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《Journal of Yangtze River Scientific Research Institute》 2009-09
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Application of Pattern Search Optimization in Calculation of Normal Depth in Trapezoidal Canal

ZHANG Kuan-di,LV Hong-xing,WANG Zheng-zhong,ZHAO Yan-feng(College of Water Resources and Architectural Engineering,Northwest A & F University,Yangling Shaanxi 712100,China)  
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.
【Fund】: 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)
【CateGory Index】: TV133.1
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