Application of a hybrid ANFIS with metaheuristic algorithms to estimate the aeration design parameters

Cavitation is a common and complex hydraulic phenomenon on the chute spillways and may cause damage to the structure. Aeration in the water flow is one of the best ways to prevent cavitation. To design an aerator, estimation of aeration coefficient (β), jet length (L/h0), and jet impact angle on chute (tanγ) are important in this study. The potential of a hybrid Adaptive Neuro-Fuzzy Interface System (ANFIS) with metaheuristic algorithms was investigated to estimate the required parameters to design an aerator. The ANFIS was combined with four metaheuristic algorithms, including Differential Evolution (DE), Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). Experimental data and dimensionless parameters were used to develop the proposed hybrid ANFIS models. Three statistical indicators, including Root Mean Square Error (RMSE), Mean Average Error (MAE), and coefficient of determination (R2), were employed to compare the proposed methods with empirical relations. According to the statistical indicators, among the data-driven methods, the ANFIS–DE method had the best prediction in estimating β (RMSE = 0.018, R2 = 0.984, MAE = 0.013), L/h0 (RMSE = 1.293, R2 = 0.963, MAE = 1.082), and tanγ (RMSE = 0.009, R2 = 0.939, MAE = 0.007).