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-  2018 

基于累积损伤模型的多阶段系统可靠性分析路集组合方法
Path Sets Combination Method for Reliability Analysis of Phased-Mission Systems Based on Cumulative Exposure Model

Keywords: 多阶段系统,贝叶斯网络,可靠性分析,路集组合,故障树
phased-mission systems
,Bayesian networks,reliability analysis,path set combination,fault tree

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Abstract:

多阶段系统因阶段任务的关联性,元件的共用性,导致系统可靠性建模难度大,求解过程复杂,对此提出基于累积损伤模型的多阶段系统可靠性分析路集组合方法。针对元件跨阶段相关性以及各阶段失效率不同问题,利用元件累积损伤模型,考虑元件历史损伤,求取元件各阶段累积失效分布进行描述。系统路集组合方法利用多阶段系统故障树映射成贝叶斯网络方法建立多阶段系统可靠性模型,通过遍历贝叶斯网络求取各阶段最小路集。针对路集间的相关性以及规模过大问题,采用变量消元法推导出的不交化公式实现路集去相关性与共用元件的条件概率关系缩减最小不交路集规模。再按元件条件概率关系对各阶段最小不交路集进行组合求和。该方法避免了传统贝叶斯网络方法因阶段状态离散过多造成的条件概率表规模大、存储空间需求大、运算量大的问题以及PMS-BDD方法对变量排序有严格要求的限制与难以求解含有多种分布类型元件的系统可靠性问题。对某地球同步轨道卫星进行了多阶段系统可靠性建模与求解,并与PMS-BDD方法相对比,验证了路集组合方法的正确性。
The modeling of phased-mission systems is difficult and the solving process is complex because of the relevance of the phase tasks and the sharing of components existing in different phases or between phases. To solve the problem, based on the cumulative exposure model, the path sets combination method of phased-mission systems is proposed. Aiming at the problem of the cross-stage correlation of components and its different failure rate in each phase, the cumulative exposure model considering the historical damage of components is used to solve by obtaining the cumulative damage distribution of each component in each phase. Firstly, a phased-mission systems reliability model is build by mapping phased-mission system fault trees into a Bayesian network. By traversing the Bayesian network, the minimal path sets of each phase are obtained. Secondly, the disjoint formulas introduced by variable elimination method are used to do the disjoint operation of the minimal path sets of each phase and the conditional probability relations of the common components are used to reduce the minimal path sets scale. Finally, the minimum disjoint path sets of each phase are combined and summed according to the component conditional probability relation. The path sets combination method of phased-mission systems avoids the large conditional probability table, large storage and large computation problems caused by the excessive discrete states in the traditional Bayesian method and the problem that the PMS-BDD method has strict requirements for variable ordering and is difficult to solve the system reliability with multiple failure distribution types of components. In the end, a phased-mission systems reliability modeling and solving is carried out for a geosynchronous orbit satellite, and compared with the PMS-BDD method, which verifies the correctness of the method

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