Estimation of clear-water scour depth around bridge piers using machine learning techniques

Four machine learning (ML) techniques (artificial neural network with particle swarm optimisation (ANN–PSO), adaptive neuro-fuzzy inference system (ANFIS), multivariate adaptive regression splines (MARS) and M5 Tree) were used to model scour depth around bridge piers under clear-water scour (CWS) conditions. A total of 912 datasets collected under experimental and field conditions were compiled from published literature. The most influential input parameter combinations were identified using the gamma test. Among 37 combinations involving the pier width to flow depth ratio (b/y), approach velocity to critical velocity ratio (V/V_c), critical Froude number (Fr_c), pier width to median sediment size ratio (b/d₅₀) and sediment gradation (σ_g), the optimal combination was selected based on minimum gamma and V_ratio values. The results indicate that the MARS model achieved superior performance, yielding a coefficient of determination (R²) of 0.942 and a mean absolute percentage error (MAPE) of 0.086, outperforming the ANN–PSO, ANFIS and M5 Tree models. The trained models were further validated using independent field datasets from Chemung, Honey Creek, Tanana and Clarks Fork Rivers and compared with ten existing scour prediction equations. The MARS and ANFIS models consistently showed higher accuracy, with R² > 0.90 and MAPE < 33%. The findings demonstrate the superiority of ML approaches over empirical models and identify key parameters governing CWS, supporting reliable bridge scour assessment.