Side weirs are widely used to measure and control flows passing through main canals. In this study, a hybrid model is developed to approximate the discharge coefficient of side weirs located on converging canals for the first time, meaning that the adaptive neuro‐fuzzy inference system (ANFIS) network is optimized by means of the firefly algorithm. After that, six ANFIS and adaptive neuro‐fuzzy inference system‐firefly algorithm (ANFIS‐FA) models are introduced using input parameters. In addition, in this study, Monte Carlo simulation is employed to study the modelling accuracy. Furthermore, the k‐fold cross‐validation approach is implemented to validate the modelling results. Analysing the modelled results demonstrates that the hybrid models are more accurate than the ANFIS ones. The superior model simulates the discharge coefficient values with reasonable accuracy. For example, the values of the determination coefficient (R²), the mean absolute error (MAE) and the root mean square error (RMSE) for the superior model are calculated as 0.993, 0.011 and 0.015, respectively. Also, about 98% of the superior model results have errors less than 12%. According to the uncertainty analysis results, the superior model has an overestimated performance. A sensitivity analysis indicates that the flow Froude number at the side weir downstream is the most effective input parameter. © 2020 John Wiley & Sons, Ltd.

中文翻译：

---

一种拟议的基于ANFIS并结合萤火虫算法的新型混合智能模型，用于预测会聚运河旁堰的排水系数*

侧堰被广泛用于测量和控制流经主渠的流量。在这项研究中，首次建立了一个混合模型来近似估算位于汇流渠上的侧堰的流量系数，这意味着利用萤火虫算法对自适应神经模糊推理系统（ANFIS）网络进行了优化。之后，使用输入参数引入了六个ANFIS和自适应神经模糊推理系统萤火虫算法（ANFIS-FA）模型。另外，在这项研究中，蒙特卡罗模拟被用来研究建模的准确性。此外，k实施交叉交叉验证方法以验证建模结果。分析建模结果表明，混合模型比ANFIS模型更准确。上级模型以合理的精度模拟排放系数值。例如，确定系数的值（R ²），上级模型的平均绝对误差（MAE）和均方根误差（RMSE）分别计算为0.993、0.011和0.015。同样，约有98％的高级模型结果误差小于12％。根据不确定性分析结果，上级模型的性能被高估了。敏感性分析表明，下游侧堰的流动弗洛德数是最有效的输入参数。分级为4 +©2020 John Wiley＆Sons，Ltd.