| 摘要: |
| 【目的】 基于模式搜索算法求解梯形明渠的临界水深。【方法】 针对梯形明渠临界水深计算无显函数形式的表达式，及传统计算中的试算法或查图法计算过程繁琐复杂且计算精度不高的现状，引入一个无量纲参数——单位水面宽度，对梯形明渠临界流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。【结果】 将求解临界流水深的问题等价于一非线性优化问题，并用确定性优化方法——模式搜索算法进行求解。【结论】 实例计算及误差分析表明，该算法具有收敛速度快和求解精度高的特点，为梯形断面的水力计算提供了一种新思路。 |
| 关键词: 梯形明渠 临界水深 单位水面宽度 模式搜索算法 |
| DOI： |
| 分类号: |
| 基金项目:国家973计划项目（2007CB407201）；国家自然科学基金重点项目(40335050) |
|
| Application of pattern search optimization in calculation of critical depth in trapezoidal canal |
|
|
| Abstract: |
| 【Objective】 The study was to solve the trapezoidal open canal critical depth of water based on the pattern search algorithm.【Method】 Critical depth is an important parameter occurring in the design of irrigation canals.Direct analytic solution of critical depth problems is not possible,as the governing equations for the practical canal sections are implicit.The traditional solving methods like trial method and chart method are very complicated with low precision. In order to improve this situation，a new formula is derived from transforming identically the critical flow equation in trapezoidal canal through introducing a non dimensional parameter-unit surface width.Also,it is proved to be monotonic function.【Result】 So,calculation of critical depth problem is converted into a nonlinear constrained optimization problem,which can be solved by the pattern search optimization method.【Conclusion】 Error analysis and an illustration computed using this method show that the new algorithm is capable of improving the convergence performance singnificantly in convergence ability and solution precision.So it provids a new tool for obtaining normal depth of open canal in trapezoid section problem. |
| Key words: open trapezoidal canal critical depth unit surface width pattern search algorithm |
