本文關鍵詞：中國的風速概率分布統(tǒng)計分析　出處：《山東大學》2017年碩士論文　論文類型：學位論文

  更多相關文章： 中國 風速 概率 分布 統(tǒng)計分析

【摘要】：空氣似乎看不見摸不著;事實上,我們一直都可以觀察到它的運動,在風暴中,空氣的運動能被清楚地感知到�？耧L可以把建筑物上的屋頂掀飛,能吹起電線桿和樹木,并能刮翻汽車和卡車而引起道路事故。在這個快速發(fā)展的時代,無論是建造大型基礎設施項目,機場,快速列車,還是用來發(fā)電的風電場,都離不開風速分析。風速分析可以幫助我們掌握關于極端風力事件周期期望值的地理分布情況,并為工程師們對于是否對暴露于風場中建筑結構進行必要加固的決策提供依據(jù)。大量的研究使用Weibull分布來模擬風速數(shù)據(jù)。在這項研究中,我們不僅對于給定分布的擬合結果進行了比較,而且提出了靈活分布模型以及混合分布模型,這些對于將來的研究具有很重要的意義。本研究主要分為兩個部分,第一部分,我們分別利用六個分布函數(shù)對中國所有地區(qū)的風速數(shù)據(jù)進行分析;第二部分,我們利用單變量和混合極值分布對山東省以及中國四個直轄市的風速數(shù)據(jù)進行討論。首先,在這項研究中,我們分別使用六種概率分布來分析風速,包括Weibull分布,Extreme Value 分布,Generalized Extreme Value 分布,Rayleigh 分布,tlocation-scale 分布和Burr type Ⅻ分布。之后,我們用蒙特卡羅模擬的方法根據(jù)這些確定好參數(shù)的分布生成風速的隨機預測值。并且通過實際/真實值和預測值之間的比較來分析預測的有效性。我們使用的數(shù)據(jù)是從中國氣象數(shù)據(jù)服務中心獲取的1951-2015年期間中國23個省,4個自治區(qū),和4個直轄市,區(qū)一共171個站點的數(shù)據(jù)。通過設定檢驗標準可以對模型進行評價。在本文中我們使用以下幾種標準:均方根誤差(RMSE),它可以用來度量理論分布與觀測風速數(shù)據(jù)的經(jīng)驗分布之間的距離。相關系數(shù)(R2),這一系數(shù)表征了它們之間的線性關系的強度。估計分布似然函數(shù)負對數(shù)的最大值(-ln L),Akaike信息準則(AIC),-ln L和AIC用來表征ML估計的擬合優(yōu)度。貝葉斯信息準則(BIC),選擇的模型應該使得BIC值盡可能的小。RMSE和R2與風速類型有關,而與上面兩個標準不同,-ln L和AIC不依賴于風速類型的數(shù)量。因此,在分布模型的選擇上,-ln L,AIC和BIC是十分重要的準則。選擇最佳分布的第一優(yōu)先級是RMSE的最小值,然后是R2的高值,然后是-LnL,AIC和BIC的最小值。其次,本文通過混合分布來研究風速分布。利用Gumbel,Weibull,Frechet和廣義極值分布四個極值分布來模擬和分析極端風速。Mood等人在1974的文獻中引入了混合概率分布:Pr(X ≤ ε)= F(x)= pF1（x)+(1-p)F2(x),其中p是用于每個分布的權(0p1)。該混合概率分布用于對來自兩個分布的數(shù)據(jù)樣本進行建模。Escalante-Sandoval Carlos Agustin在2012建立了兩個極值分布的混合概率分布。本文研究的目的是對Mood et al.方程進行改進,構建三個分布函數(shù)的混合分布,特別地,三個極值分布的混合分布:Pr(X≤ε)= F(x)= pF1(x)+ rF3(x)+(1-p-r)F3(x)其中p和r是相關的參數(shù)且0p + r1.分別使用單一極值分布、兩個分布的混合分布、三個分布的混合分布來對風速數(shù)據(jù)進行分析。一共考慮了 14種情況下的分布。對于混合極值分布的參數(shù)估計利用解最小值的方法直接通過使用Matlab獲得�；跀M合優(yōu)度檢驗選擇最佳的模型。在本文中,模型應用于山東省的風速數(shù)據(jù)并給出極端風速的估計。171個樣本觀測站的數(shù)據(jù)分析結果如下:· t location-scale分布表現(xiàn)更好的風站數(shù)為65個,占風站總數(shù)的38%:廣義極值(GEV)分布表現(xiàn)更好風站數(shù)為45個,占風站總數(shù)的26%�！� Burr type ⅩⅡ分布表現(xiàn)更好的風站數(shù)為42個,占風站總數(shù)的25%�！� Weibull分布表現(xiàn)更好的風站數(shù)為17個,占風站總數(shù)的10%�！� Extreme Value(EV)分布表現(xiàn)更好的風站數(shù)為1個,占風站總數(shù)的0.5%�！� Rayleigh分布表現(xiàn)更好的風站數(shù)為1個,占風站總數(shù)的0.5%。上述結果可以歸納如下:首先,因為備選的六個分布中的某些分布族已經(jīng)足夠靈活,它們完全可以用來擬合風速數(shù)據(jù)的分布函數(shù),通過研究可以看出,對于風速分布的分析,相對于其他分布,在給定的模型選擇標準下,t location-scale分布,Burr type Ⅻ分布和Generalized Extreme Value(GEV)分布更靈活更合適。特別地,t location-scale分布是對于風速數(shù)據(jù)的最佳擬合分布。因此,t location-scale分布,Burr type Ⅻ分布和Generalized Extreme Value(GEV)分布可以用作準確估計風速分布的替代選擇。研究的第二部分的結果如下:·在所有研究的10個風電站(濟南,成山,定陶,惠民縣,濰坊,兗州,北京,重慶,上海,天津)中,五個風電站的數(shù)據(jù)更適合使用混合分布刻畫,其余五個站的數(shù)據(jù)更適合使用單變量分布刻畫�！ぴ诨旌戏植贾�,GFW,GFGEV,GGEV和GW更適合分析風速。對于兗州,北京兩個風站,GFGEV分布的結果更準確,而GFW,GGEV和GW分別更適合分析惠民縣,成山,濟南的觀測站數(shù)據(jù)�！ぴ趩巫兞糠植贾�,Weibull和GEV分布具有更好的結果�！� Weibull分布更適合重慶,天津兩站的數(shù)據(jù),GEV更適合定鼎,濰坊,上海三站的數(shù)據(jù)。通過以上結果得出結論:由于每個混合分布方程有更多的未知參數(shù),通過直接計算最小值點的方法得到混合極值分布的參數(shù)估計,進而通過這些混合分布生成隨機數(shù)。研究發(fā)現(xiàn),混合分布的表現(xiàn)要優(yōu)于單變量分布,增加了更多的參數(shù)可以得到更好的擬合結果。研究說明混合分布作為統(tǒng)計上分析極端風速數(shù)據(jù)的一種新的數(shù)學工具來說是很重要的。
[Abstract]:The air seems invisible; in fact, we have observed its movement in the storm, the air movement can be clearly perceived. The wind can put the roof buildings on the fly, can blow the poles and trees, and the wind overturned cars and trucks and the road the accident. In this era of rapid development, whether it is the construction of large infrastructure projects, the airport express train, or used for wind power generation, all cannot do without the wind. The wind speed of analysis can help us grasp on the extreme wind event cycle expectations and distribution, and for the engineers to provide the basis for whether or not exposure to the building structure in the wind field is necessary to reinforce the