In the current research, a modern learning machine algorithm named “Weighted Regularized Extreme Learning Machine (WRELM)" is implemented for the first time for the simulation of the coefficient of discharge of side slots. For this purpose, an effective variable on the coefficient of discharge of side slots is firstly introduced, then five distinctive WRELM models are produced by it for the estimation of the coefficient. In the next stage, a database is created for verification of WRELM results. it should be mentioned that 70% of the data are utilized for training the WRELM models, while the rest (i.e. 30%) for testing them. After that, the optimal number of hidden layer neurons as well as the best activation function of the WRELM algorithm are chosen. In addition, the best regularization parameter and also the weight function of the WRELM are achieved. By conducting a sensitivity analysis, the most effective variable for the simulation of the coefficient of discharge along with the WRELM superior model is introduced. The WRELM superior model estimates values of the coefficient of discharge with the maximum exactness and the highest correlation. For instance, the estimations of the correlation coefficient and scatter index for this model are computed to be 0.930 and 0.051, respectively. The sensitivity analysis shows that the ratio of the side slot crest height to its length and the Froude number should be considered as the most important input variables. A comparison between the WRELM with the ELM displays that the former works much better. Furthermore, an uncertainty analysis is executed for both models. Eventually, an equation is suggested for the estimation of the coefficient of discharge and a partial derivative sensitivity analysis is performed on it.

可以获得最佳的正则化参数以及WRELM的权函数。通过进行敏感性分析，介绍了用于模拟放电系数的最有效变量以及WRELM高级模型。WRELM上级模型以最大的准确性和最高的相关性估算放电系数的值。例如，此模型的相关系数和分散指数的估计分别计算为0.930和0.051。灵敏度分析表明，应将侧槽波峰高度与其长度的比值和弗洛德数视为最重要的输入变量。WRELM与ELM之间的比较显示，前者的效果要好得多。此外，对两个模型都执行不确定性分析。