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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.
Highlights
The process of channels widening until you reach equilibrium or stable state is continued in the channels, and the final state of this process causes the threshold channel (Yu1 3 Vol.:(0123456789) 40 Page 2 of 14Applied Water Science (2019) 9:40 banks. Parker (1978) justified the non-uniform shear stress distribution on the banks and channel bed by considering the lift force on the channel banks
Models adaptive neuro-fuzzy inference systems (ANFIS), ANFIS evolved with the use of differential evolution (DE) and hybrid ANFIS-DE/ singular value decomposition (SVD) model by defining two objective functions and using of Pareto curve to predict the shape profile formed in the stable channel banks are designed and evaluated
Review of the results shows that in different flow discharges, all three models are capable of predicting the stable channel profiles accurately and are in good conformity with experimental data
Summary
The process of channels widening until you reach equilibrium or stable state is continued in the channels, and the final state of this process causes the threshold channel (Yu1 3 Vol.:(0123456789) 40 Page 2 of 14Applied Water Science (2019) 9:40 banks. Parker (1978) justified the non-uniform shear stress distribution on the banks and channel bed by considering the lift force on the channel banks. Vigilar and Diplas (1997) by providing a numerical model considered the transition of momentum caused by the turbulence as a function of the flat bed width of the channel. They presented the three-degree polynomial function for shape profile of stable channel. Gholami et al (2018b) for the first time investigated the ability of artificial intelligence (AI) method in prediction of banks shape profile of threshold channels based on different observed datasets using robust gene expression programming (GEP) model They presented a reliable relationship in estimating vertical boundary levels of channel banks with acceptable accordance with observed values
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