迭代逼近─逐次优化拟合方法在水力计算中的应用研究

发布时间：2018-07-11 14:31

  本文选题：迭代法 + 逐次优化拟合　； 参考：《水利水电技术》2017年06期

【摘要】：半立方抛物线形断面明渠收缩水深的计算理论上无解析解,但该参数在工程计算中运用十分频繁且有较高的计算精度要求。针对现有的同类公式精度不够高的问题,通过简单的数学变换推得半立方抛物线形断面无量纲收缩水深的基本方程,引入高次方程近似求解的迭代逼近—逐次优化拟合方法,基于迭代理论建立合适的函数模型并选取适当的拟合参数,以剩余标准差最小为目标对其进行逐次优化拟合,得到一套直接计算公式。误差分析及实例计算结果表明,在工程适用范围内,该直接计算公式的最大相对误差绝对值仅为0.039%,平均相对误差小于0.024%,拟合相关系数达1.000 0。该公式的建立较好地弥补了现有的同类公式计算精度的不足,为渠道工程的设计和运行管理提供了参考,也为涉及高次方程求解的各类工程水力计算提供了有益的借鉴。
[Abstract]:There is no analytical solution for the calculation of shrinkage water depth of semi-cubic parabolic section open channel theoretically, but this parameter is frequently used in engineering calculation and has high calculation accuracy. In view of the problem that the accuracy of the existing similar formulas is not high enough, the basic equations of dimensionless shrinking water depth of semi-cubic parabola section are derived by simple mathematical transformation, and the iterative approximation-successive optimization fitting method for approximate solution of the higher order equation is introduced. Based on the iterative theory, an appropriate function model is established and appropriate fitting parameters are selected. The minimum residual standard deviation is taken as the objective of successive optimization fitting, and a set of direct calculation formulas are obtained. The results of error analysis and example calculation show that the absolute value of the maximum relative error of the direct calculation formula is only 0.03939, the average relative error is less than 0.024, and the fitting correlation coefficient is 1.000. The establishment of the formula can make up for the deficiency of the calculation precision of the same kind of formula, and provide a reference for the design and operation management of channel engineering, as well as for the hydraulic calculation of various kinds of engineering involving the solution of the high order equation.
【作者单位】： 扬州大学水利与能源动力工程学院;溧阳市水利局;扬州市江都区沿运灌区管理处;苏州市水利局;
【基金】：“十二五”国家科技支撑计划项目(2015BAB07B01) 江苏省水利科技项目(2016049) 江苏高校优势学科建设工程资助项目(PAPD)
【分类号】：TV131
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本文编号：2115507