关键词: Copula, 结构系统, 可靠性, 疲劳, 失效相关

Abstract: Failure-dependence commonly exists in engineering structure, which is an important factor influencing the precision for system reliability analysis. Aiming at the typical condition of random constant and variable amplitude loading, the product-moment coefficient and Kendall's τ are derived, and the fatigue failure dependence mechanism of components in a structure system is discussed from the qualitative and quantitative perspective respectively. Dependence of component lives is originated from the randomness of characteristic quantity of the stress process, and eliminated by the randomness of material properties. According to the failure-dependence mechanism, Clayton Copula affiliated to the Archimedean family is introduced to build reliability models for series and parallel structural systems composed of identical components. Theoretical analysis shows that the Clayton Copula possesses a terse form, by which we can successfully depict the asymmetric morphology of contours of the joint probability density function of logarithmic lives and high precision models used for probabilistic analysis at the system level are built. The numerical example verifies the rationality and feasibility of the proposed method. The new models can be used in probability prediction of symmetric structural systems under common stochastic cyclic load, which give a new path for reliability-based design and probability assessment in mechanical equipments with multi-mode damage coupling.

Key words: Copula, failure-dependence, fatigue, reliability, structure system