Prediction of the hydraulic jump length on sloping rough beds using meta- heuristic neuro-fuzzy model and differential evolution algorithm

Generally, Hydraulic jumps usually happen at the downstream of hydraulic structures like ogee spillways. In addition, one of the parameters affecting the proper design of stilling basin is calculation of the hydraulic jump length. In this study, a hybrid method (ANFIS-DE) was proposed for modeling hydraulic jumps on sloping rough beds for first time. This approach forecasts values of the jump length by combining the Adaptive Neuro-Fuzzy Inference System (ANFIS) and the Differential Evolution (DE) algorithm. First, the variables affecting the hydraulic jump length including the ratio of bed roughness, the Froude number, the ratio of sequent depths and the bed slope were identified. Then, by combining the input parameters, five different numerical models were introduced. Furthermore, the k-fold cross validation (k=4) was utilized so as to verifying the numerical models. The results of the analysis of different numerical models indicated that the model with four input parameters (superior model) simulated the length of the hydraulic jump with higher accuracy. For the best model, the mean absolute percent error (MAPE), the correlation coefficient (R) and the root mean square error (RMSE) were predicted 4.875, 0.978 and 0.807, respectively. Finally, two parameters including the ratio of sequent depths and the Froude number were identified as the most important parameters in modeling the hydraulic jump length on sloping rough beds.