Comparative Study on the Machine Learning and Regression-Based Approaches to Predict the Hydraulic Jump Sequent Depth Ratio

The hydraulic jump phenomenon plays a significant role in dissipating the energy of the upstream current in either natural or artificial waterways. River's bed roughness is defined as a key parameter that affects the characteristics of the hydraulic jump. In this study, a non-linear regression algorithm was developed to predict the sequent depth ratio of hydraulic jumps over a smooth and rough bed surface using the experimental hydraulic data extracted from the previous studies. Four popular machine learning techniques, known as adaptive network-based fuzzy inference system (ANFIS), ANFIS-Particle Swarm Optimization (ANFIS-PSO), bayesian model averaging (BMA), least absolute shrinkage and selection operator (LASSO), are applied to check the accuracy of the proposed algorithm. The dimensional analysis and Gamma Test model are used to select the effective parameters on the hydraulic jump. In this study, four major parameters named the roughness height (k(s)), hydraulic radius (R), velocity and Froude number at the upstream of the hydraulic jump control volume were selected as more effective parameters. To compare the performance of the models in prediction of both sequent hydraulic depths, the coefficient of determination, root mean square error (RMSE), mean error, Mean Absolute Error and Nash-Sutcliffe efficiency (NSE) were calculated in both training and testing subsets. It is shown that the proposed model, along with two other non-linear methods, ANFIS and ANFIS-PSO, predicted the hydraulic jump sequent depth ratio more accurately compared to the linear regression techniques, BMA and LASSO. However, the statistical measures show an acceptable accuracy for the linear regression techniques. The results show that the proposed model increases the correlation between observed and predicted values up to 0.987 and decreases the RMSE to 0.324. Simultaneously, the last two linear techniques have RMSE, correlation coefficient 0.333 and 0.98, respectively. Finally, a new non-linear formula addressing the hydraulic jump sequent depth ratio over smooth and rough beds have been proposed. A comparison between the resulted formula of the present study with the previous studies proves the accuracy of the developed equation. Moreover, a dimensionless primary roughness coefficient is presented as a non-linear function of the roughness height (ks) and hydraulic radius (R) parameters.