decision. A large number of studies using Weibull to simulate the distribution of wind speed data. In this study, we not only for the given distribution fitting results were compared, and A flexible distribution model and mixed distribution model, which has very important significance for future research. This research is mainly divided into two parts, the first part, we were all Chinese area of wind speed data were analyzed by using six distribution functions; the second part, we use the single variable and mixed data on the distribution of extreme wind Shandong province and Chinese four municipalities are discussed. Firstly, in this study, we use six kinds of probability distribution of wind speed distribution, including Weibull, Extreme Value Generalized Extreme distribution, Value distribution, Rayleigh distribution, tlocation-scale distribution and Burr distribution type XII. After that, we use the method of Monte Carlo simulation based on these parameters determine the stochastic prediction of wind speed distribution to generate value. And through the real / true value and compare the value between forecast analysis and forecast Effective. We use the data obtained from Chinese meteorological data service center during 1951-2015 Chinese 23 provinces, 4 autonomous regions and 4 municipalities, district a total of 171 sites. By setting the standard test data can be evaluated on the model. In this paper we use the following criteria: the root mean square error (RMSE), it can be used to measure the distribution of experience between the theoretical distribution and wind speed data of the distance. The correlation coefficient (R2), the coefficient to characterize the linear relationship between them. The intensity distribution of the maximum likelihood estimation of the negative logarithm (-ln L), the Akaike information criterion (AIC). -ln L and AIC are used to estimate the goodness of fitting characterization of ML. The Bayesian information criterion (BIC), the model should be as small as possible so that the BIC value of.RMSE and R2 and the wind speed is related to the type, but different from the above two standards, -ln L and AIC does not depend on the type of wind speed The number of distribution model. Therefore, in the choice of -ln, L, AIC and BIC is very important to choose the best distribution criteria. The first priority is the minimum value of RMSE, then the high value of R2, then -LnL, the minimum value of AIC and BIC. Secondly, this paper studies the mixture distribution of wind speed distribution. By using Gumbel, Weibull, Frechet and generalized extreme value distribution four extreme value distribution to simulate and analysis of extreme wind speed.Mood et al. In 1974 the literature introduces a hybrid probability distribution: Pr (X = epsilon) = F (x) = pF1 (x) + (1-p) F2 (x), which is used for P each distribution rights (0p1). The mixed probability distribution for the distribution of data from two samples in 2012 Agustin Carlos.Escalante-Sandoval model established two extreme value distribution of mixed probability distribution. The purpose of this paper is on the Mood et al. equation was improved, the mixture distribution to construct three special distribution function. No, the three extreme value distribution of mixed distribution: Pr (X < epsilon) = F (x) = pF1 (x) + rF3 (x) + (1-p-r) F3 (x) P and R are related to the parameters and 0P + r1. respectively using a single value distribution, the distribution of the two mixed distribution three, the distribution of the mixture distribution of wind speed data were analyzed. Considering the distribution of a total of 14 cases. The parameters of the mixture