Prediction of Relative Length of Hydraulic Jump Using Machine Learning Techniques in Rough Sloping Surfaces

Abstract

Accurate prediction of the relative length of a hydraulic jump (Lj/d1) is essential for the safe and economical design of energy dissipation structures in open channels. In rough sloping channels, this prediction becomes challenging due to strong nonlinear interactions among inflow Froude number (Fr1), bed roughness height (h), and channel slope (θ), which are inadequately represented by conventional empirical equations. The objective of this research is to develop robust ML models for predicting Lj/d1 under combined rough and sloping bed situation and to find the most efficient modeling approach. The study utilized 452 experimental data consisting extensive range of Fr1 (2.49 to 7.62), h (0 to 30 mm), θ (0° to 6°). Four ML models such as ANN, RF, AdaBoost, and CatBoost were trained using 70% of the experimental data and tested on the remaining 30%. Model effectiveness was analyzed through graphical assessment, statistical evaluation, rank analysis, and SHapley Additive exPlanations based sensitivity analysis. Results demonstrated that all models attain high predictive accuracy; however, CatBoost performs better than others with excellent generalization, obtaining R² values of 0.9998 and 0.9952, MARE values of 0.0047 and 0.0201 during training and testing of experimental data, respectively. SHAP analysis validates Fr1 as the predominant parameter, followed by surface roughness and bed slope. The novelty of this research lies in the integrated application and comparison of multiple ML techniques, particularly CatBoost, for predicting hydraulic jump length in the combined rough sloping scenario, providing an accurate, interpretable, and practical framework for hydraulic engineering applications.