基于广义退化的机械结构模糊时变可靠性分析

航天在轨机械产品样本量少的特点导致其相关参数和动态退化失效判据具有模糊性，而现有的模糊可靠性模型一般针对静态问题进行分析，并不能描述机械产品可靠性的时变、模糊问题。本文基于广义应力强度干涉模型，同时考虑变量和失效判据的模糊性，提出了模糊时变可靠性建模及分析方法。该方法首先将模糊判据转化为极限状态方程中的随机变量；然后利用模糊论中的截集法处理模糊随机变量，建立机械产品的模糊时变可靠性模型；之后基于PHI2方法（一种基于上穿方法的结构时变可靠性分析方法）提出了求解模糊时变可靠度的新方法（FPHI2）；最后结合数值算例和工程案例验证了该方法的可行性。

Fuzzy time-variant reliability analysis of mechanical structure based on generalized degradation

The character that the specimen number of on-orbit mechanical products in space is small leads to the fuzziness of relative parameters and the dynamic degraded failure criterion. The existing fuzzy reliability model mainly aims at static problems, which cannot describe the time-variant and fuzzy problem. This paper proposes a fuzzy time-dependent reliability modeling and analysis method which is based on the interference model of generalized stress-strength and takes account of the fuzziness of both variables and failure criterion at the same time. First, fuzzy criterion can be transferred into random variables equivalently. Then the theory of cut set in fuzzy math can be used to deal with the fuzzy random variables, and thus the fuzzy time-variant reliability model is built. After that, a new method (FPHI2) is presented, based on the method of PHI2 which is a tool for time-variant reliability computation based on the outcrossing approach, to compute the fuzzy time-variant reliability. In the end, a numerical case and an engineering case are provided to verify the feasibility of the proposed method.