基于通用生成函数的系统寿命可靠性分析
收稿日期: 2013-01-06
修回日期: 2013-05-05
网络出版日期: 2013-05-14
基金资助
国家自然科学基金（51175425）;航空科学基金（2011ZA53015）
Reliability Analysis for System Life Based on Universal Generating Function
Received date: 2013-01-06
Revised date: 2013-05-05
Online published: 2013-05-14
Supported by
National Natural Science Foundation of China (51175425);Aeronautical Science Foundation of China (2011ZA53015)
提出一种基于通用生成μ函数的液压系统可靠性分析新方法，并对某液压系统可靠性进行分析，为改进系统提供依据。首先从系统失效数据出发，将部件工作状态分类，根据失效数据得到部件处于各状态的概率，建立部件的μ函数模型，描述部件性能的不确定性。然后依据系统的结构功能逻辑关系，借助μ函数特性和逻辑算子，得到系统μ函数。最后基于所提μ函数的系统可靠性指标，完成系统可靠性分析。与传统Monte Carlo（MC）方法相比，所提方法直接从失效数据出发，确定部件状态并构造反应其不确定性性能分布的μ函数，通过μ函数将部件不确定性传递到系统，并基于系统μ函数直接进行可靠性分析，避免了传统MC方法拟合部件级不确定性概率分布的误差。以某液压系统为例验证所提方法的正确性和高效性。
关键词： μ函数; 液压系统; Z变化; 可靠性分析; Monte Carlo方法
任博 , 吕震宙 , 李贵杰 , 唐樟春 . 基于通用生成函数的系统寿命可靠性分析[J]. 航空学报, 2013 , 34(11) : 2550 -2556 . DOI: 10.7527/S1000-6893.2013.0252
A novel technique for the reliability analysis of a hydraulic system is presented based on the universal generating μ function and useful information can be obtained for system analysts and design engineers to guide effective system improvement both in the design phase and during operation. First, according to the fault data, the states and their corresponding probabilities for the constitutive elements of the system are determined by the histogram technique. Then, based on the determined state probabilities for all elements, an individual μ function for each element is defined by means of μ function. Finally, by using the composition operators over the μ function of individual elements and their logic combinations in the entire system structure, the μ function of the entire system can be obtained by simple algebraic operations, and this μ function expresses the output performance distribution for the system. Due to the definition of reliability measures about the μ function, reliability analysis can be easily completed from this output performance distribution compared with traditional Monte Carlo (MC) method. As the method is performed without estimating the distribution of the elements, the errors of truncation and numerical fitting are reduced. The example of a certain hydraulic system is used to illustrate the correctness and effectiveness of the novel method.
Key words： μ function; hydraulic system; Z transform; reliability analysis; Monte Carlo method
[1] Jing X,Hong Y J.Assessment method of system reli ability.Beijing: National Defense Industry Press,2007: 57-60.(in Chinese) 金星,洪延姬.系统可靠性与可用性分析方法.北京: 国防工业出版社,2007: 57-60.
[2] Xue J,Yang K.Dynamic reliability analysis of coherent multi-state systems.IEEE Transactions on Reliability,1995,44(4): 683-688.
[3] Gong Q X,Gu Z Z,Song Z C,et al.Aircraft design handbook-reliability and maintainability.Beijing: Aviation Industry Press,1999: 100-109.(in Chinese) 龚庆祥,顾振中,宋占成,等.飞机设计手册-可靠性、维修性设计分册.北京: 航空工业出版社,1999: 100-109.
[4] Song S F,Lv Z Z.Reliability sensitivity analysis method for structural system and its application.Journal of Mechanical Strength,2007,29(1): 53-57.(in Chinese) 宋述芳,吕震宙.系统可靠性灵敏度分析方法及应用研究.机械强度,2007,29(1): 53-57.
[5] Song B F,Feng Y W,Liu X D,et al.Reliability engineering of aircraft.Xi'an: Northwestern Polytechnical University Press,2006: 98-101.(in Chinese) 宋笔锋,冯蕴雯,刘旭东,等.飞行器可靠性工程.西安: 西北工业大学出版社,2006: 98-101.
[6] Ushakov I.Optimal standby problem and a universal generating function.Computer System Science,1987,25(4): 61-73.
[7] Gnedenko B,Ushakov I.Probabilistic reliability engineering.New York: Wiley Inc.,1995: 195-197.
[8] Lisnianski A,Levitin G,Ben-Haim H,et al.Power system structure optimization subject to reliability constraints.Electronic Power System Research,1996,39(2): 145-152.
[9] Lisnianski A,Levitin G.Multi-state system reliability: assessment,optimization and applications.Singapore: World Scientific,2003: 263-267.
[10] Li C Y,Chen X,Yi X S,et al.Reliability analysis of multi-state system with multiple performance parameters based on vector-universal generating function.Acta Armamentarii,2010,31(12): 1604-1610.(in Chinese) 李春洋,陈循,易晓山,等.基于向量通用生成函数的多性能参数多态系统可靠性分析.兵工学报,2010,31(12): 1604-1610.
[11] Shang Y L,Cai Q,Zhao X W,et al.Multi-state reliability for pump group in nuclear power system based on UGF and semi-markov process.Nuclear Power Engineering,2012,33(1): 117-123.(in Chinese) 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.核动力工程,2012,33(1): 117-123.
[12] Zhao Y.Data analysis of reliability.Beijing: National Defense Industry Press,2011: 8-13.(in Chinese) 赵宇.可靠性数据分析.北京: 国防工业出版社,2011: 8-13.
[13] Rice J A.Mathematical statistics and data analysis.2nd Edition.Beijing: China Machine Press,2003: 143-148.(in Chinese) 赖斯.数理统计与数据分析(英文版).第2版.北京: 机械工业出版社,2003: 143-148.
[14] Liu S T.Signals and system.Xi'an: Xi'an Jiaotong University Press,1998: 256-263.(in Chinese) 刘树棠.信号与系统.西安: 西安交通大学出版社,1998: 256-263.
[15] Levitin G,Lisnianski A.Structure optimization of multi-state system with two failure modes.Reliability Engineering and System Safety,2001,71(1): 75-89.
[16] Barton R M,Damon W W.Reliability in a multi-state system.Proceedings of the Sixth Annual Southeastem Symposium on Systems Theory,1974: 169-173.
[17] Barlow R E,Wu A S.Coherent systems with multi-state components.Mathematics of Operations Research,1978,3(4): 275-281.
[18] Han M X,Yao L Q.The probability distribution and reliability analysis of the life of air-engine's main axl beaings.Jounal of Nanjing University of Science and Technology: Nature Science,2002,26(5): 552-556.(in Chinese) 韩茂祥,姚鲁群.航空发动机主轴轴承使用寿命的概率分布与可靠性分析.南京理工大学学报:自然科学版,2002,26(5): 552-556.
[19] Gregory L.An universal generating function approach for the analysis of multi-state systems with dependent elements.Reliability Engineering and System Safety,2004,84(3): 285-292.
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