中国的风速概率分布统计分析

发布时间：2018-01-07 09:04

  本文关键词：中国的风速概率分布统计分析　出处：《山东大学》2017年硕士论文　论文类型：学位论文

  更多相关文章： 中国 风速 概率 分布 统计分析

【摘要】：空气似乎看不见摸不着;事实上,我们一直都可以观察到它的运动,在风暴中,空气的运动能被清楚地感知到。狂风可以把建筑物上的屋顶掀飞,能吹起电线杆和树木,并能刮翻汽车和卡车而引起道路事故。在这个快速发展的时代,无论是建造大型基础设施项目,机场,快速列车,还是用来发电的风电场,都离不开风速分析。风速分析可以帮助我们掌握关于极端风力事件周期期望值的地理分布情况,并为工程师们对于是否对暴露于风场中建筑结构进行必要加固的决策提供依据。大量的研究使用Weibull分布来模拟风速数据。在这项研究中,我们不仅对于给定分布的拟合结果进行了比较,而且提出了灵活分布模型以及混合分布模型,这些对于将来的研究具有很重要的意义。本研究主要分为两个部分,第一部分,我们分别利用六个分布函数对中国所有地区的风速数据进行分析;第二部分,我们利用单变量和混合极值分布对山东省以及中国四个直辖市的风速数据进行讨论。首先,在这项研究中,我们分别使用六种概率分布来分析风速,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,我们用蒙特卡罗模拟的方法根据这些确定好参数的分布生成风速的随机预测值。并且通过实际/真实值和预测值之间的比较来分析预测的有效性。我们使用的数据是从中国气象数据服务中心获取的1951-2015年期间中国23个省,4个自治区,和4个直辖市,区一共171个站点的数据。通过设定检验标准可以对模型进行评价。在本文中我们使用以下几种标准:均方根误差(RMSE),它可以用来度量理论分布与观测风速数据的经验分布之间的距离。相关系数(R2),这一系数表征了它们之间的线性关系的强度。估计分布似然函数负对数的最大值(-ln L),Akaike信息准则(AIC),-ln L和AIC用来表征ML估计的拟合优度。贝叶斯信息准则(BIC),选择的模型应该使得BIC值尽可能的小。RMSE和R2与风速类型有关,而与上面两个标准不同,-ln L和AIC不依赖于风速类型的数量。因此,在分布模型的选择上,-ln L,AIC和BIC是十分重要的准则。选择最佳分布的第一优先级是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,本文通过混合分布来研究风速分布。利用Gumbel,Weibull,Frechet和广义极值分布四个极值分布来模拟和分析极端风速。Mood等人在1974的文献中引入了混合概率分布:Pr(X ≤ ε)= F(x)= pF1（x)+(1-p)F2(x),其中p是用于每个分布的权(0p1)。该混合概率分布用于对来自两个分布的数据样本进行建模。Escalante-Sandoval Carlos Agustin在2012建立了两个极值分布的混合概率分布。本文研究的目的是对Mood et al.方程进行改进,构建三个分布函数的混合分布,特别地,三个极值分布的混合分布:Pr(X≤ε)= F(x)= pF1(x)+ rF3(x)+(1-p-r)F3(x)其中p和r是相关的参数且0p + r1.分别使用单一极值分布、两个分布的混合分布、三个分布的混合分布来对风速数据进行分析。一共考虑了 14种情况下的分布。对于混合极值分布的参数估计利用解最小值的方法直接通过使用Matlab获得。基于拟合优度检验选择最佳的模型。在本文中,模型应用于山东省的风速数据并给出极端风速的估计。171个样本观测站的数据分析结果如下:· t location-scale分布表现更好的风站数为65个,占风站总数的38%:广义极值(GEV)分布表现更好风站数为45个,占风站总数的26%。· Burr type ⅩⅡ分布表现更好的风站数为42个,占风站总数的25%。· Weibull分布表现更好的风站数为17个,占风站总数的10%。· Extreme Value(EV)分布表现更好的风站数为1个,占风站总数的0.5%。· Rayleigh分布表现更好的风站数为1个,占风站总数的0.5%。上述结果可以归纳如下:首先,因为备选的六个分布中的某些分布族已经足够灵活,它们完全可以用来拟合风速数据的分布函数,通过研究可以看出,对于风速分布的分析,相对于其他分布,在给定的模型选择标准下,t location-scale分布,Burr type Ⅻ分布和Generalized Extreme Value(GEV)分布更灵活更合适。特别地,t location-scale分布是对于风速数据的最佳拟合分布。因此,t location-scale分布,Burr type Ⅻ分布和Generalized Extreme Value(GEV)分布可以用作准确估计风速分布的替代选择。研究的第二部分的结果如下:·在所有研究的10个风电站(济南,成山,定陶,惠民县,潍坊,兖州,北京,重庆,上海,天津)中,五个风电站的数据更适合使用混合分布刻画,其余五个站的数据更适合使用单变量分布刻画。·在混合分布中,GFW,GFGEV,GGEV和GW更适合分析风速。对于兖州,北京两个风站,GFGEV分布的结果更准确,而GFW,GGEV和GW分别更适合分析惠民县,成山,济南的观测站数据。·在单变量分布中,Weibull和GEV分布具有更好的结果。· Weibull分布更适合重庆,天津两站的数据,GEV更适合定鼎,潍坊,上海三站的数据。通过以上结果得出结论:由于每个混合分布方程有更多的未知参数,通过直接计算最小值点的方法得到混合极值分布的参数估计,进而通过这些混合分布生成随机数。研究发现,混合分布的表现要优于单变量分布,增加了更多的参数可以得到更好的拟合结果。研究说明混合分布作为统计上分析极端风速数据的一种新的数学工具来说是很重要的。
[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.

【学位授予单位】：山东大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P425;O211.3

【参考文献】

中国期刊全文数据库 前1条

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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本文编号：1391874