多状态网络可靠度下界的矩阵分解算法

发布时间：2018-04-24 02:22

本文选题：网络可靠度 + 多状态网络　；参考：《小型微型计算机系统》2013年07期

【摘要】：为减少计算多状态网络可靠度精确值的复杂性,提出基于分解计算多状态网络不可靠度精确值的思想,在此基础上提出一个求解多状态网络不可靠度动态上界(对应于可靠度动态下界)的算法.算法先通过分解运算去除某些边引起的d-最小割集之间的相关性,将网络不可靠度转化为多个互斥事件的概率之和,再应用MESP界求取这些事件的概率,计算网络不可靠度上界,对应得到可靠度下界,并计算了得到的可靠度下界与精确值间的绝对误差界.通过定义d-最小割集矩阵,利用矩阵分解实现算法,结构清晰、便于编程计算.相关引理的证明及算例分析表明随着分解的深入,算法能够得到满足精度要求的可靠度下界.
[Abstract]:In order to reduce the complexity of computing the exact value of reliability of multi-state network, the idea of computing the exact value of reliability of multi-state network based on decomposition is proposed. On this basis, an algorithm for solving the dynamic upper bound (corresponding to the dynamic lower bound of reliability) of multi-state network is proposed. The algorithm first removes the correlation between the d- minimum cut sets caused by some edges by decomposing operations, converts the network unreliability into the sum of the probability of multiple mutually exclusive events, then applies the MESP bound to obtain the probability of these events, and calculates the upper bound of the network unreliability. The corresponding lower bound of reliability is obtained, and the absolute error bound between the lower bound of reliability and the exact value is calculated. By defining d- minimum cut set matrix and using matrix decomposition to realize the algorithm, the structure is clear and easy to program and calculate. The proof of correlation Lemma and the example analysis show that with the deepening of decomposition, the algorithm can obtain the lower bound of reliability to meet the precision requirement.
【作者单位】：第二炮兵工程学院一系;第二炮兵士官学院一系;第二炮兵装备研究院二所;
【基金】：总装预研基金项目(51301010102,51301060304)资助第二炮兵工程学院创新性探索研究基金项目(XY2010JJB23,XY2011JJB09)资助
【分类号】：TP393.06

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