迭代逼近─逐次优化拟合方法在水力计算中的应用研究  

Study on application of iterative approximation—progressive optimization fitting approach to hydraulic calculation

作　　者：陈诚 龚懿 沈刚 朱卫彬 钮佳民 曹孟晔 

机构地区：[1]扬州大学水利与能源动力工程学院,江苏扬州225009 [2]溧阳市水利局,江苏溧阳213300 [3]扬州市江都区沿运灌区管理处,江苏扬州225261 [4]苏州市水利局,江苏苏州215011

出　　处：《水利水电技术》2017年第6期75-79,共5页Water Resources and Hydropower Engineering

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)

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。No any analytic solutions are theoretically there for the calculation of the contracted water depth in open channel with semi-cubic parabolic section, but the parameter is frequently used in the engineering calculation with higher demand of precision. For the problem that calculation precisions of the similar existing formulas are not so high, a fundamental equation of non-dimen- sional contracted water depth for the semi-cubical parabolic section is derived through simple mathematical transformation and the iterative approximation--progressive optimization fitting approach for the approximate solution of high-order equation is introduced as well, while a suitable functional model is established according to the iteration theory concerned, and then adaptable fitting pa- rameters are selected, for which the progressive optimization fitting is made by taking the minimum of the residual-standard devia- tion as the target, thus a set of direct calculation formulas is obtained. The relevant error analysis and actual case calculation in- dicate that the absolute value of the maximum relative error from the direct calculation formula is only O. 039%, the mean relative error is less than 0. 024% and the fitting correlation coefficient is 1. 000 0 within the engineering adaptable range. The precision deficiencies of the similar existing formulas are made up by the establishment of the formula, whieh not only provides a reference for design and operation management of canal project, but also gives a beneficial referenee for the studies made on all kinds of hy- draulic engineering calculations related to the solution of high-order equation.

关 键 词：迭代法 逐次优化拟合 半立方抛物线 收缩水深 水力计算 

分 类 号：TV133[水利工程—水力学及河流动力学]