In this paper, a novel weighted regularized extreme learning machine (WRELM) was used for the first time to simulate the scour depth around J-, I- and W-shaped stone weirs in curved canals. In the first step, dimensionless parameters affecting the scour depth around stone weirs were detected. Then, six WRELM models were developed using these parameters. It is worth mentioning that three different experimental models were utilized for verifying the WRELM models. Moreover, 70% of the experimental data were used to train the models and the remaining 30% to test them. After that, the number of neurons existing within the hidden layer was chosen to be 13. Then the best activation function of the WRELM model was selected. The optimal regularization parameter was also found for this activation function. Conducting a comprehensive sensitivity analysis in the next step detected the best WRELM model, as well as the most influencing input variables. The results of the superior model were compared with the regularized extreme learning machine (RELM) and extreme learning machine (ELM) models to prove the noticeable superiority of the WRELM. Furthermore, a formula was proposed to compute the scour gap around stone weirs with different shapes situated in curved canals. Finally, the sensitivity of the input variables on scour values was examined.

中文翻译：

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使用加权正则化极限学习机在弯曲运河中进行石堰冲刷建模*

在本文中，一种新型加权正则化极限学习机（WRELM）被首次用于模拟弯曲运河中 J 形、I 形和 W 形石堰周围的冲刷深度。第一步，检测影响石堰周围冲刷深度的无量纲参数。然后，使用这些参数开发了六个 WRELM 模型。值得一提的是，使用了三种不同的实验模型来验证 WRELM 模型。此外，70% 的实验数据用于训练模型，其余 30% 用于测试它们。之后，选择隐藏层内存在的神经元数量为13，然后选择WRELM模型的最佳激活函数。还为该激活函数找到了最佳正则化参数。在下一步中进行全面的敏感性分析检测到最佳 WRELM 模型，以及最具影响力的输入变量。将优越模型的结果与正则化极限学习机（RELM）和极限学习机（ELM）模型进行比较，证明了 WRELM 的显着优越性。此外，还提出了一个公式来计算位于弯曲运河中的不同形状的石堰周围的冲刷间隙。最后，检查了输入变量对冲刷值的敏感性。提出了一个公式来计算位于弯曲运河中的不同形状的石堰周围的冲刷间隙。最后，检查了输入变量对冲刷值的敏感性。提出了一个公式来计算位于弯曲运河中的不同形状的石堰周围的冲刷间隙。最后，检查了输入变量对冲刷值的敏感性。