Data-driven prediction of critical water velocity for sediment incipient motion using genetic programming and machine learning

The critical mean water velocity for sediment incipient motion (Vc) is a key factor in regulating sediment transport. In this study, a Genetic Expression Programming (GEP) model was developed using 261 experimental datasets, incorporating dimensionless input parameters, including riverbed slope (S), grain size to water depth ratio (d50/h), dimensionless critical shear stress (θc), and dimensionless particle diameter (D*) as input parameters. The predictive performance of the model was assessed by comparing it with five empirical equations and two artificial intelligence models, namely, random forest (RF) and K-nearest neighbors. Model evaluation was conducted using coefficient of determination (R2), root mean square error, and mean absolute error. The results indicate that the GEP model (R2 = 0.9317) and RF model (R2 = 0.9069) exhibit superior predictive accuracy. The sensitivity analysis results demonstrate that in the GEP model, the critical mean water velocity for sediment incipient motion Vc exhibits an approximately linear increase with the dimensionless particle diameter D*, a linear decrease with increasing riverbed slope S, a linearly increases with increasing dimensionless critical shear stress θc, and a U-shaped variation as the grain size to water depth ratio d50/h increases. Partial dependence plots further elucidate the intricate interdependencies among the input variables, while SHapley Additive exPlanations analysis substantiates the dominant influence of d50/h in model predictions, followed by D*, S, and θc.