基于广义逆理论的河网糙率反演研究
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摘要
引入广义逆和Backus-Gilbert反演理论,构造了牛顿-广义逆方法和自然逆方法计算优化算法的搜索方向,进行河网糙率反演,并推导了两种算法反演解估计的分辨率矩阵和单位协方差矩阵.理论分析表明,牛顿-广义逆优化算法具有二阶收敛速度.在反演过程中结合Wiggins方法控制观测数据中的噪声,能够有效调节河道糙率反演结果的分辨率和方差.数值仿真表明这两种算法与Wiggins方法相结合,选取适当的控制参数,既能达到较高的精度,又能有效地抑制噪声,提高数值计算的稳定性.
According to generalized inverse theory and Backus-Gilbert inverse theory,singular value decomposition(SVD) and Newton-generalized inverse matrix were used to analyze the optimization orientation.The resolution matrix and covariance matrix was deduced,which could describe inversion results reliability.Theoretical analysis showed that the degree of convergence of Newton-generalized inverse optimal algorithm was second-order.During the computation procedure, Wiggins method was integrated into the optimization algorithm.Numerical simulation showed that noise can be suppressed effectively and inversion result approach genuine solution,when proper control parameter is used,and the method can improve numerical stability.
According to generalized inverse theory and Backus-Gilbert inverse theory,singular value decomposition(SVD) and Newton-generalized inverse matrix were used to analyze the optimization orientation.The resolution matrix and covariance matrix was deduced,which could describe inversion results reliability.Theoretical analysis showed that the degree of convergence of Newton-generalized inverse optimal algorithm was second-order.During the computation procedure, Wiggins method was integrated into the optimization algorithm.Numerical simulation showed that noise can be suppressed effectively and inversion result approach genuine solution,when proper control parameter is used,and the method can improve numerical stability.
引文
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[19]KHATIBI R H,WILLIAMS J J R,WORMALEA-TON P R.Identification problem of open channel fric-tion parameters[J].Journal of Hydraulic Engineering,1997,123(12):1078-1088.
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[24]石琳柯,孙铭心,王广国,等.地球物理遗传反演方法[M].北京:地震出版社,2000.
[25]何旭初.广义逆矩阵地基本理论何计算方法[M].上海:上海科学技术出版社,1985:47-48.
[26]陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2001.
[27]孙继广.矩阵扰动分析[M].北京:科学出版社,2001.
[28]程伟平.流域洪水演进建模方法与河网糙率反分析研究[D].杭州:浙江大学,2004.CHENG Wei-ping.Strudy on basin flood model and in-verse analysis of channel friction[D].Hangzhou:Zhe-jiang University,2004.
[29]WIGGINS R A.The general linear inverse problem:implication of surface waves and free oscillations forsurface structures[J].Rev.Geophysics and SpacePhysics,1972,10:251-285.
[2]BECKER L,YEH W W G.Identification of multiplereach channel parameters[J].Water Resources Re-search,1973,9(2):326-335.
[3]YEH W W G,BECKER L.Linear programming andchannel flow identification[J].Journal of the HydraulicsDivision,ASCE,1973,99(11):2013-2021.
[4]FREAD D L,SMITH G F.Calibration techniques for 1-D unsteady flow models[J].Journal of the HydraulicDiv,ASCE,1977,104(7):1027-1043.
[5]蔡晓鸣,王连祥.关于一维河床糙率的计算程序[J].水利学报,1988,12:53-58.CAI Xiao-ming,WANG Lian-xiang.Calculation pro-gram of one-dimension channel friction parameter[J].Journal of Hydraulic Engineering,1988,12:53-58.
[6]韩龙喜,朱羿,蒋莉华.一维水力数值模拟糙率确定方法[J].水文,2002,22(6):16-18,62.HAN Long-xi,ZHU Yi,JIANG Li-hua.Roughnesscalculation method for 1-d numerical simulation of hy-drodynamics in mountainous river[J].Hydrology,2002,22(6):16-18,62.
[7]杨永德,刘炳衡.糙率变化过程的推算模型与长江三峡糙率探讨[J].人民长江,1991,22(12):9-15.YANG Yong-de,LIU Bing-heng.Reckon model of fric-tion parameter variety and friction parameter discussionof Yangtz river three gorges[J].Yangtz River,1991,22(12):9-15.
