發(fā)布時(shí)間：2018-05-02 03:29

  本文選題：部分概率權(quán)重矩 + 廣義極值分布��； 參考：《西北農(nóng)林科技大學(xué)》2014年碩士論文

【摘要】：在估計(jì)洪水頻率分布參數(shù)時(shí)，小洪水樣本在估計(jì)大重現(xiàn)期設(shè)計(jì)洪水值上表現(xiàn)出滋擾行為。為了避免使用這些小洪水值影響，本文應(yīng)用Q.J.Wang (1990)提出的部分概率權(quán)重矩(PPWM)進(jìn)行洪水頻率分布參數(shù)估計(jì)的原理與方法，探索PPWM在陜北地區(qū)洪水頻率分布參數(shù)估計(jì)中的普適性。本文在前人探索與研究的基礎(chǔ)上，采用MATLAB編程進(jìn)行廣義極值分布(GEV)和皮爾遜三型分布(P-III)的PPWM參數(shù)數(shù)值求解；應(yīng)用Monte Carlo模擬試驗(yàn)，研究不同低刪失樣本下PPWM估計(jì)量的統(tǒng)計(jì)特性；采用基于PPWM的GEV分布和P-III分布參數(shù)估計(jì)方法，研究研究區(qū)12個(gè)測(cè)站的年最大洪峰流量系列洪水頻率參數(shù)估計(jì)，并對(duì)不同低刪失樣本下理論分布的擬合效果進(jìn)行評(píng)價(jià)。本文所取得的主要研究結(jié)果如下： (1)獲得了低刪失樣本下基于PPWM的GEV分布和P-Ⅲ分布參數(shù)的數(shù)值求解，對(duì)于PPWM的推廣和應(yīng)用具有現(xiàn)實(shí)意義。 應(yīng)用積分原理和特殊函數(shù)推求出GEV分布的PPWM，進(jìn)而推導(dǎo)出PPWM和分布參數(shù)之間的關(guān)系式。對(duì)于給定樣本，利用這些關(guān)系式由樣本PPWM的無偏估計(jì)量實(shí)現(xiàn)參數(shù)估計(jì)。 但是由于PPWM進(jìn)行P-Ⅲ分布參數(shù)估計(jì)中，含有特殊函數(shù)，如果要按照嚴(yán)格的數(shù)學(xué)推導(dǎo)求解參數(shù)是很困難的。本文基于粒子群優(yōu)化算法(PSO)和MATLAB軟件編寫了參數(shù)求解程序，實(shí)現(xiàn)了基于PPWM的P-Ⅲ分布參數(shù)的數(shù)值求解。這種數(shù)值計(jì)算方法的求解精度較高，而且利用MATLAB軟件大大減少了工作量，簡化了PPWM估計(jì)分布參數(shù)的估計(jì)求解。 (2)Monte Carlo模擬試驗(yàn)研究表明，在適度的刪失水平(F0)取值下，低刪失樣本的PPWM估計(jì)量有較好的統(tǒng)計(jì)特性。雖然對(duì)統(tǒng)計(jì)參數(shù)的估計(jì)效果隨著F0的增大不斷劣化，但是它在高分位數(shù)的估計(jì)方面呈現(xiàn)出良好的有效性，在一定范圍內(nèi)，，并不會(huì)隨著F0的增大而估計(jì)效果變差，甚至在取某些F0值下，PPWM設(shè)計(jì)值估計(jì)量的統(tǒng)計(jì)特性優(yōu)于PWM。據(jù)此可以認(rèn)為，在以獲取高分位數(shù)(大重現(xiàn)期的設(shè)計(jì)洪水)為目標(biāo)的估計(jì)中，應(yīng)用低刪失樣本PPWM不會(huì)影響其估計(jì)的有效性。 Monte Carlo模擬試驗(yàn)結(jié)果還表明，雖然PPWM使用刪失樣本估計(jì)分布參數(shù)，但增加樣本容量是改善GEV分布參數(shù)估計(jì)效果的一種有效手段，對(duì)于是否為改善P-Ⅲ分布參數(shù)估計(jì)效果的有效手段還不能妄下結(jié)論，有待進(jìn)一步的探討和分析。 (3)對(duì)陜北地區(qū)12個(gè)水文測(cè)站的年最大洪峰流量系列，在不同低刪失樣本下采用PPWM所建立的GEV分布和P-Ⅲ分布基本上都是合理的。在本文所考慮的六種F0取值情況下，采用不同的擬合效果評(píng)價(jià)方法得到最優(yōu)理論分布對(duì)應(yīng)的F0取值不同，不管采用哪一種評(píng)價(jià)方法，大多數(shù)測(cè)站的最優(yōu)理論分布對(duì)于實(shí)測(cè)系列的擬合效果較好，表明PPWM在陜北地區(qū)洪水頻率分布參數(shù)估計(jì)中具有一定的適用性。
[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.

【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：P333.2

【參考文獻(xiàn)】

相關(guān)期刊論文 前6條

1 陳子全;宋松柏;曾智;李揚(yáng);;基于模擬退火算法的皮爾遜Ⅲ型分布參數(shù)估計(jì)[J];人民黃河;2012年05期

2 郭生練;葉守澤;;洪水頻率的非參數(shù)估計(jì)[J];水電能源科學(xué);1991年04期

3 周川;陳元芳;魏琳;程龍;黃琴;曹雪芹;;適線法在洪水超定量系列頻率分析中的應(yīng)用研究[J];水電能源科學(xué);2011年03期

4 張靜怡,徐小明;極值分布和P-III型分布線性矩法在區(qū)域洪水頻率分析中的檢驗(yàn)[J];水文;2002年06期

5 郭化文;皮爾遜Ⅲ型分布的參數(shù)估計(jì)[J];泰安教育學(xué)院學(xué)報(bào)岱宗學(xué)刊;1999年04期

6 郭生練;考慮歷史洪水資料的頻率計(jì)算方法[J];武漢水利電力學(xué)院學(xué)報(bào);1988年01期

本文編號(hào)：1832191