Abstract One type of long-crested weir is oblique weir. Oblique weirs are longer than standard weirs. Therefore, they can pass more discharge capacity than weirs at the given channel width. The main objective of the present study was to investigate the efficacy of several intelligent models including multiple linear regression (MLR), Gaussian process regression (GPR), artificial neural network (ANN) and multiple models driven by ANN (MM-ANN) methods in estimating oblique weir discharge coefficient (Cd). Different input combinations were predicted using the variables of H/P, P/Le, and W/Le and the output coefficient of discharge. Prediction models were analyzed by statistical index, including root mean square error (RMSE), correlation coefficient (R), error percentage chart, relative error (RE%) plot, Kling-Gupta efficiency (KGE), probability density function (PDF) plot, scatter plot, scatter plot of error residuals and Taylor's diagram. Obtained results showed that the ANN model performed best by combining the inputs of the three variables (i.e., H/P, P/Le, and W/Le) with R = 0.746 and RMSE = 0.065 among the standalone models. Eventually, the proposed hybrid model MM-ANN was most accurate in estimating the oblique weir Cd by improving the prediction results of the implemented models.

中文翻译：

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一种基于混合包容多重模型的斜堰流量系数预测新方法

摘要 斜堰是长顶堰的一种。斜堰比标准堰长。因此，在给定的通道宽度下，它们可以通过比堰更多的放电容量。本研究的主要目的是研究多种智能模型的功效，包括多元线性回归 (MLR)、高斯过程回归 (GPR)、人工神经网络 (ANN) 和由 ANN (MM-ANN) 方法驱动的多种模型。估算斜堰流量系数 (Cd)。使用 H/P、P/Le 和 W/Le 变量和排放输出系数预测不同的输入组合。通过统计指标对预测模型进行分析，包括均方根误差（RMSE）、相关系数（R）、误差百分比图、相对误差（RE%）图、Kling-Gupta效率（KGE）、概率密度函数 (PDF) 图、散点图、误差残差散点图和泰勒图。获得的结果表明，ANN 模型通过将三个变量（即 H/P、P/Le 和 W/Le）的输入与独立模型中的 R = 0.746 和 RMSE = 0.065 相结合而表现最佳。最终，通过改进实施模型的预测结果，所提出的混合模型 MM-ANN 在估计斜堰 Cd 方面是最准确的。