变量相关情况下基于马尔可夫链样本模拟的线抽样可靠性灵敏度分析方法  

Line Sampling Based on Markov Chain Simulation for Reliability Sensitivity Analysis with Correlative Variables

作　　者：何红妮[1] 吕震宙[1] 

机构地区：[1]西北工业大学航空学院,陕西西安710072

出　　处：《航空学报》2009年第8期1413-1420,共8页Acta Aeronautica et Astronautica Sinica

基　　金：国家自然科学基金(10572117);国家"863"计划(2007AA04Z401);教育部"新世纪优秀人才支持计划"(NCET-05-0868);航空科学基金(2007ZA53012)

摘　　要：针对变量具有相关性的可靠性灵敏度分析问题,提出了一种变量相关情况下基于马尔可夫链样本模拟的线抽样可靠性灵敏度分析方法。在所提方法中,首先将相关变量等价转换为独立正态变量,然后采用基于马尔可夫链样本模拟的线抽样方法,求解失效概率对等价独立正态变量分布参数的偏导数,最后利用等价变换前后变量分布参数之间的解析关系和复合函数求导法则,求得失效概率对相关变量分布参数的可靠性灵敏度。为了解所提方法的效率和精度,对所提方法的可靠性灵敏度估计值进行了方差分析。由于所提方法采用马尔可夫链快速产生失效域中的条件样本,这些失效域中的样本可用来准确获取重要方向,并可作为线抽样的随机样本,因而该方法具有很高的抽样效率。算例结果表明,所提方法是一种计算相关变量可靠性灵敏度的高效率、高精度方法。For the reliability sensitivity （RS） problem with correlative normal variables, a RS analysis method by line sampling is presented on the basis of Markov chain simulation. In the method, the correlative normal variables are first transformed into equivalent independent variables. Then, the line sampling algorithm based on Markov chain simulation is employed to estimate the RS of the failure probability with respect to the distribution parameters of the equivalent independent normal variables. Finally, taking advantage of the relationship between the correlative variables and the independent normal variables, the RS of the failure probability with respect to all distribution parameters of the correlative normal variables can be obtained by the chain rule of derivatives. In order to investigate the convergence and precision of the proposed method, the variance and the variation coefficients of the RS estimation are derived. Since Markov chain is employed to simulate the samples located at the failure region, and these simulated samples are used to obtain the important direction of line sam- pling and also used as random samples of the line sampling, the proposed method has high efficiency. The results of the examples show the efficiency and the precision of the method.

关 键 词：可靠性 灵敏度分析 相关变量 马尔可夫链 线抽样 变异系数 

分 类 号：TB114.3[理学—概率论与数理统计]