本文選題：洪水頻率分析　切入點(diǎn)：高階概率權(quán)重矩　出處：《西北農(nóng)林科技大學(xué)》2014年碩士論文

【摘要】：隨著全球氣候變化，人類活動加劇和社會經(jīng)濟(jì)快速發(fā)展等影響，洪水極值事件在全球范圍頻繁發(fā)生，人類將面臨越來越嚴(yán)峻的防洪安全形勢，準(zhǔn)確估計(jì)洪水設(shè)計(jì)值對降低洪水災(zāi)害十分重要。 針對洪水頻率分析中，因經(jīng)驗(yàn)頻率曲線中高尾部分與低尾部分經(jīng)驗(yàn)點(diǎn)據(jù)分布趨勢不一致，不能用一條光滑的理論頻率曲線來擬合所有經(jīng)驗(yàn)點(diǎn)據(jù)這一問題，本文查閱了近年來國內(nèi)外有關(guān)頻率計(jì)算研究文獻(xiàn)，，采用Wang Q.J.博士20世紀(jì)90年代提出的洪水頻率分布參數(shù)高階概率權(quán)重矩估計(jì)方法與理論，以陜北地區(qū)年最大洪峰流量資料為例，采用高階概率權(quán)重矩、普通概率權(quán)重矩、普通矩法和極大似然法進(jìn)行洪水頻率分析計(jì)算，以期為研究區(qū)水利工程的規(guī)劃、設(shè)計(jì)、施工和管理提供合理依據(jù)。本文的主要研究內(nèi)容和結(jié)論如下： （1）廣義極值（GEV）分布和P-III分布的高階概率權(quán)重矩及參數(shù)表達(dá)式推求。運(yùn)用GEV分布的高階概率權(quán)重矩法原理，推求P-III分布的高階概率權(quán)重矩公式，引入P-III分布的高階概率S函數(shù)，利用高斯-勒讓德數(shù)值積分法計(jì)算P-III分布的高階概率權(quán)重矩，并應(yīng)用特殊函數(shù)等方法推求參數(shù)表達(dá)式。 （2）研究區(qū)基于高階概率權(quán)重矩的洪水頻率分析計(jì)算。以陜北地區(qū)12個水文測站的年最大洪峰流量資料為例，將高階概率權(quán)重矩法分別應(yīng)用到GEV分布和P-III分布參數(shù)估計(jì)中，估算出各分布的參數(shù)值，并將不同階數(shù)下理論頻率曲線與年最大洪峰流量實(shí)測序列進(jìn)行擬合。研究發(fā)現(xiàn)，當(dāng)提高PWM階數(shù)時，除個別測站外，GEV分布理論頻率曲線與經(jīng)驗(yàn)頻率曲線的高尾部分?jǐn)M合較好，且實(shí)測洪水值與設(shè)計(jì)洪水值累積誤差平方和較小，而對P-III分布來說，提高PWM階數(shù)改善其擬合效果和有效地減小誤差有待于進(jìn)一步研究。 （3）普通矩法和極大似然法在洪水頻率分析中的應(yīng)用。將普通矩法和極大似然法分別應(yīng)用到GEV分布和P-III分布參數(shù)估計(jì)中，計(jì)算出研究區(qū)各測站參數(shù)估計(jì)值，并繪制理論頻率曲線。研究發(fā)現(xiàn)，普通矩法計(jì)算結(jié)果誤差較大，與洪水頻率曲線高尾部分?jǐn)M合較差，而極大似然法的擬合效果較好，誤差也較小，但需求解似然函數(shù)，尤其是對分布函數(shù)較為復(fù)雜的P-III分布，求解過程比較復(fù)雜。 （4）研究區(qū)年最大洪峰流量序列分布模型及參數(shù)估計(jì)方法的確定。將陜北地區(qū)各個水文測站的參數(shù)估計(jì)值及較大洪水值的擬合效果進(jìn)行對比分析，其中有7個測站選用GEV分布作為其理論分布模型較好，另外5個測站選用P-III分布較好；GEV分布參數(shù)估計(jì)方法中，選用高階PWM法較好，對于P-III分布，由于高維數(shù)值積分誤差，提高高階PWM法擬合效果有待于進(jìn)一步研究。 （5）采用蒙特卡洛模擬分析高階PWM法的統(tǒng)計(jì)性能。本文運(yùn)用Monte Carlo法進(jìn)行樣本的多次獨(dú)立重復(fù)隨機(jī)模擬，對比分析參數(shù)估計(jì)值及洪水設(shè)計(jì)值的偏差、標(biāo)準(zhǔn)誤差和均方根誤差，以進(jìn)一步研究高階PWM法在洪水頻率分布參數(shù)估計(jì)中的應(yīng)用。結(jié)果表明，高階PWM在GEV分布中的應(yīng)用優(yōu)勢明顯。
[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.

【學(xué)位授予單位】：西北農(nóng)林科技大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：TV122

【參考文獻(xiàn)】

相關(guān)期刊論文 前10條

1 李俠;;陜北黃土高原區(qū)地質(zhì)災(zāi)害發(fā)育特征及防治對策[J];安徽農(nóng)業(yè)科學(xué);2010年20期

2 熊立華,郭生練;兩變量極值分布在洪水頻率分析中的應(yīng)用研究[J];長江科學(xué)院院報(bào);2004年02期

3 李太星;宋萌勃;;皮爾遜Ⅲ型分布參數(shù)估計(jì)方法的對比分析[J];長江工程職業(yè)技術(shù)學(xué)院學(xué)報(bào);2008年03期

4 劉光祖,史美英,邊寬江;陜北地區(qū)主要河流年降雨輸沙規(guī)律的統(tǒng)計(jì)分析[J];干旱地區(qū)農(nóng)業(yè)研究;1998年04期

5 張興榆;曹明明;雷敏;;陜北地區(qū)水資源安全及需求預(yù)測分析[J];干旱區(qū)資源與環(huán)境;2007年11期

6 周玉文，李玉華;極大似然法求暴雨強(qiáng)度P－Ⅲ分布統(tǒng)計(jì)參數(shù)的可行性研究[J];哈爾濱建筑大學(xué)學(xué)報(bào);1996年05期

7 陳望春,趙立鋒;權(quán)函數(shù)法在P-Ⅲ型分布中的應(yīng)用[J];浙江水利科技;2002年04期

8 周玉文,周勝昔,曹麗虹;極大似然法求皮爾遜 Ⅲ 型分布參數(shù)[J];給水排水;1997年06期

9 董秋瑤;石建省;葉浩;吳利杰;石迎春;郭嬌;曹文庚;;陜北黃土區(qū)不同土地利用方式的土壤肥力研究[J];南水北調(diào)與水利科技;2010年06期

10 趙曉慎;王衛(wèi)東;;皮爾遜-Ⅲ型分布曲線最佳配線及自動化繪圖[J];人民黃河;2007年04期

本文編號：1658291