Application of Hybrid AI Models for Accurate Prediction of Scour Depths under Submerged Circular Vertical Jet

This study utilized hybrid artificial intelligence (AI) models, created by integrating the extreme gradient boosting model with particle swarm optimization (XGBoost-PSO) and differential evolution (XGBoost-DE) algorithms. These models are applied to predict scour depths for two conditions, i.e., static (jet is turned off) and dynamic (jet is operational), that are formed due to submerged circular vertical jets. To assess the model’s effectiveness, a comparative analysis is conducted among individual AI models, including support vector regression, adaptive neuro-fuzzy inference system, and traditional regression methods, such as multiple linear regression and multiple nonlinear regression. The results from the cross-validation analysis reveal that the XGBoost-DE and XGBoost-PSO models showcase the highest performance metrics. In the testing dataset, both models achieve a high coefficient of determination (${\mathrm{R}}^2$) of 0.93 for static scour depth prediction. For dynamic scour depth, the XGBoost-DE model achieves an ${\mathrm{R}}^2$ value of 0.88, while the XGBoost-PSO model achieves an ${\mathrm{R}}^2$ value of 0.91, confirming their predictive capabilities. The XGBoost-DE model exhibited low values of root mean square error (RMSE) and mean absolute error (MAE) at 0.199 and 0.09, respectively, in static scour depth prediction. Similarly, the XGBoost-PSO model posted RMSE and MAE values of 0.227 and 0.159 for dynamic scour depths. In a nutshell, the significance of the study includes: (1) the utilization of first-hand hybridized AI models to predict the scour depths under submerged circular vertical jets and (2) the demonstrated superiority of these hybrid models over existing methods. These advancements provide valuable support to civil engineers in accurately estimating scour depths under submerged circular vertical jets.