Analyzing bank profile shape of alluvial stable channels using robust optimization and evolutionary ANFIS methods

Abstract In natural rivers and artificial channels in addition to the channel dimensions (widening, reduction in slope and depth in the channel banks), formed shape profile in the case that the sediment on the banks with no movement (thresholds state) is of considerable importance for engineers. To determine the bank shape profiles, various theoretical, empirical and statistical relations have been provided based on physical and numerical models by different researchers. In this study, a simple model of adaptive neuro-fuzzy inference systems (ANFIS) is combined with two algorithms of differential evolution (DE) and singular value decomposition value (SVD) and the performance of these models to predict the stable shape profiles of the channels is evaluated and compared. In this paper, the main goal is to assess extensively the effect of hybrid models based on optimized algorithms (ANFIS-DE) and multi-objective evolutionary algorithm (ANFIS-DE/SVD) in improvement of performance of ANFIS and ANFIS-DE models, respectively. Accordingly, the results assessment show that all three ANFIS, ANFIS-DE and ANFIS-DE/SVD models are perfectly able to predict shape profiles in accordance with the observed profiles for the threshold channels. Using optimized and evolutionary algorithms has a positive impact on the performance of simple model of ANFIS. As compared to the simple ANFIS model, ANFIS-DE approximately 10.1% and ANFIS-DE/SVD model 7.2% is improved compared to the ANFIS-DE model. The accuracy of ANFIS-DE/SVD model showed better performance as well about 18.6% compared to the simple ANFIS model. Therefore, it can be said that not only DE optimization algorithms have a significant impact on increasing the performance of a simple ANFIS model but also using evolutionary algorithms (ANFIS-DE/SVD) reduce the ANFIS-DE model error accordingly. Polynomial equations of bank profiles proposed by hybrid ANFIS models in the present study can be used in design and implementation of cross section of stable channels