[8]杨世孝,肖子良.反求糙率的一种数值方法[J].数值计算与计算机应用,1994,4:247-260.YANG Shi-xiao,XIAO Zi-liang.One numerical valuemethod of friction parameter inversion[J].NumericalSolution and Computer Application,1994,4:247-260.
[9]韩龙喜,金忠青.平原河网的水量计算和参数率定———改进的湄公河模型[J].水动力学研究与进展,1991,12(6):39-45.HAN Long-xi,JIN Zhong-qing.The flood plain net-work model-the improved modong river model[J].Jour-nal of Hydrodynamics,1991,12(6):39-45.
[10]金忠青,韩龙喜,张健.复杂河网的水力计算及参数反问题.[J].水动力学研究与进展,1998,13(3):280-285.JIN Zhong-qing,HAN Long-xi,ZHANG Jian.Theinverse problem of roughness parameter in hydrauliccalculation of complicated river[J].Journal of Hydro-dynamics,1998,13(3):280-285.
[11]韩龙喜,金忠青.三角联解法力水质模型的糙率反演及面污染源计算[J].水利学报,1998,(7):30-34.HAN Long-xi,JIN Zhong-qing.Roughness calibrationand formula of pollution sources basing on“three stepsmethod”in river network[J].Journal of Hydraulic En-gineering,1998,(7):30-34.
[12]董文军,杨则燊.一维圣维南非常的反问题研究与计算方法[J].水力学报,2002,9:61-65.DONG Wen-jun,YANG Ze-hen.Calculation methodfor inverse problem of 1-D st.Venant equations[J].Journal of Hydraulic Engineering,2002,9:61-65.
[13]董文军,姜亨余.一维水流方程中曼宁糙率的参数辨识[J].天津大学学报,2001,34(2):201-204.DONG Wen-jun,JIANG Heng-yu.Parameter identifi-cation of Manning friction parameter in one-dimensionflow equation[J].Journal of Tianjin University,2001,34(2):201-204.
[14]WASANTHA LAL A M.Calibration of river bedroughness[J].Journal of Hydraulic Engineering,1995,121(9):664-671.
[15]GEORGES D.Nonlinear model identification and state-observer design for water distribution systems[A].Control′94.Volume2[C].Coventry,UK:IEEE,1994:887-893.
[16]KHATIBI R H,WORMALEATON P R,WILLIAMSJ J R.Parameter quality conditions in open-channel in-verse problems[J].Journal of Hydraulic Research,1995,38(6):447-457.
[17]KHATIBI R H.Sample size determination in openchannel inverse problems[J].Journal of Hydraulic En-gineering,2001,8:678-688.
[18]KHATIBI R H,WILLIAMS J J R,WORMALEA-TON P R.Predict parameters for flows in nearly flattidal channels[J].Journal of Hydraulic Engineering,2000,126(10):741-749.
[19]KHATIBI R H,WILLIAMS J J R,WORMALEA-TON P R.Identification problem of open channel fric-tion parameters[J].Journal of Hydraulic Engineering,1997,123(12):1078-1088.
[20]李光炽.流域洪水演进模型及其参数反问题研究[D].南京:河海大学,2001.LI Guan-chi,Evolvement model of drainage area floodand study on parameter inversion[D].Nanjin:HehaiUniversity,2001.
[21]William Menke.地球物理数据分析———离散反演理论[M].王明光,等译.北京:地质出版社,1988.
[22]杨文采.地球物理反演的理论与方法[M].北京:地质出版社,1997.
[23]杨文采.地球物理反演和地震层析成像[M].北京:地震出版社,1989.
[24]石琳柯,孙铭心,王广国,等.地球物理遗传反演方法[M].北京:地震出版社,2000.
[25]何旭初.广义逆矩阵地基本理论何计算方法[M].上海:上海科学技术出版社,1985:47-48.
[26]陈景良,陈向晖.特殊矩阵[M].北京:清华大学出版社,2001.
[27]孙继广.矩阵扰动分析[M].北京:科学出版社,2001.
[28]程伟平.流域洪水演进建模方法与河网糙率反分析研究[D].杭州:浙江大学,2004.CHENG Wei-ping.Strudy on basin flood model and in-verse analysis of channel friction[D].Hangzhou:Zhe-jiang University,2004.
[29]WIGGINS R A.The general linear inverse problem:implication of surface waves and free oscillations forsurface structures[J].Rev.Geophysics and SpacePhysics,1972,10:251-285.
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