一种解决混联系统组合爆炸问题的贝叶斯网络
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摘要
针对传统三层节点贝叶斯网络(Bayesian network,BN)在系统可靠性分析中的组合爆炸问题,提出了一种适用于复杂混联系统的级联BN建模方法.首先,在引入s类(f类)节点基础上建立了描述并联(串联)逻辑的信息通路模型,进而通过为通路模型各节点赋予同逻辑的条件概率参数,提出了构建并联(串联)系统等价级联BN的方法;其次,结合"超级方框"的概念分析了将典型串并联、并串联系统转化为等价级联BN的方法,并基于系统可靠性框图(RBD)相关矩阵,设计了将复杂混联系统转化为等价级联BN的算法-Generate-Chain-BN;最后,分别建立了某混联系统RBD的等价三层节点BN和级联BN模型,对两种BN进行了对比计算.理论和实例分析均表明,本文建立的级联BN可将原三层节点BN的空间和时间复杂性由指数级降到线性级,解决了三层节点BN固有的组合爆炸问题,可成为复杂混联系统可靠性分析的有效手段.
When traditional Bayesian network(BN) with three-layer nodes is applied to system reliability analysis, the parameter number of each node in the BN will increase exponentially, which eventually cause the problem of combinational explosion. To solve the explosion problem, a method for converting complicated compound system(a system consisting of complicated serial and parallel structure) into its equivalent chain-like BN is proposed. Firstly, by introducing a new kind of node Node s/Node f, an information flow model for characterizing the logics of parallel/series system is built; Furthermore, the theory for transforming parallel/series system into its equivalent chain-like BN is depicted by assigning conditional probability parameters to the node of the defined information flow model, which describes the logic meaning of parallel/series system quantitatively; Moreover, the method for converting typical serial-parallel system and parallel-serial system into their equivalent chain-like BN by introducing the concept of super-block is analyzed, separately; And then, by combining the converting principle and the correlation matrix of system reliability block diagram(RBD), a complete algorithm(Generate-ChainBN) for transforming a complicated compound system into its equivalent chain-like BN is designed in the paper; Eventually, both the equivalent three-layer nodes BN and chain-like BN of the RBD of a complicated compound system are built, computed and compared; Both the theory and the case show that the chain-like BN built in the paper can avoid the combinational explosion problem of the traditional three-layer ntodes BN by lowering the time and space complexity of the traditional three-layer nodes BN from exponent to linearity, which exhibits a great potential of the new chain-like BN in the field of system reliability analysis in place of three-layer nodes BN.
When traditional Bayesian network(BN) with three-layer nodes is applied to system reliability analysis, the parameter number of each node in the BN will increase exponentially, which eventually cause the problem of combinational explosion. To solve the explosion problem, a method for converting complicated compound system(a system consisting of complicated serial and parallel structure) into its equivalent chain-like BN is proposed. Firstly, by introducing a new kind of node Node s/Node f, an information flow model for characterizing the logics of parallel/series system is built; Furthermore, the theory for transforming parallel/series system into its equivalent chain-like BN is depicted by assigning conditional probability parameters to the node of the defined information flow model, which describes the logic meaning of parallel/series system quantitatively; Moreover, the method for converting typical serial-parallel system and parallel-serial system into their equivalent chain-like BN by introducing the concept of super-block is analyzed, separately; And then, by combining the converting principle and the correlation matrix of system reliability block diagram(RBD), a complete algorithm(Generate-ChainBN) for transforming a complicated compound system into its equivalent chain-like BN is designed in the paper; Eventually, both the equivalent three-layer nodes BN and chain-like BN of the RBD of a complicated compound system are built, computed and compared; Both the theory and the case show that the chain-like BN built in the paper can avoid the combinational explosion problem of the traditional three-layer ntodes BN by lowering the time and space complexity of the traditional three-layer nodes BN from exponent to linearity, which exhibits a great potential of the new chain-like BN in the field of system reliability analysis in place of three-layer nodes BN.
引文
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[14] Mi J, Li Y, Huang H Z, et al. Reliability analysis of multi-state systems with common cause failure based on Bayesian Networks[C]//2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering(ICQR2MSE), IEEE, 2012:1117-1121.
[15] Yontay P, Sanchez L M, Pan R. Bayesian network for reliability prediction in functional design stage[C)//Reliability and Maintainability Symposium(RAMS), 2015 Annual. IEEE, 2015:1-6.
[16] Ciobanu A, Munteanu F, Nemes C. Bayesian networks utilization for reliability evaluation of power systems[C]//2016 International Conference and Exposition on Electrical and Power Engineering(EPE), IEEE, 2016:837-841.
[17]董艳,阚树林.基于模糊贝叶斯r网络的汽车软关系系统可T靠性研究i方法和优化[J].系统科学-与数学,2017, 37(6):1391-1403.Dong Y, Kan S L. Reliability research method and optimization of automobile soft relationship system based on fuzzy Bayesian network[J]. System Science and Mathematics, 2017, 37(6):1391-1403.
