相关性失效下二终端网络系统可靠性评估模型
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摘要
文章引入余因子算法和改进的二元决策图(BDD, Binary Decision Diaram)算法,求得不交化的弧序列。系统的可靠度就是每个弧序列的可靠度之和。考虑弧序列之间相关性干涉影响,借助Copula函数和差分运算,进行相关干涉下二终端网络系统问题的可靠度建模。在评估节点不可靠的情况时,将节点视为弧,并进行相应的统计建模,从而实现计算简化。
This paper introduces cofactor algorithm and the modified Binary Decision Diagram(BDD) arithmetic to obtain the disjoint arc sequence. The reliability of the system is the sum of the reliability of each arc sequence. Considering the influence of correlation interference between arc sequences, the paper carries out the reliability modeling of two-terminal network system under correlation interference with the help of copula function and differential operation. In the case of assessing unreliable nodes,the paper treats the nodes as arcs and performs the corresponding statistical modeling so as to achieve the computational simplification.
This paper introduces cofactor algorithm and the modified Binary Decision Diagram(BDD) arithmetic to obtain the disjoint arc sequence. The reliability of the system is the sum of the reliability of each arc sequence. Considering the influence of correlation interference between arc sequences, the paper carries out the reliability modeling of two-terminal network system under correlation interference with the help of copula function and differential operation. In the case of assessing unreliable nodes,the paper treats the nodes as arcs and performs the corresponding statistical modeling so as to achieve the computational simplification.
引文
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[11]季峰,蔡兴国,王俊.基于混合Copula函数的风电功率相关性分析[J].电力系统自动化,2014,38(2).
[12]唐家银,何平.基于Copula对随机变量间相依性的度量[J].江汉大学学报(自然科学版),2006,34(4).
[13]唐建,艾芙莉,邵发明,张蕉蕉.基于SimEvents仿真获取网络不交化最小路集[J].系统仿真学报,2016,28(4).
[14]武小悦,沙基昌.构造网络不交化最小路集的一中新算法[J].系统工程理论与实践,2000,(1).
[15]Nelsen R B.An Introduction to Copulas(2nd Edition)[M].New York:Springer Series in Statistics,2006,(1).
[16]盛骤,谢式千,潘承毅.概率论与数理统计(第四版)[M].北京:高等教育出版社,2008.
[17]Jeffreys H.Theory of Probability[M].New York:The Clarendon Press Oxford University Press,1998.
[2]曹晋华,程侃.可靠性数学引论[M].北京:高等教育出版社,2006.
[3]程世娟,何平.一种计算网络两点间最小路集的方法[J].西南交通大学学报,2002,37(1).
[4]史玉芳,陆宁,李慧民.基于改进的不交化最小路集的网络系统可靠性算法[J].计算机工程与科学,2011,33(1).
[5]Sing H,Vaithilingam S,Anne R K,et al.Terminal Reliability Using Binary Decision Diagrams[J].Microelectron Reliability,1996,36(3).
[6]Yeh W C.An Improved Sum-of-disjoint-products Technique for the Symbolic Network Reliability Analysis With Known Minimal Paths[J].Reliability Engineering&System Safety,2007,92(2).
[7]Kuo S Y,Lu S K,Yeh F M.Determining Terminal-pair Reliability Based on Edge Expansion Diagrams Using OBDD[J].IEEE Transactions on Reliability,1996,48(3).
[8]Yeh F M,Lu S K,Kuo S Y.OBDD-Based Evaluation of K-termina Network Reliabilit[J].IEEE Transactions on Reliability,2002,51(4).
[9]Luo T,Trivedi K S.An Improved Algorithm for Coherent-system Reliability[J].IEEE Transactions on Reliability,1998,47(1).
[10]唐家银,何平,梁红,琴王沁.多故障模式高长寿命产品相关性失效的综合可靠性评估[J].机械工程学报,2013,29(12).
[11]季峰,蔡兴国,王俊.基于混合Copula函数的风电功率相关性分析[J].电力系统自动化,2014,38(2).
[12]唐家银,何平.基于Copula对随机变量间相依性的度量[J].江汉大学学报(自然科学版),2006,34(4).
[13]唐建,艾芙莉,邵发明,张蕉蕉.基于SimEvents仿真获取网络不交化最小路集[J].系统仿真学报,2016,28(4).
[14]武小悦,沙基昌.构造网络不交化最小路集的一中新算法[J].系统工程理论与实践,2000,(1).
[15]Nelsen R B.An Introduction to Copulas(2nd Edition)[M].New York:Springer Series in Statistics,2006,(1).
[16]盛骤,谢式千,潘承毅.概率论与数理统计(第四版)[M].北京:高等教育出版社,2008.
[17]Jeffreys H.Theory of Probability[M].New York:The Clarendon Press Oxford University Press,1998.