基于Copula函数的广义随机空间内相关变量的可靠性分析  

RELIABILITY ANALYSIS OF CORRELATED INPUT VARIABLES BASED ON COPULA FUNCTION IN GENERALIZED RANDOM SPACE

作　　者：申焱华[1] 石博强[1] 

机构地区：[1]北京科技大学机械工程学院,北京100083

出　　处：《机械强度》2011年第5期679-684,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金(50475173);北京市自然科学基金(3093022)资助项目~~

摘　　要：非正态相关变量的产品可靠性分析,需要应用变量间的联合概率密度函数进行转换。然而,实际工程中由于概率信息的不完备,难以求取准确的联合概率密度函数,而变量的边缘分布及其相关关系易于得到。文中采用Copula函数,利用变量的边缘分布以及相关关系,构造出系统的联合概率密度函数。同时指出,目前常用的Nataf变换只是基于Copula变换的一种特例。基于Copula函数的可靠性分析能更精确地描述实际情况,是一种基于非线性相关的模型,使问题的解决更加方便、灵活。In reliability-based analysis of complex product with non-Gaussian,correlated input variables,a joint probability distribution function（PDF） is required to transform the correlated input variables into independent standard Gaussian variables.However,in practical industry application,a joint probability distribution function is difficult to be constructed for the related probability information is non-complete.However,the information about the n-dimensional correlated variables（such as the marginal PDF and covariance matrix） can be achieved easily.So Copula function is introduced to build the joint PDF using the marginal PDF and covariance matrix.It is demonstrated that the Nataf transformation is one of Copulas.Copula transformation can deal with the non-linear correlated relationship.The reliability analysis results based on Copula are more applicable and accurate by numerical example.

关 键 词：相关变量 COPULA函数 Nataf变换 可靠性分析 

分 类 号：TB114.3[理学—概率论与数理统计]