为了得到半立方、平方、立方抛物线形断面收缩水深的直接计算公式,通过对这3种抛物线形断面收缩水深的基本方程恒等变形,得到了一个无量纲收缩水深的高次方程。该方程无法直接求得其理论解,而继续推导得到了无量纲收缩水深的迭代公式。且利用1stopt软件,基于遗传算法,对给定非线性函数模型进行参数优化拟合,建立了半立方、平方、立方抛物线形渠道收缩水深的直接计算公式。误差分析和实例计算结果表明:在工程常用范围λ∈[0.01,0.6]内,半立方、平方、立方抛物线形渠道收缩水深的最大相对误差分别仅为0.064%,-0.091%,0.136%,直接计算公式形式简捷、精度高、使用范围广。
Abstract
In order to get the direct calculation formula of water depth in semi-cubic, square, and cubic parabola-shaped channels with contracted section, we identically transformed the basic equation of contraction water depth and obtained higher degree equation of non-dimensional contraction depth. But it could not be solved theoretically, so we obtained the iterative calculation formula of non-dimensional contraction depth by further transformation. Furthermore we employed 1stOpt software to optimize and fit the established nonlinear model parameters based on genetic algorithm and built the direct calculation formula of contraction depth for the semi-cubic, square, and cubic parabola-shaped sections. Error analysis and calculation example show that the maximum relative error is respectively 0.064%, -0.091%, and 0.136% within common engineering range λ∈[0.01,0.6]. The direct calculation formula is convenient, and has high precision and wide range of application.
关键词
半立方抛物线形断面 /
平方抛物线形断面 /
立方抛物线形断面 /
1stopt软件 /
遗传算法 /
收缩水深
Key words
semi-cubic parabola-shaped section /
square parabola-shaped section /
cubic parabola-shaped section /
1stOpt software /
genetic algorithm /
contraction water depth
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参考文献
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