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暴雨频率分析的适线方法研究

Study on Curve Fitting Methodology of Frequeney Analysis of Rainstorms

【作者】 张婷

【导师】 谭炳卿;

【作者基本信息】 合肥工业大学 , 水文学及水资源, 2015, 硕士

【摘要】 水文频率曲线研究是水文学中的一项重要内容,而其中适线方法的研究又是该内容的核心部分,通过频率曲线与实测点据的最优拟合获得水文统计曲线参数,从而利用已有的资料系列来研究水文现象的统计规律,以样本的统计参数来代替其总体,为设计年径流、暴雨和洪水提供依据。本文在已有研究的基础上,针对设计暴雨和设计洪水中关注的问题,研究频率曲线的适线方法,着眼于优化方法中适线准则的改进,提出按暴雨大小设置不同权重的分段曲线优化准则,具体寻优目标设置为:频率小于10%的曲线段按实测和拟合曲线两者差值的4次方之和计算,10%~25%的曲线段按两者差值绝对值的3次方之和计算,25%~90%的曲线段按两者差值的平方和计算,90%~95%按两者差值绝对值的0.5次方和计算,其余的拟合曲线段按两者差值的绝对值之和计算,以各曲线段总的拟合误差最小为最优。利用邻域搜索的逼近原则,结合模拟退火算法的原理,实现上述目标的寻优过程。本论文研究的主要内容和获得的结论有:1、统计了研究区各站点的各历时10min、60min、6h、24h和3d)暴雨值,并建立数据库,将各站点数据统计至2013年,比以往的统计数据增加了15年系列长度;2、在统计数据的基础上,采用本文提出方法计算了各站(122站)各历时的均值Ex、变差系数Cv及偏态系数Cs值,并统计分析了不同历时暴雨均值的分布规律,结果表明研究区内南部暴雨均值较北部大;3、通过对研究区内大量站点数据的统计,采用最小二乘法及本文提出的分段设置优化准则的方法,对研究区内有资料站点进行逐站各历时适线,通过对比,分段设置优化准则的方法所得拟合曲线在频率≤10%的区域拟合效果更佳,符合设计洪水适线重点考虑稀遇点据的要求,可用于设计暴雨和设计洪水。

【Abstract】 The study of Hydrological frequency curve is one of the important content in hydrology, and the study of curve fitting methodology which is the core content. Through fitting the frequency curve and the measured data points, obtain the best hydrological statistical parameters of the curve, so then to use some data series to study the statistical laws of hydrological phenomena, statistical parameters instead of the overall sample, provide the basis for the design of annual runoff, storms and floods.Based on the research in existence of this area, focus on the issue for the design storm and flood of interest in the design, the author research methodology of frequency curve fitting, and aimed at improving the proper line optimization criteria, so then proposed by storm size setting different weights curve segments optimization criteria. The specific optimization goal setting is:the curve segment which the frequency is less than 10% is calculated the 4th power of the sum of the absolute value of the difference between the measured data and the fitted curve, the curve segment which the frequency is between 10%~25% is calculated the 3th power of the sum of the difference, the curve segment which the frequency is 25%~90% is calculated the quadratic sum of the difference, the curve segment which the frequency is 90%~95% is calculated the 0.5 party of the difference, and computing power of the rest of the fitted curve segment by both the absolute value of the difference, the calculated result of the total minimum fitting error for each curve segment is optimal. Utilizing the principle of local search approach, and combining the principles of simulated annealing algorithm optimization process to achieve these goals. The main contents of this thesis and conclusions obtained are:1, sort out each lasted statistical study of the site area (10min,60min,6h,24/2 and 3d) storm value, and establish a database, renew the data of the site up to 2013, the series increase 15 years longer than the previous series of statistical data;2, On the basis of statistical data, use the method proposed in this paper to calculate The mean value Ex, coefficient of variation Cv and the coefficient of skew Cs values of the various stations (122 stations)and statistical analysis of the distribution of different duration rain storm, the results of the study area shows that the storm mean value of the southern bigger than the northern;3, Through a large number of sites in the study area of statistical data, using the least squares method and the optimization criteria of setting segmentation proposed in this paper, fitting the sites with which has measured data by different duration curve in the study area. By comparison with the two methods, segmentation settings the resulting optimization criterion curve fitting methods in the frequency region of≤10% is better, in line with the appropriate design flood line key consideration dilute and can be used to design storm and flood design.

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