Embedded fuzzy-based models in hydraulic jump prediction

This study aims to evaluate the learning ability and performance of five meta-heuristic optimization algorithms in training forward and recurrent fuzzy-based machine learning models, such as adaptive neuro-fuzzy inference system (ANFIS) and RANFIS (recurrent ANFIS), to predict hydraulic jump characteristics, i.e., downstream flow depth (h2) and jump length (Lj). To meet this end, the firefly algorithm (FA), particle swarm algorithm (PSO), whale optimization algorithm (WOA), genetic algorithm (GA), and moth-flame optimization algorithm (MFO) are embedded with the fuzzy-based models, which represent the main contribution of this study. The analysis of the results of predicting hydraulic jump characteristics shows that the embedded ANFIS and RANFIS models are more accurate than the empirical relations proposed by the previous researchers. Comparing the performance of the embedded RANFISs and ANFISs methods in predicting Lj represents the superiority of the RANFIS models to the ANFISs. The results of the sensitivity analysis show that among the input independent parameters, flow discharge (Q) is the most important factor in predicting downstream flow depth in weak, oscillating, and steady hydraulic jumps (1.7 < Froude number < 9), while the upstream flow depth (h1) is more important than the other input parameters in strong hydraulic jumps (Froude number > 9).