Sluice gate is a common tool to regulate water conveyance systems like irrigation channels or pipelines. The interaction between the flow and sediment particles downstream of the sluice gate may initiate scouring phenomenon and extend the resulted scour hole beneath the sluice gate foundation. The consequence of this procedure is undermining the whole structure, interrupting the flow passage, and regulation. Thus, the scour process downstream of a sluice gate is a critical point and robust scour depth prediction is still a crucial issue for hydraulic engineers. This paper proposes several novel hybrid adaptive neuro-fuzzy inference system (ANFIS) methods called ANFIS-PSO (particle swarm optimization), ANFIS-ACO (ant colony optimization), ANFIS-DE (differential evolution) and ANFIS-GA (genetic algorithm) as predictive models to estimate scour depth downstream of a sluice gate. To this end, some physical and hydraulic parameters such as $d_{50}$(median diameter of bed material), $b$(gate opening), $h$(tail water depth), $l$(apron length), $U$(mean velocity of the jet) and ${\sigma }_g$(geometric standard deviation of sediment grain size) are considered as predictive variables in form of non-dimensional parameters. To provide a reliable predictive model, three combinations of input variables are prepared by eliminating some predictive variables. To assess adequacy of proposed models, some error indices are employed in both training and testing phases. Results show the optimistic predictive model is ANFIS-PSO ($\mathit{RMSE}=0.437$ and $R^2=0.946$) when all mentioned non-dimensional parameters are employed except $\frac{h}{b}$. Furthermore, the proposed model has the largest accuracy compared to the previously developed AI and empirical models. Ultimately, it can be concluded that the hybrid ANFIS-PSO is a robust approach for scour depth prediction downstream of a sluice gate.

水闸是调节灌溉系统或灌溉管道等输水系统的常用工具。闸门下游的水流和沉积物颗粒之间的相互作用可能引发冲刷现象，并在闸门基础下方扩展冲刷孔。此过程的结果是破坏了整个结构，中断了流路并进行了调节。因此，闸门下游的冲刷过程是关键点，而可靠的冲刷深度预测对于水力工程师而言仍然是关键问题。本文提出了几种新颖的混合自适应神经模糊推理系统（ANFIS）方法，称为ANFIS-PSO（粒子群优化），ANFIS-ACO（蚁群优化），ANFIS-DE（差分演化）和ANFIS-GA（遗传算法）作为预测模型，用于估算闸门下游的冲刷深度。为此，一些物理和液压参数例如$d_{50}$（床身材料的中值直径）， $b$（开门）， $H$（尾水深度）， $升$（围裙长度）， $ü$（射流的平均速度）和 ${\sigma }_G$（沉积物粒度的几何标准偏差）被视为无量纲参数形式的预测变量。为了提供可靠的预测模型，通过消除一些预测变量来准备输入变量的三种组合。为了评估所提出模型的适当性，在训练和测试阶段都采用了一些误差指标。结果表明，乐观的预测模型是ANFIS-PSO（$\mathit{RMSE}=0.437$ 和 ${\mathrm{[R}}^2=0.946$）当使用所有提到的无量纲参数时 $\frac{H}{b}$。此外，与先前开发的AI和经验模型相比，所提出的模型具有最高的准确性。最终，可以得出结论，混合ANFIS-PSO是用于闸门下游冲刷深度预测的可靠方法。