling on model performance. Results indicate that the hybrid CXGB and the SA-CNN models outperform other models in terms of accuracy of the estimation of the time-dependent scour depth with R2 = 0.997 in pointwise and R2 = 0.878 in case-wise split strategies, respectively. This not only demonstrates the effectiveness of these sophisticated algorithms in time-dependent scour estimation but also clarifies the effects of various data sampling techniques on model performance. Finally, the contribution of features in provided estimations is discussed utilizing SHapley Additive exPlanations values. Results indicated that the time (T) and the ratio of the flow velocity to critical velocity U0/Uc had the greatest effect on the model outputs, while side slopes indicated a negligible effect on model output compatible with the physics of the problem.