Prediction of Transverse Shear Stress in a Rectangular Channel Using Shannon Entropy and Support Vector Regression

Abstract

In open channel flow, determining the boundary shear stress and its distribution over the wetted perimeter is a significant problem. The shear stress distribution (SSD) is primarily affected by secondary flows, sediment transport rate, erosion or sedimentation, and geometry of the channels. The presented research uses Shannon entropy and support vector regression (SVR) approach to predict the SSD in rectangular channels (RCs). First, the entropy technique proposed by Sterling and Knight, (2002) is used to construct the probability density function of transverse SSD, and the constant coefficients of density are obtained by comparing experimental results in various aspect ratios. Second, to estimate the transverse SSD in a smooth RC, SVR methods have been used. According to the results of the sensitivity analysis, the aspect ratio B/H is the most essential parameter for SSD estimation. The SVR model performed better when the (b/B), (z/H), and (B/H) parameters were also used as input. For the aspect ratios (B/H) 2.86, 4.51, 7.14, and 13.95, the SVR model, with an average MAE of 0.044 in bed and 0.053 in wall, gives higher accuracy than the Shannon entropy, which has an average MAE of 0.062 in bed and 0.073 in wall for all flow depths. The Shannon entropy overestimates shear stress as compared to SVR. As a result, the costs of construction of channels may be significant.

Keywords

• smooth rectangular channel
• support vector regression (svr)
• shannon entropy
• shear stress transverse distribution