Live-Bed Scour Depth Modelling Around the Bridge Pier Using ANN-PSO, ANFIS, MARS, and M5Tree

In the present research, an attempt is made to use four machine learning technique techniques such as artificial neural network combined with particle swarm optimization (ANN-PSO), adaptive neuro-fuzzy inference system (ANFIS), multivariate adaptive regression splines (MARS), and M5Tree machine learning (ML) approaches to model the scour depth. A total of 534 live bed scouring (LBS) experimental and field datasets are collected for bridge pier scouring from the previously published literature, and a gamma test has been performed to identify the best input parameter combination. A total of 36 combinations were tested in the gamma test, five distinct input combinations such as pier width to flow depth (b/y), approach flow velocity to sediment incipient velocity (V/V_c), critical Froude number (F_rc), pier width to median sediment size (b/d₅₀), geometric standard deviation of bed material (σ_g) were selected based on the lowest gamma value and V_ratio. The developed models have been validated using field datasets of Pearl River, Mississippi, USA, by Mueller and Wagner (2005) and Ganga River, Patna, India, by Kumar and Singh (2022) and compared with six other existing scour depth predictive models. Results indicate that the proposed M5Tree scour depth prediction model (R² = 0.9196, RMSE = 0.0837) provided better accuracy for all combinations of input variables (b/y, V/V_c, F_rc, b/ d₅₀, σ_g) compared to other ML models. The developed M5Tree model was successfully applied to the field condition for Ganga River, Patna, India and Pearl River, Mississippi, USA, and the mean absolute percentage error (MAPE) value is found to be less than 12% and the coefficient of determination (R²) more than 0.98.