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基于失效概率积分和马尔可夫链模拟的可靠性灵敏度分析
引用本文:袁修开,吕震宙. 基于失效概率积分和马尔可夫链模拟的可靠性灵敏度分析[J]. 工程力学, 2008, 25(1): 49-53
作者姓名:袁修开  吕震宙
作者单位:西北工业大学航空学院,西安,710072;西北工业大学航空学院,西安,710072
基金项目:国家自然科学基金(10572117),新世纪优秀人才支持计划(NCET-05-0868)资助
摘    要:可靠性灵敏度可以被表达为失效概率对基本随机变量分布参数的偏导数的形式,利用失效概率为基本变量的联合概率密度函数在失效域上的积分表达式,并且利用马尔可夫链能够高效模拟感兴趣区域样本的性质,一种针对单个失效模式和系统多个失效模式的可靠性灵敏度分析方法被提出。由于可靠性参数灵敏度可以表达为一个与联合概率密度函数相关的函数在失效域中的数学期望的形式,所提方法采用马尔可夫链来高效模拟失效域中的样本,进而采用样本均值替代总体均值的方法来得到可靠性灵敏度的估计值。与已有的基于Monte-Carlo模拟的可靠性灵敏度分析方法相比,所提方法在保证计算精度的基础上计算效率有显著提高,尤其是针对小失效概率的可靠性灵敏度分析问题。该算例充分说明了所提方法的合理可行性。

关 键 词:可靠性  灵敏度  马尔可夫链  参数  Monte-Carlo
文章编号:1000-4750(2008)01-0049-05
收稿时间:2006-05-12
修稿时间:2007-03-09

RELIABILITY PARAMETER SENSITIVITY BASED ON FAILURE PROBABILITY INTEGRATION AND MARKOV CHAIN SIMULATION
YUAN Xiu-kai,LU Zhen-zhou. RELIABILITY PARAMETER SENSITIVITY BASED ON FAILURE PROBABILITY INTEGRATION AND MARKOV CHAIN SIMULATION[J]. Engineering Mechanics, 2008, 25(1): 49-53
Authors:YUAN Xiu-kai  LU Zhen-zhou
Abstract:Reliability Sensitivity (RS) is usually defined as partial derivatives of failure probability with respect to distribution parameter of basic random variable. Based on the definition of failure probability, the integration of joint Probability Density Function (PDF) of the basic random vector in failure region, an efficient RS analysis method is presented by use of Markov chain simulation, which possesses high efficiency to draw samples from the interested region. The presented method is suitable for a system with single failure mode or with multiple faiure modes. The RS can be expressed as an expectation of a function related to PDF in failure region. The expectation is evaluated by means of samples in failure region, and the samples in failure region are drawn by Markov chain simulation. Since Markov chain simulation can efficiently draw sample from the interested region, the presented method has higher efficiency than the method based on Monte-Carlo simulation, especially for the small failure probability cases. After explaining the basic concept and the detailed implementation, a few examples are given to illustrate the rationality and the feasibility of the presented method.
Keywords:reliability  sensitivity  Markov chain  parameter  Monte-Carlo
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