中文摘要：

Copula以灵活的函数形式实现多元随机向量的概率建模,能描述变量之间复杂的统计相关特征。在结构系统可靠性分析中引入Copula函数,初步探讨利用Copula实现对称结构系统可靠性建模的思路与方法。根据元件失效相关机理,以孪生应力、元件强度为基本变量,以元件安全裕度为分析变量,分别阐述利用高斯Copula和阿基米德Copula实现对称结构系统可靠性建模的基本步骤。与高斯Copula相比,阿基米德Copula对系统失效相关机理的刻画能力更强,可根据秩相关系数和临界失效点信息调节各待定参数,适用于基本变量为非正态的场合。数值算例验证了模型的合理性与可行性。Copula可靠性模型可为失效相关的机电装备系统可靠性评估与可靠性设计提供新途径。

英文摘要：

Copula is a new tool of statistical analysis,by which the probabilistic models for the multiple random vector can be built in terms of flexible expression,and by which the complex feature of statistcal dependence of random variables can be depicted.Copula is introduced in the reliability analysis of structural system.Copula-based method is put forward for the reliability modeling of structural systems composed of identical components.According to the failure-dependence mechanism of components,the modeling steps based on Gauss Copula and Archimedean Copulas are discussed by taking the twin stress and components strength as the basic variables and the safety margins as the analytic variables.Compared with Gauss Copula,Archimedean Copulas has a powerful capability to describe the failure-dependence mechanism since it can determine the adjustable parameters from the rank correlation coefficient and the information about the critical failure point.Archimedean Copula-based reliability models are applicable to non-normal situations.A numerical example shows that the new method is reasonable and feasible.Copula-based reliability model provides a new way for reliability assessment and reliability-based design of complex electromechanical equipment systems with failure-dependence.