The uncertainty of the Shannon entropy model for shear stress distribution in circular channels

Abstract

The shear stress distribution at alluvial stream beds and banks is one of the essential parameters in channel stability analysis. In the current paper, a novel uncertainty analysis method based on the framework of a Bayesian Forecasting System (BFS) is presented to evaluate the Shannon entropy model for prediction of the shear stress distribution in both circular rigid-bed and alluvial-bed channels. The Johnson and Box-Cox transformation functions were applied to select the optimum sample size (SS) and corresponding transformation factor for determining a 95% confidence bound (CB) for the Shannon entropy model. The Shapiro-Wilk (SW) test is applied according to the SS used to evaluate the power of transformation functions in the data normalization. The results show that the error distribution between predicted and experimental shear stress values generated using the Box-Cox transformation is closer to a Gaussian distribution than the generated using the Johnson transformation. The indexes of the percentage of the experimental values within the CB (Nin) and Forecast Range Error Estimate (FREE) are applied for the uncertainty analyses. The lower values of FREE equal to 1.724 in the circular rigid-bed channel represent the low uncertainty of Shannon entropy in the prediction of shear stress values compared to the uncertainty for the circular alluvial-bed channel with a FREE value equal to 7.647.