基于Monte Carlo法的极值分布类型及其参数估计方法比较

A comparative study of extreme value distribution and parameter estimation based on the Monte Carlo method

摘要:

为探讨极值概率分布模型(极值Ⅰ型、Ⅱ型、Ⅲ型分布)在工程场地重现期内极值风速预测中的适用性,以工程上常用的风速分布模型为依据,采用Monte Carlo数值模拟法分别产生服从指数分布、正态分布、瑞利分布、威布尔分布、对数正态分布、广义极值分布的伪风速母样．基于以上伪风速母样分别使用极大似然参数估计法和概率权矩法对极值Ⅰ型、Ⅱ型、Ⅲ型分布模型中的参数进行估计,并与伪风速母样的理论极值分布进行对比分析．结果表明:极大似然参数估计法适用性较强,参数估计精度较高;重现期内极值风速的估算对风速母样分布类型敏感,服从不同分布的风速母样,应有针对性选用极值分布类型估算重现期内极值风速．

Abstract:

To explore the applicability of extreme value distribution models, known as type I, II and III extreme value distribution, to the extreme wind velocity evaluations of project site during the return period, and according to the wind speed distribution model commonly used in engineering fields, Monte Carlo simulation method is used to produce the pseudo wind speed samples, respectively fitting exponential distribution, normal distribution, Rayleigh distribution, Weibull distribution, lognormal distribution and the generalized extreme value (GEV) distribution. The maximum likelihood parameter estimation method and probability weighted moment method are used to estimate the parameters of the type I, II and III extreme value distributions. A comparative study of different parameter estimation methods for every extreme value distribution has been done by comparing with the theoretical extreme value distribution of the pseudo wind speed. The analysis shows that the maximum likelihood parameter estimation method is optimal for the type I, II and III extreme value distribution. The extreme value wind velocity evaluations of the pseudo wind speed samples during the return period are sensitive to the parent distribution of the pseudo wind speed samples, so different parent distributions of wind speed should be targeted to the selection of different type of extreme value distribution.