Assessment of Data-Driven Models for Modeling the Coefficient of Pressure Fluctuations in a Hydraulic Jump

Pressure fluctuations in a hydraulic jump can prove critical in achieving the safe, economical design of stilling basins. This paper describes the application of data-driven methods and experimental measurements to estimate the dimensionless coefficient of pressure fluctuations ($${C}_{p}^{{\prime}}$$) for forced and free hydraulic jumps in a horizontal channel. White-box data-driven methods, including Multivariate Adaptive Regression Splines (MARS), Gene Expression Programming (GEP), Group Method of Data Handling (GMDH), M5 Model Tree (M5MT), Classification and Regression Tree (CART) method, Stronger Variable Creator Machines (SVCM), Evolutionary Polynomial Regression (EPR), and Multi Expression Programming (MEP), were used to estimate $${C}_{p}^{{\prime}}$$. The methods were evaluated using statistical indices and graphical plots. The results indicated that white-box models perform well in predicting $${C}_{p}^{{\prime}}$$. Two black-box data-driven models were also examined based on an artificial neural network (ANN) and Support Vector Regression (SVR), and both were hybridized with the Particle Swarm Optimization (PSO) algorithm. SHapley Additive exPlanations (SHAP) method and sensitivity analysis were used to assess effective parameters for $${C}_{p}^{{\prime}}$$. Although the accuracy of black-box and white-box models in estimating $${C}_{p}^{{\prime}}$$ is close. Of all the methods considered, the ANN-PSO and SVR-PSO were the best predictive models, achieving the lowest values of Objective Function (OBJ) of 0.0035 and 0.0022 for forced and free jumps, respectively. Our findings highlight the potential of data-driven methods for solving complex nonlinear problems in environmental fluid mechanics.