Predicting hydraulic jump characteristics in a gradually expanding stilling basin with roughness elements by Sugeno Fuzzy Logic

The hydraulic behavior of a hydraulic jump can be challenging to estimate in order to design gradually expanding stilling basins with roughness elements on the bed. In this study, five dependent variables were identified that comprise: (i) the sequent depth ratio; (ii) the relative length of the jump; (iii) the relative roller length of the jump; (iv) the relative energy dissipation; and (v) the water surface profile. This study undertook a set of formulations based on the regression analysis and Sugeno Fuzzy Logic (SFL) to predict these variables based upon experimental data. Results demonstrate that the trained SFLs predicted the behavior of the dependent variables with the Nash-Sutcliffe Coefficient (NSC) greater than 0.96 in the testing phase. In contrast, the NSC values for the regression models are greater than 0.79. The higher accuracy of SFL is attributed to its capability in managing uncertainty and imprecise data owing to water surface profile oscillations of the hydraulic jump. Also, the results indicate that the prediction residuals for SFL are homoscedastic for all hydraulic parameters investigated except for the water surface profile, which prediction residuals for the regression equations are heteroscedastic.