More accurate stable channel design methods are necessary for analyzing the complex bank profile cross sections of alluvial channels that achieve equilibrium state. This study introduces a new hybrid method that combines an adaptive neuro-fuzzy inference system (ANFIS), Differential Evolution (DE) algorithm and Singular Value Decomposition (SVD) to predict the bank profile of a threshold channel. SVD and DE serve to optimally determine the consequent linear parameters and antecedent nonlinear parameters of the TSK-type fuzzy rules in ANFIS. Moreover, by defining two objective functions and using the Pareto curve, the tradeoff of function is selected as the optimal modeling point. The authors carried out laboratory experiments at four discharge rates of 1.16, 2.18, 2.57 and 6.20 l/s to measure the coordinates of the points in a stable channel boundary profile. The ANFIS-DE/SVD results are compared with the results of a simple ANFIS model and 7 previous research works (based on numerical and experimental models and mathematical principles). The RMSE error index (0.019) of the ANFIS-DE/SVD model is lower than the ANFIS model (0.027), but both models outperform the best available model (CKM, Cao and Knight, 1998) (RMSE=0.120). The ANFIS-DE/SVE model is more accurate for larger y (water surface level) values than the simple ANFIS model. Moreover, the superior performance of the hybrid ANFIS-DE/SVD over the simple ANFIS model is more pronounced at greater discharge rates. ANFIS-DE/SVD estimates the bank profile shape of a stable channel as a third-degree polynomial equation, which can be used to design and implement stable alluvial channels.

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