认知不确定多态系统模糊可靠性评估
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摘要
针对高可靠部件短时间内很难获得足够的性能分布信息,致使对部件的认知存在一定的不确定性问题,为降低其对部件性能分析的影响,实现对系统可靠性的准确估计,假定部件性能分布参数为模糊数,根据模糊集合分解定理,建立基于β-截集变量的性能分布模型,给出了部件模糊状态性能区间的定义和状态模糊概率的计算方法。对传统的通用生成函数方法进行改进,定义了α-截集通用生成函数及其运算法则。提出了考虑认知不确定的多态系统模糊可靠性评估方法,并以仿真实例进行验证说明。该方法不仅克服了性能分布信息缺少,无法准确地建立状态信息分析模型的不足,且方法简单、思路清晰,具有强通用性和工程应用性。
There is epistemic uncertainty on high-reliability components since it is hard to obtain adequate performance data of the components within a short time.The components′performance distribution parameter is assumed as a fuzzy number,according to the decomposition theorem of the fuzzy set,aperformance distribution model based onβ-level cut set is built,and a definition of the components′performance interval in the fuzzy state and a computational method of the fuzzy state probability are provided.The traditional universal generating function is improved,theα-level cut set universal generating function and its algorithm are defined.An assessment method of fuzzy reliability of multi-state system in consideration of epistemic uncertainty is proposed,and verification and illustration are conducted with simulation examples in order to reduce the influence on components′performance analysis and achieve precise estimation of system reliability.This method overcomes the shortcoming that a state information analysis model cannot be accurately built on account of the deficiency of performance distribution information.It can be widely used and has great engineering application value.
There is epistemic uncertainty on high-reliability components since it is hard to obtain adequate performance data of the components within a short time.The components′performance distribution parameter is assumed as a fuzzy number,according to the decomposition theorem of the fuzzy set,aperformance distribution model based onβ-level cut set is built,and a definition of the components′performance interval in the fuzzy state and a computational method of the fuzzy state probability are provided.The traditional universal generating function is improved,theα-level cut set universal generating function and its algorithm are defined.An assessment method of fuzzy reliability of multi-state system in consideration of epistemic uncertainty is proposed,and verification and illustration are conducted with simulation examples in order to reduce the influence on components′performance analysis and achieve precise estimation of system reliability.This method overcomes the shortcoming that a state information analysis model cannot be accurately built on account of the deficiency of performance distribution information.It can be widely used and has great engineering application value.
引文
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[11]Wu S,Da C.Theorems of interval fuzzy set and its operation rules[J].Transactions of Nanjing University of Aeronautics&Astronautics,2012,29(2):136-144.
[12]高峰记.可能度及区间数综合排序[J].系统工程理论与实践,2013,33(8):2033-2040.Gao Fengji.Possibility degree and comprehensive priority of interval numbers[J].Systems Engineering-Theory and Practice,2013,33(8):2033-2040.
[13]茆诗松.统计手册[M].北京:科学出版社,2003.Mao Shisong.Statistics hand book[M].Beijing:Science Press,2003.
[14]邱志平.非概率集合理论凸方法及其应用[M].北京:国防工业出版社,2005.Qiu Zhiping.Convex method of non-probabilistic settheory and its application[M].Beijing:National Defense Industry Press,2005.
[2]史新红,齐先军,王治国.基于UGF的发电系统区间可靠性评估及其仿射算法改进[J].合肥工业大学学报(自然科学版),2014,37(3):286-291.Shi Xinhong,Qi Xianjun,Wang Zhiguo.Interval reliability estimation of power generating system based on UGF method and its modification by using affine arithmetic[J].Jouranl of Heifei University of Technology,2014,37(3):286-291.
[3]Wei G,Wang Y,Piatkiewicz L.A simple universal generating function method for estimating the reliability of general multi-state node networks[J].Iie Transactions,2009,41(1):3-11.
[4]尚彦龙,蔡琦,赵新文,等.基于UGF和Semi-Markov方法的反应堆泵机组多状态可靠性分析[J].核动力工程,2012,33(1):117-123.Shang Yanlong,Cai Qi,Zhao Xinwen,et al.Multistate reliability for pump group in nuclear power system based on UGF and semi-Markov process[J].Nuclear Power Engineering,2012,33(1):117-123.
[5]Ding Y,M J Z.Fuzzy multi-state systems:General definitions,and performance assessment[J].IEEE Transactions on Reliability,2008,57(4):589-594.
[6]Ding Y,Lisnianski A.Fuzzy universal generating functions for multi-state system reliability assessment[J].Fuzzy Sets and Systems,2008,159(3):307-324.
[7]鄢民强,杨波,王展.不完全覆盖的模糊多状态系统可靠性计算方法[J].西安交通大学学报,2011,45(10):109-114.Yan Minqiang,Yang Bo,Wang Zhan.Reliability assessment for multi-state system subject to imperfect fault coverage[J].Journal of Xi′an Jiao tong University,2011,45(10):109-114.
[8]Li C Y,Chen X,Yi X S,et al.Interval-valued reliability analysis of multi-state systems[J].IEEE Transactions on Reliability,2011,60(1):323-330.
[9]Destercke S,Sallak M.An extension of universal generating function in multi-state systems considering epistemic uncertainties[J].Reliability Engineering and System Safety,2013,62(2):504-514.
[10]王光远,张跃.模糊随机过程论[M].贵阳:贵州科技出版社,1994.Wang Guangyuan,Zhang Yue.The theory of fuzzy stochastic processes[M].Guiyang:Guizhou Science and Technology Press,1994.
[11]Wu S,Da C.Theorems of interval fuzzy set and its operation rules[J].Transactions of Nanjing University of Aeronautics&Astronautics,2012,29(2):136-144.
[12]高峰记.可能度及区间数综合排序[J].系统工程理论与实践,2013,33(8):2033-2040.Gao Fengji.Possibility degree and comprehensive priority of interval numbers[J].Systems Engineering-Theory and Practice,2013,33(8):2033-2040.
[13]茆诗松.统计手册[M].北京:科学出版社,2003.Mao Shisong.Statistics hand book[M].Beijing:Science Press,2003.
[14]邱志平.非概率集合理论凸方法及其应用[M].北京:国防工业出版社,2005.Qiu Zhiping.Convex method of non-probabilistic settheory and its application[M].Beijing:National Defense Industry Press,2005.