用模式搜索算法求解梯形明渠正常水深  

Application of Pattern Search Optimization in Calculation of Normal Depth in Trapezoidal Canal

作　　者：张宽地[1] 吕宏兴[1] 王正中[1] 赵延风[1] 

机构地区：[1]西北农林科技大学水利与建筑工程学院,陕西杨凌712100

出　　处：《长江科学院院报》2009年第9期25-28,34,共5页Journal of Changjiang River Scientific Research Institute

基　　金：国家973计划课题(2007CB407201);国家自然科学基金重点项目(40335050);西北农林科技大学创新团队建设计划(01140202)

摘　　要：梯形明渠正常水深在水力设计中经常遇到,但其求解无显函数形式的表达式,传统计算中的试算法或查图法不仅计算过程繁琐复杂,而且计算精度不高。通过引入一个无量纲参数——单位水面宽度,对梯形明渠正常水深的基本方程进行恒等变形,得到了求解单位水面宽度的超越函数,并证明该方程为单调函数。为此,将求解正常水深的问题等价于一非线性优化问题,并用模式搜索算法求解。实例计算及误差分析表明:该算法计算经济、收敛性好,为梯形断面水力计算提供了一种新的求解思路。Normal depth is an important parameter occurring in the design of irrigation canals. Direct analytic solution of normal-depth problems is not possible, as the governing equations for the practical canal sections are implicit. The solution requires tedious methods of trial and error. Tabular and graphical methods also available for solution are subject to errors of double interpolation and errors of judgment in reading the graphs. In order to improve this situation, a new formula is derived from transforming identically the uniform flow equation in trapezoidal canal through introducing a non-dimensional parameter-unit surface width. Also, it is proved to be monotonic function. So, the calculation of normal depth problem was converted into a nonlinear constrained optimization problem, which can be solved by the pattern search optimization method. Finally, Error analysis and an illustration computed using this method show that it is much more applicable, precise and simple than tradition methods. So it provided a new tool for obtaining normal depth of open channel in trapezoid section problem.

关 键 词：正常水深 模式搜索算法 梯形明渠 单位水面宽度 

分 类 号：TV133.1[水利工程—水力学及河流动力学]