高阶概率权重矩在洪水频率分布参数估计中的应用研究

发布时间：2018-03-24 12:28

本文选题：洪水频率分析　切入点：高阶概率权重矩　出处：《西北农林科技大学》2014年硕士论文

【摘要】：随着全球气候变化，人类活动加剧和社会经济快速发展等影响，洪水极值事件在全球范围频繁发生，人类将面临越来越严峻的防洪安全形势，准确估计洪水设计值对降低洪水灾害十分重要。针对洪水频率分析中，因经验频率曲线中高尾部分与低尾部分经验点据分布趋势不一致，不能用一条光滑的理论频率曲线来拟合所有经验点据这一问题，本文查阅了近年来国内外有关频率计算研究文献，，采用Wang Q.J.博士20世纪90年代提出的洪水频率分布参数高阶概率权重矩估计方法与理论，以陕北地区年最大洪峰流量资料为例，采用高阶概率权重矩、普通概率权重矩、普通矩法和极大似然法进行洪水频率分析计算，以期为研究区水利工程的规划、设计、施工和管理提供合理依据。本文的主要研究内容和结论如下：（1）广义极值（GEV）分布和P-III分布的高阶概率权重矩及参数表达式推求。运用GEV分布的高阶概率权重矩法原理，推求P-III分布的高阶概率权重矩公式，引入P-III分布的高阶概率S函数，利用高斯-勒让德数值积分法计算P-III分布的高阶概率权重矩，并应用特殊函数等方法推求参数表达式。（2）研究区基于高阶概率权重矩的洪水频率分析计算。以陕北地区12个水文测站的年最大洪峰流量资料为例，将高阶概率权重矩法分别应用到GEV分布和P-III分布参数估计中，估算出各分布的参数值，并将不同阶数下理论频率曲线与年最大洪峰流量实测序列进行拟合。研究发现，当提高PWM阶数时，除个别测站外，GEV分布理论频率曲线与经验频率曲线的高尾部分拟合较好，且实测洪水值与设计洪水值累积误差平方和较小，而对P-III分布来说，提高PWM阶数改善其拟合效果和有效地减小误差有待于进一步研究。（3）普通矩法和极大似然法在洪水频率分析中的应用。将普通矩法和极大似然法分别应用到GEV分布和P-III分布参数估计中，计算出研究区各测站参数估计值，并绘制理论频率曲线。研究发现，普通矩法计算结果误差较大，与洪水频率曲线高尾部分拟合较差，而极大似然法的拟合效果较好，误差也较小，但需求解似然函数，尤其是对分布函数较为复杂的P-III分布，求解过程比较复杂。（4）研究区年最大洪峰流量序列分布模型及参数估计方法的确定。将陕北地区各个水文测站的参数估计值及较大洪水值的拟合效果进行对比分析，其中有7个测站选用GEV分布作为其理论分布模型较好，另外5个测站选用P-III分布较好；GEV分布参数估计方法中，选用高阶PWM法较好，对于P-III分布，由于高维数值积分误差，提高高阶PWM法拟合效果有待于进一步研究。（5）采用蒙特卡洛模拟分析高阶PWM法的统计性能。本文运用Monte Carlo法进行样本的多次独立重复随机模拟，对比分析参数估计值及洪水设计值的偏差、标准误差和均方根误差，以进一步研究高阶PWM法在洪水频率分布参数估计中的应用。结果表明，高阶PWM在GEV分布中的应用优势明显。
[Abstract]:With the global climate change, the intensification of human activities and the rapid development of social economy, the extreme events of flood occur frequently in the world. People will face more and more serious flood safety situation. Accurate estimation of flood design value is very important for reducing flood disasters.
For flood frequency analysis, due to the high tail empirical frequency curve part and low tail part according to experience points distribution trend is not the same, not a smooth theoretical frequency curve to fit all experience points according to this problem, this paper reviewed the recent relevant research literature at home and abroad frequency calculation, the method and theory of flood frequency the distribution of parameters of high-order probability weighted moments estimation proposed by Dr. Q.J. Wang in 1990s, in the north of Shaanxi annual peak flow data as an example, using higher order probability weighted moments, ordinary probability weighted moments, ordinary moment method and maximum likelihood method for flood frequency analysis, with a view to the study of water conservancy project area planning and design. To provide a reasonable basis for construction and management. The main research contents and conclusions are as follows:
(1) generalized extreme value (GEV) distribution and P-III distribution of high order probability weighted moments and parameter expressions for high order. By using the principle of probability weighted moment method for GEV distribution, P-III distribution of high order probability weighted moment formula, introducing high-order probability distribution of P-III S function, the calculation of higher-order probability weighted moments of P-III distribution by using Gauss - Legendre numerical integral method, and the application of special function method to derive the parameter expression.
(2) the study area of flood frequency analysis based on high-order probability weighted moment calculation. In 12 hydrological stations in Shanbei area annual peak flow data as an example, the high order probability weighted moment method were applied to the GEV distribution and P-III distribution parameter estimation, estimate the parameters of value distribution, and the theory the frequency curve under different number and annual maximum peak flow measurement sequence was fitted. The study found that when the PWM order, except for individual stations, high end part fitting GEV distribution theory frequency curve and empirical frequency curve is better, and the measured value and the value of Design Flood flood cumulative error square and small, and the distribution of P-III, improve the PWM order to improve the fitting effect and effectively reduce the error needs to be further studied.
(3) the application of ordinary moment method and maximum likelihood method in flood frequency analysis. The general moment method and maximum likelihood method are applied to the GEV distribution and P-III distribution parameter estimation, calculate the study area of each station in the parameter estimates, and draw the theory frequency curve. The study found that the calculation results of ordinary moment method error the larger, and the flood frequency curve of high end part of the fitting is worse, and the fitting effect of the maximum likelihood method is better, the error is smaller, but the demand solution of likelihood function, especially the P-III distribution of the distribution function is complex, the solving process is complex.
(4) the study area annual maximum flood peak series distribution model and parameter estimation method. The fitting effect will be determined in Northern Shaanxi each hydrological station parameter estimates and large flood value were analyzed, which has 7 stations with GEV distribution as its theoretical model is good, the other 5 stations selected the P-III distribution is better; GEV distribution parameter estimation method, using high order PWM method is better for P-III distribution, because the integral high dimensional numerical error, improve the high order PWM method fitting effect needs to be further studied.
(5) using Monte Carlo simulation statistical performance analysis of high order PWM method. This paper uses Monte Carlo method to sample multiple independent repeated stochastic simulation, comparative analysis of parameter estimation deviation and flood design value, standard error and root mean square error, to further study the application of high-order PWM method in the estimation of flood frequency distribution parameters in. The results show that the advantages of high order PWM in the GEV distribution is obvious.

【学位授予单位】：西北农林科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TV122

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