洪水频率分析中目标函数的统计试验研究
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摘要
基于回归分析理论和误差分布规律,采用统计试验途径对比分析基于8种无权目标函数和4种加权目标函数的洪水频率分析方法的统计特性。定量分析表明,采用平均绝对根误差作为目标函数的洪水频率分析方法整体上精度高且稳健性优良,尤其在设计值无偏性上的优势更为明显;权重函数并不能有效提高洪水设计值的有效性,反而会增大洪水设计值的不确定性。以雅砻江流域甘孜站设计洪水为例,采用RMAE为目标函数的NOES方法计算的洪水设计值要大于采用MAE为目标函数的NOES方法计算的洪水设计值,两者相对误差平均值为0. 14%。
Based on the theory of regression analysis and the law of error distribution,the statistical analysis is used to compare and analyze the statistical characteristics of flood frequency analysis methods based on eight unweighted objective functions and four weighted objective functions. The quantitative analysis shows that,( a) the flood frequency analysis method with average absolute root error as the objective function has high precision and good robustness,especially the unbiased design value is more obvious,and( b) the weight function cannot effectively improve the effectiveness of flood design value,but rather increases the uncertainty of flood design values. Taking the design flood of Ganzi Hydrological Station in Yalong River basin as an example,the flood design value calculated by the NOES method using RMAE as the objective function is larger than that calculated by the NOES method using MAE as the objective function,and the average relative error is 0. 14%.
Based on the theory of regression analysis and the law of error distribution,the statistical analysis is used to compare and analyze the statistical characteristics of flood frequency analysis methods based on eight unweighted objective functions and four weighted objective functions. The quantitative analysis shows that,( a) the flood frequency analysis method with average absolute root error as the objective function has high precision and good robustness,especially the unbiased design value is more obvious,and( b) the weight function cannot effectively improve the effectiveness of flood design value,but rather increases the uncertainty of flood design values. Taking the design flood of Ganzi Hydrological Station in Yalong River basin as an example,the flood design value calculated by the NOES method using RMAE as the objective function is larger than that calculated by the NOES method using MAE as the objective function,and the average relative error is 0. 14%.
引文
[1]丛树铮，胡四一．洪水频率分析的现状与展望[J]．水文，1987(6):52-58．
[2]郭生练，刘章君，熊立华．设计洪水计算方法研究进展与评价[J]．水利学报，2016,47(3):302-314．
[3]王国安．中国设计洪水研究回顾和最新进展[J]．科技导报，2008,26(21):86-89．
[4]刘光文．水文频率计算评议[J]．水文，1986(3):10-18．
[5]金光炎．水文统计原理与方法[M]．北京:中国工业出版社，1964．
[6]谢平，郑泽权．水文频率计算有约束加权适线法[J]．武汉水利电力大学学报，2000,33(1):49-52．
[7]王文川，雷冠军，刘宽，等．模糊加权优化适线法的改进及统计特征分析[J]．水文，2017,37(5):1-7．
[8]康有，马顺刚，樊明兰，等．基于次序统计量理论的洪水频率分析方法研究[J]．水文，2017,37(3):1-6．
[9]SINGH V P.Handbook of applied hydrology[M].2nd ed.New York:Mc Graw-Hill Education,2016．
[10]ROBERT C P,CASELLA G.Monte Carlo statistical methods[M].2nd ed.New York:Springer,2005．
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[12]丛树铮，谭维炎，黄守信，等．水文频率计算中参数估计方法的统计试验研究[J]．水利学报，1980(3):1-14.
[2]郭生练，刘章君，熊立华．设计洪水计算方法研究进展与评价[J]．水利学报，2016,47(3):302-314．
[3]王国安．中国设计洪水研究回顾和最新进展[J]．科技导报，2008,26(21):86-89．
[4]刘光文．水文频率计算评议[J]．水文，1986(3):10-18．
[5]金光炎．水文统计原理与方法[M]．北京:中国工业出版社，1964．
[6]谢平，郑泽权．水文频率计算有约束加权适线法[J]．武汉水利电力大学学报，2000,33(1):49-52．
[7]王文川，雷冠军，刘宽，等．模糊加权优化适线法的改进及统计特征分析[J]．水文，2017,37(5):1-7．
[8]康有，马顺刚，樊明兰，等．基于次序统计量理论的洪水频率分析方法研究[J]．水文，2017,37(3):1-6．
[9]SINGH V P.Handbook of applied hydrology[M].2nd ed.New York:Mc Graw-Hill Education,2016．
[10]ROBERT C P,CASELLA G.Monte Carlo statistical methods[M].2nd ed.New York:Springer,2005．
[11]MCKAY M D,BECKMAN R J,CONOVER W J.A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J].Technometrics,1979,21(2):239-245．
[12]丛树铮，谭维炎，黄守信，等．水文频率计算中参数估计方法的统计试验研究[J]．水利学报，1980(3):1-14.