are estimated using the method of extreme value distribution of the minimum value of the solution obtained directly by using Matlab. The goodness of fit test to select the best model in this paper. Based on the wind speed, the number of model application in Shandong according to the province and gives the extreme wind speed estimation of.171 sample observation station data analysis results are as follows: the number of air station t location-scale distribution better 65, accounting for 38% of the total wind station: generalized extreme value (GEV) distribution better wind station number 45, accounting for 26%. of the total number of Burr wind station type XII distribution performance The number of wind station is 42, accounting for the total number of wind wind station station 25%. - Weibull distribution better for 17, accounting for 10%. of the total wind station - Extreme Value (EV) the number of wind stations distributed better 1, accounting for the total number of wind wind station station 0.5%. - Rayleigh distribution better for 1, accounting for 0.5%. of the total wind station the results can be summarized as follows: firstly, because some distributions of six alternative distribution in is flexible enough, they can be used to fit the distribution function of wind speed data, it can be seen, for the analysis of wind speed distribution, relative to other distribution, in the standard choice the given model, t location-scale distribution, Burr distribution and Generalized Extreme Value type XII (GEV) distribution is more flexible and more suitable. In particular, the T location-scale distribution is the best fit for the data of wind speed distribution. Therefore, the distribution of T location-scale, Bu RR type and Generalized Extreme Value XII distribution (GEV distribution) can be used for accurate estimation of wind speed distribution alternative. The second part of the research results are as follows: in 10 of all wind power plant (Ji'nan, Chengshan, Dingtao, Huimin County, Weifang, Yanzhou, Beijing, Chongqing, Shanghai, Tianjin, five) a wind power plant data is more suitable for mixed distribution characterization, the remaining five station data is more suitable for single variable distribution. In the mixed distribution, GFW, GFGEV, GGEV and GW are more suitable for the analysis of wind speed. For Yanzhou, the Beijing two wind station, GFGEV distribution more accurate results and GFW, GGEV and GW were more suitable for the analysis of Huimin County, Ji'nan mountain, observation data. In univariate distribution, Weibull distribution and GEV has better results. Weibull distribution is more suitable for Chongqing, the Tianjin two station data, GEV is more suitable for Weifang, Shanghai three Dingding, station data. The above results we conclude that because each mixture distribution equation has more unknown parameters, by directly calculating the minimum point of the method of estimation of parameters of mixed extreme value distribution, and then through the mixed distribution random number generation. The study found that mixed distribution is superior to the single variable distribution, fitting results can be obtained better more the study shows that the mixture distribution parameters. The statistical analysis is a new mathematical tool of extreme wind speed data is very important.

【學位授予單位】：山東大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：P425;O211.3

【參考文獻】

中國期刊全文數(shù)據(jù)庫 前1條

1 SHI Pei-Jun;ZHANG Gang-Feng;KONG Feng;YE Qian;;Wind speed change regionalization in China(1961-2012)[J];Advances in Climate Change Research;2015年02期

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本文編號：1391874