Uncertainty Assessment of Entropy-Based Circular Channel Shear Stress Prediction Models Using a Novel Method

Abstract

Entropy models have been recently adopted in many studies to evaluate the shear stress distribution in open-channel flows. Although the uncertainty of Shannon and Tsallis entropy models were analyzed separately in previous studies, the uncertainty of other entropy models and comparisons of their reliability remain an open question. In this study, a new method is presented to evaluate the uncertainty of four entropy models, Shannon, Shannon-Power Law (PL), Tsallis, and Renyi, in shear stress prediction of the circular channels. In the previous method, the model with the largest value of the percentage of observed data within the confidence bound (Nin) and the smallest value of Forecasting Range of Error Estimation (FREE) is the most reliable. Based on the new method, using the effect of Optimized Forecasting Range of Error Estimation (FREEopt) and Optimized Confidence Bound (OCB), a new statistic index called FREEopt-based OCB (FOCB) is introduced. The lower the value of FOCB, the more certain the model. Shannon and Shannon PL entropies had close values of the FOCB equal to 8.781 and 9.808, respectively, and had the highest certainty, followed by ρgRs and Tsallis models with close values of 14.491 and 14.895, respectively. However, Renyi entropy, with the value of FOCB equal to 57.726, had less certainty.

Keywords

• water resources
• uncertainty
• shear stress distribution
• circular channel
• entropy
• Shannon