Uncertainty analysis of shear stress estimation in circular channels by Tsallis entropy

Abstract

Accurate prediction of the shear stress distribution is essential for the successful design of stable erodible-bed channels and for the sediment transport studies. Considerable attention in recent years has been given to the estimation of velocity distribution using entropy concept in open channels. Despite the importance of knowledge about shear stress distribution, there are very few studies on the application of the entropy methods for prediction of the shear stress distribution in open channels. The Tsallis entropy has been employed in this study for estimating the shear stress in open channels. In this approach, a pair of mean and maximum shear stresses are used to evaluate the shear stress distribution on the entire channel cross-section. We then calculated the prediction uncertainty of the shear stress obtained from the Tsallis entropy in a circular open channel. Moreover, the distribution of prediction error for the Tsallis approach is examined in two cases, both before and after data normalization. The quantitative results from this uncertainty analysis showed satisfactory results for the Tsallis entropy model for estimating shear stress in the entire section. The 95% Confidence Bounds (CB) are obtained for the shear stress distribution predicted by the model closely match the observed values.