Atistical Analysis Of Wind Speed Distributions In China

The air seems to be nothing;in fact,we have been watching it,but in the storm,the air makes its existence known.The wind can push the roof of the building,blow off wires and trees,and cause road accidents as gusts push cars and trucks.In this developing era either constructing large infrastructure projects,airports,fast trains,or producing energy by the wind farm all of these profoundly dependent on the analysis of wind speed.It help us,to find the information about the geographical distribution of expected return period of extreme wind events and allow structural engineers to plan appropriate reinforcement to erections exposed to the elementsThe Weibull distribution has been commonly acknowledged and suggested probability distribution to model the wind speed data.The goal of this research project is not only to draw a comparison between given distributions but also provide some flexible distributions and new mixed distribution model to analysis wind speeds for future work.This study is divided into two major parts,in the first part the analysis has been conducted individually by using six distributions for all regions in China while in the second part univariate and mixed extreme value distribution has been applied to Shandong province and four municipalities of China.Firstly,six probability distributions such as Weibull,Extreme Value,Generalized Extreme Value,Rayleigh,t location-scale and Burr type XII probability distributions have been used to analyze the wind speed,and Monte Carlo Simulation is used to generate the randomly predicted values for the wind speeds by distributions.The comparison has been drawn between the actual/real and predicted values to analyze the predicted power.Data is provided by China Meteorological Data Service Center has been used for 23 provinces,4 autonomous regions,4 municipalities regions,which include 171 stations across all over the China for the period of 1951-2015.The Comparison is drawn with the model criteria,and it depends on the following tests.The root means square error(RMSE)which shows the distance between major theoretical distribution and the empirical distribution of experiential wind speed data.The coefficient of determination(R2),it illustrates the strength of the linear relationship between them.Negative of the natural logarithm of the maximum value of the likelihood function corresponding to the estimated distribution(-In L).Akaike information criterion(AIC),-In L and AIC present the goodness-of-fit of ML estimates.Bayesian information criterion(BIC),the model with the lowest BIC is preferred.As different from RMSE and R2 depending on the number of the wind speed class(bins),-ln L and AIC are free from the number of wind speed class.Therefore,-In L,AIC,and BIC are important criteria for the selection of distributional model.The priority of selecting the best distribution is the minimum value of RMSE,then the high value of R2 and then the lowest value of-LnL,AIC and BIC.Secondly,this study is used to analyze the wind speed through the mixed distributions.Four extreme value distributions such as Gumbel,Weibull,Frechet and Generalized Extreme Value distributions have been used to model and analyzed the extreme wind speeds.Mood et al.,1974 introduced the construction of mixed probability distributions in the literature.Pr(X??)=F(x)=pF1(x)+(1-p)F2(X),where p is a factor used to weight the relative contribution of each population(0<p<1).This mixture probability distribution is used for modelling samples of data coming from two populations.While Escalante-Sandoval Carlos Agustin 2012,construct the mixed probability distribution with the mixture of two extreme values distributions.The aim of this study is to modify Mood et al.equation and construct the function of three distributions and in this case three extreme values distributions.Pr(X??)=F(x)=pF1(x)+rF3(x)=+(1-p-r)F3(x),where p and r are the association parameters0<p+r<1.Wind speeds data have been analyzed by univariate extreme value distributions,mixed distributions with the mixture of two distributions,and mixed distributions with the mixture of three distributions.Total 14 univariate and mixed distributions have been used.The estimationthe parameters of the mixed extreme value distribution obtained numerically by direct minimization method.The best model has selected based on a goodness-of-fit test.In this study,the model only applied on Shandong province wind speed data and estimated the extreme wind speeds.The results from the sample of 171 stations are as following,· 65 wind stations which are 38%of samples were fitted better with the t location-scale distribution,45 wind stations which are 26%of samples were fitted with the Generalized Extreme Value(GEV)distribution,· 42 wind stations which are 25%of samples were fitted with the Burr type X11 distribution,· 17 wind stations which are 10%of samples were fitted with the Weibull distribution,· 1 wind station which is 0.5%of the samples had an Extreme-Value(EV)distribution,· 1 wind station which is the 0.5%of the samples had a Rayleigh distribution.Above mentioned results can be concluded as follows,some families of distributions from given six distributions are very flexible enough to accommodate the shape of the wind speed data.This study illustrates the performance of the t location-scale,Burr type XII,and the Generalized Extreme Value(GEV)about the others distributions.Wind speed distributions show that the t location-scale,Burr type XII,and GEV are more flexible and thus more appropriate than the remaining others in modeling wind speed regarding the measured model selection criteria.Particularly t location-scale distribution provides the best fit to a variety of wind speed data.As a result,the t location-scale,Burr type XII,and GEV distributions can be used as other distributions to precisely estimate wind speed distributions.The results of the second part of the study show the follows.· Among all the studied 10 wind stations(Jinan,Chengshan,Dingtao,Huimin County,Weifang,Yanzhou,Beijing,Chongqing,Shanghai,and Tianjin),the six wind stations are better suited for the mixed distribution,and the other four stations are better suited for univariate distributions.· In the mixed distribution,GFW,GFGEV,GGEV and GW are better fitted for analyzing wind speed.The GFGEV distribution is fitted more accurately in three stations named as Yanzhou,Chongqin,and Beijing,while GFW,GGEV,and GW are better suited for stations of Huimin County,Chengshan,and Jinan,respectively.· In the univariate distribution,the Weibull and GEV distributions have better results.· The Weibull distribution is better fitted with 1 station of Tianjin,and GEV better fitted for three stations of Dingtao,Weifang,and Shanghai.Above result concluded that each mixed distribution equation has many unknown parameters.The estimation of parameters by using mixed extremum distribution will be obtained by the direct minimization method and also generate random numbers for each mixed distribution.The study found that mixed distributions are better than univariate distributions,also adding more parameters give better results.The results will illustrate that the mixed distribution is necessary to be considered as a new additional mathematical tool for analyzing extreme wind speeds.