Procedures for calculating critical depth in an open channel having a trapezoidal cross section are discussed in this paper. Among the current methods are chart look-up, trial-and-error, iterative, and approximate formula; however, practical application shows that each of these methods has some problems. This paper proposes an explicit solution to critical depth in a trapezoidal channel by introducing data from iteration solution and then applying multiple nonlinear regressions (MNLR) and artificial neural network (ANN) techniques to derive the best estimate. Results show that ANN formulation of the problem of solving for the critical depth is less successful than that by regression. The performance of MNLR in terms of R 2 (0.998) and RE (0.025) is excellent and performance of ANN in terms of R 2 (0.987) and RE (0.132) is good but its values are slightly perturbed around its numerically obtained values.

中文翻译：

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使用显式公式和 ANN 方法的梯形明渠临界深度

本文讨论了计算具有梯形横截面的明渠临界深度的程序。目前的方法有查图、试错法、迭代法和近似公式法；然而，实际应用表明，这些方法中的每一种都存在一些问题。本文通过从迭代解法中引入数据，然后应用多元非线性回归 (MNLR) 和人工神经网络 (ANN) 技术来推导出最佳估计值，从而提出了梯形通道中临界深度的显式解法。结果表明，解决临界深度问题的 ANN 公式不如回归公式成功。MNLR 在 R 2 (0.998) 和 RE (0.025) 方面的表现非常出色，ANN 在 R 2 (0.987) 和 RE (0.025) 方面的表现非常出色。