基于部分概率权重矩的洪水频率分布参数估计方法研究

发布时间：2018-05-02 03:29

本文选题：部分概率权重矩 + 广义极值分布　；参考：《西北农林科技大学》2014年硕士论文

【摘要】：在估计洪水频率分布参数时，小洪水样本在估计大重现期设计洪水值上表现出滋扰行为。为了避免使用这些小洪水值影响，本文应用Q.J.Wang (1990)提出的部分概率权重矩(PPWM)进行洪水频率分布参数估计的原理与方法，探索PPWM在陕北地区洪水频率分布参数估计中的普适性。本文在前人探索与研究的基础上，采用MATLAB编程进行广义极值分布(GEV)和皮尔逊三型分布(P-III)的PPWM参数数值求解；应用Monte Carlo模拟试验，研究不同低删失样本下PPWM估计量的统计特性；采用基于PPWM的GEV分布和P-III分布参数估计方法，研究研究区12个测站的年最大洪峰流量系列洪水频率参数估计，并对不同低删失样本下理论分布的拟合效果进行评价。本文所取得的主要研究结果如下： (1)获得了低删失样本下基于PPWM的GEV分布和P-Ⅲ分布参数的数值求解，对于PPWM的推广和应用具有现实意义。应用积分原理和特殊函数推求出GEV分布的PPWM，进而推导出PPWM和分布参数之间的关系式。对于给定样本，利用这些关系式由样本PPWM的无偏估计量实现参数估计。但是由于PPWM进行P-Ⅲ分布参数估计中，含有特殊函数，如果要按照严格的数学推导求解参数是很困难的。本文基于粒子群优化算法(PSO)和MATLAB软件编写了参数求解程序，实现了基于PPWM的P-Ⅲ分布参数的数值求解。这种数值计算方法的求解精度较高，而且利用MATLAB软件大大减少了工作量，简化了PPWM估计分布参数的估计求解。 (2)Monte Carlo模拟试验研究表明，在适度的删失水平(F0)取值下，低删失样本的PPWM估计量有较好的统计特性。虽然对统计参数的估计效果随着F0的增大不断劣化，但是它在高分位数的估计方面呈现出良好的有效性，在一定范围内，，并不会随着F0的增大而估计效果变差，甚至在取某些F0值下，PPWM设计值估计量的统计特性优于PWM。据此可以认为，在以获取高分位数(大重现期的设计洪水)为目标的估计中，应用低删失样本PPWM不会影响其估计的有效性。 Monte Carlo模拟试验结果还表明，虽然PPWM使用删失样本估计分布参数，但增加样本容量是改善GEV分布参数估计效果的一种有效手段，对于是否为改善P-Ⅲ分布参数估计效果的有效手段还不能妄下结论，有待进一步的探讨和分析。 (3)对陕北地区12个水文测站的年最大洪峰流量系列，在不同低删失样本下采用PPWM所建立的GEV分布和P-Ⅲ分布基本上都是合理的。在本文所考虑的六种F0取值情况下，采用不同的拟合效果评价方法得到最优理论分布对应的F0取值不同，不管采用哪一种评价方法，大多数测站的最优理论分布对于实测系列的拟合效果较好，表明PPWM在陕北地区洪水频率分布参数估计中具有一定的适用性。
[Abstract]:When estimating the parameters of flood frequency distribution, the small flood samples show the disturbance behavior in estimating the value of the heavy current design flood. In order to avoid the use of these small flood values, this paper applies the principle and method of estimating the parameters of the flood frequency distribution by the partial probability weight moment (PPWM) proposed by Q.J.Wang (1990), and explores the PPWM in the north of Shaanxi. On the basis of predecessors' exploration and research, this paper uses MATLAB programming to solve PPWM parameters of generalized extreme value distribution (GEV) and Pearson three type distribution (P-III), and uses Monte Carlo simulation test to study the statistical properties of PPWM estimators under different low censored samples and adopt P based on P. The GEV distribution of PWM and the estimation method of P-III distribution parameters are used to estimate the annual maximum flood frequency parameters of the 12 stations in the study area, and evaluate the fitting effect of the theoretical distribution under different low censored samples. The main results obtained in this paper are as follows:
(1) get the numerical solution of GEV distribution and P- III distribution parameters based on PPWM under low censored samples, which is of practical significance for the promotion and application of PPWM.
The PPWM of GEV distribution is deduced by using the integral principle and special function, and then the relation between PPWM and distribution parameters is derived. For given samples, the parameters are estimated by the unbiased estimators of the sample PPWM.
But because PPWM carries out the estimation of P- III distribution parameters, it contains special functions, it is very difficult to solve the parameter in accordance with the strict mathematical deduction. Based on the particle swarm optimization (PSO) and MATLAB software, the parameter solver is written in this paper, and the numerical solution of the P- III distribution parameters based on PPWM is realized. This numerical calculation method is solved. The accuracy of the solution is high, and the workload of the MATLAB software is greatly reduced, and the estimation of the distribution parameters of the PPWM estimation is simplified.
(2) the Monte Carlo simulation experiment shows that the PPWM estimator of the low censored sample has good statistical properties under the appropriate deletion level (F0) value. Although the estimation effect of the statistical parameter is deteriorating with the increase of F0, it shows a good validity in the estimation of high quantile, and it will not follow in a certain range. With the increase of F0, the estimated effect is worse. Even under some F0 values, the statistical properties of the PPWM design value estimator are better than that of PWM.. In the estimation of the high quantile (large current design flood), the application of the low censored sample PPWM will not affect the effectiveness of its estimation.
The results of Monte Carlo simulation test also show that, although PPWM uses censored samples to estimate the distribution parameters, the increase of sample size is an effective means to improve the estimation effect of GEV distribution parameters. The effective means for improving the estimation effect of P- III distribution parameters can not be discussed, and further discussion and analysis are needed.
(3) for the annual maximum flood peak flow series of 12 hydrological stations in Northern Shaanxi Province, the distribution of GEV and P- III distribution established by PPWM under different low censored samples are basically reasonable. In the case of six F0 values considered in this paper, different fitting effect evaluation methods are used to obtain the different values of the optimal theoretical distribution corresponding to the F0. The best theoretical distribution of most stations has a good fitting effect on the measured series, which shows that the PPWM has a certain applicability in the estimation of the flood frequency distribution parameters in the north of Shaanxi.

【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】：P333.2

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