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1、中国农村水利水电#2010年第1期51文章编号:1007-2284(2010)01-0051-05基于最小二乘法的绳套型水位流量关系最优定线研究董晓华,薄会娟,邓霞(三峡大学土木水电学院,湖北宜昌443002)摘要:汛期河道的水位流量关系通常呈绳套型,对其进行高精度的定线是洪水资源实施高效管理的基础。传统的定线方法效率低,误差大,因而本文使用最小二乘法为优化方法,对绳套型水位流量方程进行优化定线。首先,Saint-Ve-nant方程中的迁移惯性项和局地惯性项被去掉以简化方程,附加比降被引入以使方程能够拟合绳套型曲线;然后,简化后的方程通过取对数、多项式展开和幂级数展开
2、被线性化;最后应用最小二乘法估计线性化方程中的参数。对3个案例的应用结果表明,所获得的定线方程能有效拟合观测的水位流量曲线,对拟合结果的偏离符号检验、适线检验和偏离数值检验均符合水文资料整编规范中的定线精度要求,说明将最小二乘法应用于绳套型水位流量曲线的优化定线是有效的。关键词:最小二乘法;绳套型水位流量关系;曲线拟合中图分类号:P337-3;TV123文献标识码:AOptimalDeterminationofLoopedStage-dischargeRelationshipbytheLeastSquresMethodsDONGXiao-hua,BOHu-ijuan,
3、DENGXia(CollegeofCivilandHydropowerEngineering,ThreeGorgesUniversity,Yichang443002,HubeiProvince,China)Abstract:Thestage-dischargeinfloodingseasonsinriverchannelsnormallypresentsashapeofloop,determiningitisbasicforcon-ductinganefficientmanagementoffloodingwaterresources.Traditionalwayso
4、fdeterminingtheloopedrelationshiphassuchdisad-vantagesasinefficiency,significanterrors,etc.,thereforethispaperaimsatapplyingtheLeastSquaresMethod(LSM)tooptimaldeterminationoftheloopedstage-dischargerelationship.Theequationcapableofdepictingtheloopedstage-dischargerelationshipinriverchan
5、nelsisobtainedbasedontheoriginalSaint-Venantmomentumequation,byidentifyingthewatersurfaceslopeasthesum-mationofthechannelbottomslopeandadditionalslopeoffloodingwave.Theintroducedadditionalslopeitemenabledtheequationtosimulatetheloopedshapeofthestage-dischargerelationship.Thelocalandconv
6、ectiveinertiaitemsareremovedfromtheoriginalSaint-Venantmomentumequationforsimplification'ssake.Thesimplifiedequationisthenlinearizedbyfirstlogarithmizedelementoftheequation,andthenpolynomialandpowerseriesexpansionsforthesteadydischargeandadditionalslopeitemsareconducted.F-inally,theLSMi
7、susedtoestimatetheparametersinthelinearizedequation.Theresultsofthemethodin3casesshowthat,there-sultingfittedequationcaneffectivelysimulatetheobservedrelation.Thebiasedcodetest,fitnesstestandbiasedvaluetestonthesimulationresultsareconducted.Theresultsshowthattheycompletelymeett
