基于树形马氏链模型的可靠性分析方法

doi:10.7527/S1000-6893.2018.22643

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基于树形马氏链模型的可靠性分析方法

张洪铭¹, 顾晓辉¹, 邸忆^1,2

1. 南京理工大学机械工程学院, 南京 210094;
2. 武昌理工学院信息工程学院, 武汉 430223

收稿日期:2018-09-03 修回日期:2018-10-15 出版日期:2019-05-15 发布日期:2018-12-06
通讯作者: 顾晓辉 E-mail:gxiaohui@njust.edu.cn
基金资助:
国防科技预先研究项目（004040204）

Reliability analysis method based on Tree Markov Chain model

ZHANG Hongming¹, GU Xiaohui¹, DI Yi^1,2

1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;
2. Information and Engineering School, Wuchang University of Technology, Wuhan 430223, China

Received:2018-09-03 Revised:2018-10-15 Online:2019-05-15 Published:2018-12-06
Supported by:
National Defence Pre-research Foundation (004040204)

摘要/Abstract

摘要： 复杂系统的极限状态函数非线性程度较高，在进行可靠性分析时，易导致失效概率的计算误差大、效率低，针对上述问题，提出了树形马氏链（TMC）算法和基于该算法的可靠性分析方法。树形马氏链是对原始马尔可夫链的改进，其状态转移过程更加灵活，具备局部多链并行和自适应探索失效域边界的特性。树形马氏链通过多候选状态点扩大对失效域信息的收集，生成能充分反映失效分布特征的样本，对该样本进行自适应核密度估计得到近似最优的重要抽样分布密度函数，从而提高计算结果的准确度。文末的数值算例和工程算例验证了算法性能，计算结果表明算法对设计点、抽样起点的位置不敏感，处理强非线性及复杂串联系统问题时，能在少样本量下得到相对高准确度的计算结果，且在样本量改变时，计算结果相对稳定可靠；工程算例给出了所提方法在实际问题下的效率，体现了所提方法的工程应用价值。

关键词: 可靠性, 马尔可夫链, 重要性抽样, 核密度估计, 蒙特卡罗模拟

Abstract: In the engineering practice of system reliability analysis, the strong nonlinearity of the limit state function is likely to cause large calculation error of the system failure probability and low efficiency. To solve the problems above, the Tree Markov Chain (TMC) algorithm and the system reliability analysis method based on TMC algorithm are proposed. The TMC is an improvement of the original Markov chain, and its state transition process is more flexible, with local multi-chain parallelism and adaptive exploration of the boundary of the failure domain. Applying multiple candidate states sampling, the TMC obtains as much additional failure domain information as possible, extracting the samples that fully reflect the failure distribution characteristics. The adaptive kernel density estimation of the sample is approximately optimal, improving the accuracy of the calculation results. At the end of the paper, two sets of numerical examples are used to verify the performance of the proposed algorithm. The calculation results show that the algorithm is not sensitive to the location of the design point and the sampling starting point. When dealing with strong nonlinear and complex series of system problems, the proposed method can get highly accurate calculation results with small sample size. When the sample size changes, the calculation result is relatively stable and reliable. The efficiency of the proposed method under practical problems is calculated in engineering examples, demonstrating its engineering application value.

Key words: reliability, Markov Chain, importance sampling, kernel density estimation, Monte Carlo simulation

中图分类号:

张洪铭, 顾晓辉, 邸忆. 基于树形马氏链模型的可靠性分析方法[J]. 航空学报, 2019, 40(5): 222643-222643.

ZHANG Hongming, GU Xiaohui, DI Yi. Reliability analysis method based on Tree Markov Chain model[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2019, 40(5): 222643-222643.

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E-mail：hkxb@buaa.edu.cn

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于树形马氏链模型的可靠性分析方法

Reliability analysis method based on Tree Markov Chain model

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