A piano key weir (PK weir) is a non-linear, labyrinth-type weir that benefits of a high discharge capacity, and is well suited for low head dams. Determination of the discharge coefficient (C_d) is considered as one of the most important issues, which plays a substantial role in reducing structural and financial damages caused by floods. The main aim of the present study is to experimentally investigate the variations of PK weirs discharge coefficient (C_d) through altering the geometric parameters. The obtained results revealed that in modified PK weirs (by an 11.5% increase in weir height, changing the crest shape, and fillet installation), the C_d values were about 5–15% more than those of the standard PK weirs. The C_d values of the non-contracted weirs were increased by increasing the inlet/outlet width ratio by 1.4, while this relation was adverse for contracted weirs. In the modified PK weirs, the submergence would occur faster than the standard weirs, while the complete submergence would occur later. Moreover, robust kernel-based approaches (kernel extreme learning machine and support vector machine) were successfully employed to the extensive experimental dataset by taking into consideration the C_d as a function of dimensionless geometric variables of PK weirs. The obtained results showed that the ratio of the upstream hydraulic head (H₀) to total weir height (P) plays a significant role in the modeling process.

钢琴键堰（PK 堰）是一种非线性迷宫式堰，具有高排放能力，非常适合低水头坝。流量系数（C _d）的确定被认为是最重要的问题之一，它在减少洪水造成的结构和经济损失方面发挥着重要作用。本研究的主要目的是通过改变几何参数来实验研究 PK 堰流量系数 (C _d ) 的变化。获得的结果表明，在改进的 PK 堰中（通过增加 11.5% 的堰高度、改变顶部形状和圆角安装），C _d值比标准 PK 堰高约 5-15%。C _d通过将入口/出口宽度比增加 1.4，非收缩堰的值增加，而这种关系对收缩堰不利。在改进的 PK 堰中，淹没将比标准堰更快，而完全淹没将发生更晚。此外，通过将 C _d作为 PK 堰的无量纲几何变量的函数，将稳健的基于内核的方法（内核极限学习机和支持向量机）成功应用于广泛的实验数据集。所得结果表明上游水头 (H ₀ ) 与总堰高 (P)的比率在建模过程中起重要作用。