[18] Torres-Toledano J, Sucar L. Bayesian networks for reliability analysis of complex systems[J]. Progress in Artificial Intelligence一IBERAMIA 98,1998:465-465.
[19]王瑶,孙秦.一种不改变RBD拓扑结构的三态贝叶斯网络[J].系统工程理论与实践,2017, 37(2):486-495.Wang Y, Sun Q. A three state Bayesian network without changing the RBD topology[J]. Systems Engineering-Theory&Practice, 2017, 37(2):486-495.
[20] Darwiche A. Modeling and reasoning with Bayesian networks[M]. New York:Cambridge University Press, 2009:53-121.
[2] Kim M C. Reliability block diagram with general gates and its application to system reliability analysis[J]. Annals of Nuclear Energy, 2011, 38(11):2456-2461.
[3] Benjamin S B, Wolter J F.系统工程-与分析[M].李瑞莹,潘星,译.北京:国防工业出版社,2014:327-335.Benjamin S B, Wolter J F. System engineering and analysis[M]. Beijing:National Defense Industry Press, 2014:327-335.
[4] Bennetts R G. Analysis of reliability block diagrams by Boolean techniques[J]. IEEE Transactions on Reliability,1982, 31(2):159-166.
[5] Birolini A. Quality and reliability of technical systems:Theory, practice, management(M]. Springer Science&Business Media, 2012.
[6] Kim M C. Reliability block diagram with general gates and its application to system reliability analysis[J]. Annals of Nuclear Energy, 2011, 38(11):2456-2461.
[7] Weber P,MedinarOliva G,Simon C, et al. Overview on Bayesian networks applications for dependability, risk analysis and maintenance areas[J]. Engineering Applications of Artificial Intelligence,2012,25(4):671-682.
[8] Bobbio A, Portinale L, Minichino M, et al. Improving the analysis of dependable systems by mapping fault trees into Bayesian networks[J]. Reliability Engineering&System Safety, 2001, 71(3):249-260.
[9] Khakzad N, Khan F, Amyotte P. Safety analysis in process facilities:Comparison of fault tree and Bayesian network approaches[J]. Reliability Engineering&System Safety, 2011, 96(8):925-932.
[10]周忠宝,蜚豆豆,周经伦.贝叶斯网络在可f靠性分析lr中W的应用[J].系统i工程t理论与实S践,2006, 26(6):95-100.Zhou Z B, Dong D D, Zhou J L. Application of Bayesian network in reliability analysis[J]. Systems Engineering-Theory&Practice, 2006, 26(6):95-100.
[11]尹晓伟,钱文学,谢里阳.贝叶斯网络在机械系统可靠性l评估中的应用[J].东北大学学报(自然科学版),2008, 29(4):557-560.Yin X W, Qian W X, Xie L Y. The application of Bias network in the reliability evaluation of mechanical system[Jl. Journal of Northeastern University(Natural Science), 2008, 29(4):557-560.
[12] Bensi M, Kiureghian A D, Straub D. Efficient Bayesian network modeling of systems[Jl. Reliability Engineering&System Safety, 2013, 112:200-213.
[13]Solano-Soto J, Sucar L. A methodology for reliable systems design[J]. Engineering of Intelligent Systems, 2001:734-745.
[14] Mi J, Li Y, Huang H Z, et al. Reliability analysis of multi-state systems with common cause failure based on Bayesian Networks[C]//2012 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering(ICQR2MSE), IEEE, 2012:1117-1121.
[15] Yontay P, Sanchez L M, Pan R. Bayesian network for reliability prediction in functional design stage[C)//Reliability and Maintainability Symposium(RAMS), 2015 Annual. IEEE, 2015:1-6.
[16] Ciobanu A, Munteanu F, Nemes C. Bayesian networks utilization for reliability evaluation of power systems[C]//2016 International Conference and Exposition on Electrical and Power Engineering(EPE), IEEE, 2016:837-841.
[17]董艳,阚树林.基于模糊贝叶斯r网络的汽车软关系系统可T靠性研究i方法和优化[J].系统科学-与数学,2017, 37(6):1391-1403.Dong Y, Kan S L. Reliability research method and optimization of automobile soft relationship system based on fuzzy Bayesian network[J]. System Science and Mathematics, 2017, 37(6):1391-1403.
[18] Torres-Toledano J, Sucar L. Bayesian networks for reliability analysis of complex systems[J]. Progress in Artificial Intelligence一IBERAMIA 98,1998:465-465.
[19]王瑶,孙秦.一种不改变RBD拓扑结构的三态贝叶斯网络[J].系统工程理论与实践,2017, 37(2):486-495.Wang Y, Sun Q. A three state Bayesian network without changing the RBD topology[J]. Systems Engineering-Theory&Practice, 2017, 37(2):486-495.
[20] Darwiche A. Modeling and reasoning with Bayesian networks[M]. New York:Cambridge University Press, 2009:53-121.