Optimized case-based moment balance machine for predicting scour depth at bridge piers and abutments

Scour is a leading cause of bridge failure, making accurate prediction of scour depth essential for structural safety and risk assessment. This study proposes a novel hybrid machine learning model, ASSA-NSM-MBM, to enhance prediction accuracy, robustness, and transparency. The model is developed based on the moment balance machine (MBM), where traditional back propagation neural network (BPNN)-derived weights are replaced by a similarity index derived from a new similarity measurement (NSM). This mechanism assigns weights based on structural similarity between cases, improving data representation. The artificial satellite search algorithm (ASSA) is further employed to optimize both NSM input weights and MBM hyperparameters. The model was validated using both field and laboratory datasets covering bridge pier and abutment scour conditions. For the pier scour dataset, ASSA-NSM-MBM achieved a reference index (RI) of 0.858, improving by approximately 26.5% over the original MBM (RI = 0.678). For abutment scour, the model attained RI values up to 0.978 across different geometries. Overall, the proposed model consistently outperformed benchmark models, demonstrating strong accuracy, stability, and practical applicability for reliable scour depth prediction.