Discharge modeling and characteristic analysis of semi-circular side weir based on the soft computing method

In this study, first, support vector machine (SVM) and three optimization algorithms are used to develop a discharge coefficient (C-d) prediction model for the semi-circular side weir (SCSW). After that, we derived the input and output parameters of the model by dimensionless analysis as the ratio of the flow depth at the weir crest point upstream to the side weir diameter (h(1)/D), the ratio of main channel width to side weir diameter (B/D), the ratio of side weir height to side weir diameter (P/D), upstream of side weir Froude number (F-r), and C-d. The sensitivity coefficients for dimensionless parameters to C-d were calculated based on Sobol's method. The research shows that SVM and genetic algorithm have high prediction accuracy and generalization ability; the average error and maximum error were 0.08 and 2.47%, respectively, which were about 95.72 and 60.86% lower compared with the traditional empirical model. The first-order sensitivity coefficients S-1 and global sensitivity coefficients S-i of h(1)/D, B/D, P/D, and F-r were 0.35, 0.07, 0.13, and 0.02; 0.63, 0.25, 0.30, and 0.32, respectively. h(1)/D has a significant effect on C-d. In particular, when h(1)/D < 0.24 and 0.48 < F-r < 0.58, 0.67 < F-r < 0.72, the discharge capacity of the SCSW is relatively large.