基于规划求解的暴雨强度公式推求方法研究
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摘要
在编制暴雨强度公式时,存在原始降雨资料中包含的异常值影响暴雨强度公式的准确度,皮尔逊-III型理论频率曲线拟合工作量大等问题。针对以上问题,阐述了异常值剔除的方法,分析了变异系数(Cv)、偏态系数(Cs)对皮尔逊-III型分布曲线拟合的影响规律。同时,基于重庆市酉阳县1993-2013年共计21 a的暴雨资料,采用Excel规划求解优化皮尔逊-III型分布曲线的拟合参数,分别利用基于规划求解的最小二乘法和高斯牛顿法,推求暴雨强度公式,并对其拟合精度和误差进行了对比分析。提出的规划求解法能有效避免拟合暴雨强度公式适线过程中目估适线法所导致的主观影响,通过对比分析解析了提高收敛速度和精度的暴雨强度总公式的推求方法。
The outliers in the original rainfall samples could affect the accuracy of the formula,and the Pearson-III theory frequency curve fitting required a large amount of work when deducing the rainstorm intensity formula. Therefore,several methods of removing outliers were introduced and the influence of the coefficient of variation( Cv) and the coefficient of skew( Cs) on the Pearson-III Distribution were evaluated. Meanwhile,formula of rainstorm intensity was calculated using Excel Solver Add-in to optimize the Pearson-III curve parameters by the least square method and Gauss-Newton method based on the rainstorm data of the total 21 years from 1993 to 2013 in Youyang County of Chongqing City,and the fitting accuracy and error were analyzed. This method could effectively avoid the subjectivity of empirical fitting by eye in the process of fitting Pearson-III Curve. Through comparison and analysis,the proposed method of calculating the general formula of rainstorm intensity can improve the convergence speed and the accuracy.
The outliers in the original rainfall samples could affect the accuracy of the formula,and the Pearson-III theory frequency curve fitting required a large amount of work when deducing the rainstorm intensity formula. Therefore,several methods of removing outliers were introduced and the influence of the coefficient of variation( Cv) and the coefficient of skew( Cs) on the Pearson-III Distribution were evaluated. Meanwhile,formula of rainstorm intensity was calculated using Excel Solver Add-in to optimize the Pearson-III curve parameters by the least square method and Gauss-Newton method based on the rainstorm data of the total 21 years from 1993 to 2013 in Youyang County of Chongqing City,and the fitting accuracy and error were analyzed. This method could effectively avoid the subjectivity of empirical fitting by eye in the process of fitting Pearson-III Curve. Through comparison and analysis,the proposed method of calculating the general formula of rainstorm intensity can improve the convergence speed and the accuracy.
引文
[1]白珊,赵莹,赵然杭,等.山东省小流域短历时暴雨公式的优化及应用研究[J].水资源与水工程学报,2016,27(4):50-54.
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[19]翁窈瑶.城市暴雨强度公式推求方法研究[D].北京:北京工业大学,2012.
[20]黄泽钧. Excel绘制水文计算海森机率格纸的方法[J].湖北水利水电职业技术学院学报,2006(7):330+332.
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[22]陈鹏飞.基于MATLAB的暴雨强度公式参数推求[D].广州:广州大学,2010.
[23]王杰,万程炜,郑敏杰,等.高斯牛顿法在皮尔逊Ⅲ型曲线适线中的应用[J].人民黄河,2014,36(9):27-30.
[2]王赫,肖龙,刘勇,等.基于城市内涝浅谈海绵城市建设[J].南昌工程学院学报,2016,35(6):66-71.
[3]沈红霞,杜付然,江海涛,等.南京主城区设计暴雨计算研究[J].水资源与水工程学报,2017,28(6):74-78
[4]袁典,陈军,卿清涛,等.最小二乘法估算Pearson-III型分布参数的改进[J].地球信息科学学报,2016,18(9):1167~1173.
[5]王金辉,丛海兵.暴雨强度公式编制中皮-III型频率曲线的快速拟合[J].中国给水排水,2013,29(1):52-55
[6]高琳,周玉文,唐颖,等.城市暴雨强度公式皮尔逊Ⅲ型适线问题研究[J].给水排水,2016,52(8):47-51.
[7]李龙.宝鸡市暴雨强度公式推求与设计暴雨雨型分析[D].西安:西安建筑科技大学,2015.
[8]郭渠,廖代强,孙佳,等.重庆主城区暴雨强度公式推算和应用探讨[J].气象,2015,41(3):336-345.
[9]白珊,赵莹,赵然杭,等.山东省小流域短历时暴雨公式的优化及应用研究[J].水资源与水工程学报,2016,27(4):50-54.
[10]王睿,徐得潜.合肥市暴雨强度公式的推求研究[J].水文,2016,36(1):71-74.
[11]万永静,叶兴成,王飞,等.不同拟合方法推求暴雨强度公式研究[J].水资源与水工程学报,2017,28(5):76-79+86.
[12]张东海,段莹,周文钰,等.贵阳市暴雨强度公式推求[J].城市道桥与防洪,2016(1):95-99+11-12.
[13]住房和城乡建设部,中国气象局.城市暴雨强度公式编制和设计暴雨雨型确定技术导则[Z]. 2014.
[14] U. S. Water Resources Council. Guidelines for determining flood flow frequency[Z]. Bulletin of the Hydrology Committee(USA),No. 17B,1982.
[15]GRUBBS F E,BECK G. Extension of Sample Sizes and Percentage Points for Significance Tests of Outlying Observations[J]. Technometrics,1972,14(4):847-854.
[16]SPENCER C S,MCCUEN R H. Detection of Outliers in Pearson Type III Data[J]. Journal of Hydrologic Engineering,1996,1(1):2-10.
[17]罗雅文.新暴雨特性下重庆市暴雨强度公式修编[D].重庆:重庆大学,2012.
[18]王俊萍.推求绵阳市暴雨强度公式的问题研究[D].西安:西安建筑科技大学,2007.
[19]翁窈瑶.城市暴雨强度公式推求方法研究[D].北京:北京工业大学,2012.
[20]黄泽钧. Excel绘制水文计算海森机率格纸的方法[J].湖北水利水电职业技术学院学报,2006(7):330+332.
[21]中华人民共和国住房和城乡建设部.室外排水设计规范:GB 50014-2006[S].北京:中国计划出版社,2014.
[22]陈鹏飞.基于MATLAB的暴雨强度公式参数推求[D].广州:广州大学,2010.
[23]王杰,万程炜,郑敏杰,等.高斯牛顿法在皮尔逊Ⅲ型曲线适线中的应用[J].人民黄河,2014,36(9):27-30.