Journal of Irrigation and Drainage Engineering

Accurately forecasting energy dissipation is critical to the hydraulic design of stepped spillways. In this study, support vector machine regression (SVR) was applied to estimate the energy dissipation of a stepped spillway. To develop an accurate model, a genetic algorithm (GA) was employed to determine the SVR parameters, including the penalty parameter $C$, insensitive loss coefficient $ϵ$, and kernel constant $\sigma$. Four dimensionless parameters that influence the energy dissipation of stepped spillways, including the relative critical flow depth, drop number, number of steps, and spillway slope, were selected as the input variables in the GA-SVR model. Overall, 216 experimental data points (collected from the literature) were used for energy dissipation prediction. The predicted values of relative energy dissipation yielded root-mean-square error (RMSE), squared correlation coefficient ($R^2$), and mean relative error (MRD) values of 7.1859, 0.9540, and 0.1197, respectively, for the testing data set. Moreover, a back-propagation neural network (BPNN) was developed using the same data set. A detailed comparison of the results indicated that GA-SVR performed better than the traditional BPNN model in predicting the energy dissipation of the stepped spillway; thus, based on these results, the GA-SVR model can be successfully used to predict the energy dissipation of stepped spillways.