Abstract
In this study, the entropy concept is employed to estimate the shear stress distribution in a circular channel with flat bed and trapezoidal channel. Using the principle of maximum entropy, the shear stress distribution is derived by maximizing the Tsallis entropy by assuming averaged shear stress as a random variable. The derived shear stress equation can describe the variation of shear stress along the wetted perimeter of channel. The developed model of shear stress distribution is tested with some credible experimental data and is also compared with equations obtained by other researchers based on the Shannon entropy concept. The present model has shown good agreement with the observed data and performed better than the Shannon-based model in both cross-sections with better results of several computed quantitative criteria. The model precision in estimating shear stress in the trapezoidal channel with mean root mean square error (RMSE) of 0.0158 was higher than the circular channel with flat bed with RMSE of 0.0679.
Highlights
The shear stress distribution of a channel influences important benthic processes such as sediment transport, deposition, and channel morphology
The data extracted from the work of Knight and Sterling [6] were used to investigate the feasibility of Tsallis-based shear stress distribution in circular channels
Error (MAE), Percentage of BIAS (PBIAS), the root mean square error (RMSE) of the standard deviation of observation ratio (RSR), and Nash Sutcliffe Efficiency (NSE), respectively, which are given by these expressions: s
Summary
The shear stress distribution of a channel influences important benthic processes such as sediment transport, deposition, and channel morphology. The increasing use of new numerical methods based on a soft computing approach offers an alternative in the determination of shear stress distribution with more time effective The utilization of such approach was successfully conducted to forecast in various hydraulics-related phenomena such as the estimation of sediment transport [14,15,16], mean wall or bed shear stress in rectangular channels with smooth and rough boundaries [12,17,18], and apparent shear stress in compound channels [19]. Bonakdari et al [34] utilized the Tsallis entropy to estimate shear stress distribution in circular, rectangular, and compound channels They presented equations based on maximizing the entropy function that calculated shear stress using Lagrange multipliers, which need to solve a set of explicit relations. Tsallis-entropy based model is compared with the results from Shannon entropy-based equations, which were represented by [25]
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