大规模多阶段任务系统马尔可夫可靠性模型的存储和计算

doi:10.3969/j.issn.1000-1093.2016.09.023

兵工学报 ›› 2016, Vol. 37 ›› Issue (9): 1715-1720.doi: 10.3969/j.issn.1000-1093.2016.09.023

大规模多阶段任务系统马尔可夫可靠性模型的存储和计算

闫华，高黎，王魁，漆磊

(后勤工程学院后勤信息与军事物流工程系，重庆 401311)

收稿日期:2016-02-02 修回日期:2016-02-02 上线日期:2016-11-04
通讯作者: 闫华 E-mail:yanhua_8304@163.com
作者简介:闫华(1983—)男讲师
基金资助:
国家自然科学基金项目（71401172）

Storage and Computation of Markov Reliability Model for Large-scale Phased-mission System

YAN Hua， GAO Li， WANG Kui， QI Lei

(Department of Logistics Information & Logistics Engineering, Logistic Engineering University of PLA, Chongqing 401311, China)

Received:2016-02-02 Revised:2016-02-02 Online:2016-11-04
Contact: YAN Hua E-mail:yanhua_8304@163.com

摘要/Abstract

摘要： 由于马尔可夫模型在进行多阶段任务系统的可靠性分析时，系统状态随部件增加呈指数增长，从而导致大规模条件下模型求解所需的存储量和计算量十分巨大。而根据马尔可夫模型中转移速率矩阵Q的取值规律和稀疏特性，给出了矩阵Q中元素q_ij基于状态二进制表示的计算公式，并提出了一种Q矩阵压缩存储(QMCS)方法。在模型压缩存储的基础上，进一步提出了基于Krylov子空间的可靠性求解算法。通过算例对比了不同压缩存储方案和不同求解算法的存储量、计算时间和可靠性结果，分析表明基于QMCS和Krylov子空间的模型求解方法具有较高的存储和计算效率，特别是在矩阵规模较大的情况下，该方法的计算耗时优于其他方法，且结果精度也能满足可靠性计算需求。

关键词: 系统评估与可行性分析, 可靠性评估, 多阶段任务系统, 压缩存储, Krylov子空间

Abstract: When Markov model is used to analyzed the reliability of phased-mission system, the system state grows exponentially with the increase in the number of components, thus resulting in a huge storage space and calculated amount resolved by the model. According to the element value rules and sparsity of the transition rate matrix Q in Markov model, the formula of computing the elements q_ij is derived based on binary description of states, and a Q-matrix compressed storage scheme (QMCS) is proposed. A reliability computing algorithm using Krylov subspace method is proposed based on the model compressed storage scheme. Taking a practical phased-mission system for example, the required storage spaces, computation times and reliability results of different compressed storage schemes and different algorithms are compared. The analysis results show that the method combining QMCS and Krylov subspace method has higher efficiency in storage and computation. Especially in the case of a large matrix, the QMCS-Krylov method is superior to other methods both in computation time and accuracy.

Key words: system assessment and feasibility, reliability evaluation, phase-mission system, compressed storage, Krylov subspace

中图分类号:

闫华，高黎，王魁，漆磊. 大规模多阶段任务系统马尔可夫可靠性模型的存储和计算[J]. 兵工学报, 2016, 37(9): 1715-1720.

YAN Hua， GAO Li， WANG Kui， QI Lei. Storage and Computation of Markov Reliability Model for Large-scale Phased-mission System[J]. Acta Armamentarii, 2016, 37(9): 1715-1720.

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大规模多阶段任务系统马尔可夫可靠性模型的存储和计算

Storage and Computation of Markov Reliability Model for Large-scale Phased-mission System

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