More reliable predictions of clear-water scour depth at pile groups by robust artificial intelligence techniques while preserving physical consistency

This paper presents the results of an investigation on scour around pile groups under steady currents using artificial intelligence (AI) models. Namely, EPR (Evolutionary Polynomial Regression), GEP (Gene-Expression Programming), MARS (Multivariate Adaptive Regression Spline), and M5MT (M5 Model Tree) approaches were used to develop nonlinear regression equations for estimating the maximum equilibrium clear-water scour depth. In total, 321 datasets were collected from various literature sources for different pile group configurations also including the gap between piles and pile groups non-aligned with the flow direction. Results through training and testing phases showed that the MARS technique with Index of Agreement (IOA) of 0.984, Root Mean Square Error (RMSE) of 0.483, and Mean Absolute Error (MAE) of 0.250 provides more accurate estimates of the scour depth (normalized by the pile diameter) than EPR (IOA = 0.976, RMSE = 0.579, and MAE = 0.195), GEP (IOA = 0.972, RMSE = 0.628, and MAE = 0.295), and M5MT (IOA = 0.965, RMSE = 0.704, and MAE = 0.259) models. Conversely, the most frequently used literature formulas demonstrate unconvincing efficiency when wide range experimental data are considered. The sensitivity analysis, in terms of Sobol's index, revealed that the ratio U/U-c, between the approach flow velocity, U, and the flow velocity, U-c, at the inception of sediment motion, is the most influential parameter with Total Sobol Index (TSI) of 0.514 and an opposite trend of scour with the ratio m/n (TSI = 0.023), between the number, m, of piles inline with the flow and that, n, of piles normal to the flow, was found