Many modern structural systems usually consist of multiple failure modes. One failure mode may affect other failure modes due to the same working environment and random input variables, meaning that these failure modes are not independent. The assumption of independence among failure modes simplifies the calculation of reliability of structural systems, but it adds approximation error. Different from the dependence between two failure modes, the dependence of multiple failure modes is more complicated. In this paper, on the basis of vine copula function, which is a flexible tool to describe the multivariate dependence, the dependence of multiple failure modes of the structural systems is mainly studied and analyzed. Then Rosenblatt transformation and Monte Carlo simulation method are utilized to evaluate the reliability of structural systems. Furthermore, in order to research the importance of failure modes, two indices combined with empirical copula functions are extended, which can quantitatively measure the importance of failure modes. The multiple failure modes can be ranked based on proposed importance analysis, and the ones that have greater influence on the system can be found out, thus simplifying the system analysis. Finally, in order to confirm the applicability and rationality of the proposed method, an engineering case about a mechanism system with five failure modes is presented.

中文翻译：

---

考虑多种失效模式依赖性的结构系统可靠性评估与重要性分析

许多现代结构系统通常由多种失效模式组成。由于相同的工作环境和随机输入变量，一种故障模式可能会影响其他故障模式，这意味着这些故障模式不是独立的。失效模式之间独立性的假设简化了结构系统可靠性的计算，但增加了近似误差。与两种失效模式之间的依赖不同，多种失效模式之间的依赖更为复杂。本文以藤系copula函数作为描述多元相关性的灵活工具为基础，主要研究和分析了结构系统多种失效模式的相关性。然后利用罗森布拉特变换和蒙特卡罗模拟方法对结构系统的可靠性进行评估。此外，为了研究失效模式的重要性，扩展了结合经验copula函数的两个指标，可以定量衡量失效模式的重要性。可以根据建议的重要性分析对多种失效模式进行排序，找出对系统影响较大的失效模式，从而简化系统分析。最后，为了验证所提方法的适用性和合理性，给出了一个具有五种失效模式的机构系统的工程案例。并且可以找出对系统影响较大的，从而简化系统分析。最后，为了验证所提方法的适用性和合理性，给出了一个具有五种失效模式的机构系统的工程案例。并且可以找出对系统影响较大的，从而简化系统分析。最后，为了验证所提方法的适用性和合理性，给出了一个具有五种失效模式的机构系统的工程案例。