失效相关普遍存在于工程结构中，是影响结构系统可靠性分析精度的重要因素。针对随机恒幅载荷和随机变幅载荷两类典型工况，推导积矩相关系数和Kendall秩相关系数的计算式，从定性和定量角度分析结构系统各单元疲劳失效内在的统计相关机理。单元寿命相关性主要来自应力过程特征量的分散性，而材料性能的分散性则减轻相关程度。根据单元失效的统计相关机理，利用阿基米德族的Clayton Copula建立串联、并联结构系统的疲劳寿命可靠性模型。分析表明： Clayton Copula形式简洁，可细腻刻画单元对数寿命联合分布密度等高线呈现的非对称形态，由此建立的概率模型计算精度高。算例验证了所提方法的合理性和可行性。新模型可用于共因载荷多次作用下结构系统的疲劳寿命可靠度预测，并为考虑多模式损伤耦合的装备可靠性设计及概率评估提供新工具。
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.
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