可修系统剩余寿命分析的广义发生函数法

系统剩余寿命是机电装备面向多生命周期设计、制造与服役的重要分析指标。基于更新过程理论，通过引入广义发生函数(UGF)，提出一种针对元件及系统有限时间区间的剩余寿命概率分析的实用方法。当系统各元件承受具有整体不确定性的平稳载荷随机历程时，直接根据元件在各等效恒幅应力水平下的失效数据构建元件条件寿命发生函数，由自定义复合算子分别计算相应的系统条件剩余寿命发生函数，经统计平均得系统剩余寿命分布。运算过程中，可利用近似项合并技术大幅度提高分析效率。新方法适用于元件寿命为任意分布随机变量场合，并体现各元件因等效恒幅应力不确定而引发的失效相关性，可为装备系统剩余寿命精细化分析开辟新途径。

Residual Life Analysis of Repairable Systems Based on Universal Generating Function Approach

The residual life of systems is an important analysis index for multi-lifecycle-based design, manufacture and service of mechanical and electrical equipment. Based on the renewal process theory, a practical method for residual life probability analysis of components and the whole system in a finite time interval is put forward by means of the universal generating function (UGF). For systems undergoing stationary stochastic load process with global uncertainty, the conditional life UGFs of components are constructed according to failure data under all constant-amplitude stress levels, and the corresponding conditional residual life UGFs of the whole system can be figured out by using self-defined composition operators of UGFs. Statistical average of UGFs is employed to obtain the residual life distribution of the repairable system. When the composition operators are executed, the computational costs can be reduced by a big margin by means of collecting like terms. The new model is suitable for random variables with arbitrary distributions and embodies the failure dependence attributed to the uncertainty of equivalent stress amplitude of each component.