北京航空航天大学学报 ›› 2011, Vol. 37 ›› Issue (6): 705-710,716.

• 论文 • 上一篇    下一篇

可靠性灵敏度分析的一种偏倚蒙特卡罗方法

李静辉1, 康锐1   

  1. 1. 北京航空航天大学 可靠性与系统工程学院, 北京 100191;
    2. 美国马里兰大学帕克分校 风险与可靠性中心, 马里兰 20742
  • 收稿日期:2010-12-21 出版日期:2011-06-30 发布日期:2011-07-05
  • 作者简介:李静辉(1984-),男,湖南娄底人,博士生,sophialjh@dse.buaa.edu.cn.

Biased Monte Carlo method for reliability sensitivity analysis

Li Jinghui1, Kang Rui1, Ali Mosleh2   

  1. 1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China;
    2. Center for Risk and Reliability, University of Maryland, College Park, MD 20742, USA
  • Received:2010-12-21 Online:2011-06-30 Published:2011-07-05

摘要: 根据可靠性灵敏度分析的需求和特点,选择似然比方法作为基础的导数/梯度估计方法.立足经典可靠性系统和基于元件的蒙特卡罗方法,推导了原始蒙特卡罗仿真环境下的似然比导数估计方法.为加速仿真,进一步提出了一种偏倚技巧,该技巧在系统结构函数的基础上定义一个应用重要抽样的无偏估计量,并通过最小化该估计量的方差来获得最优偏倚参数值.该估计量拥有的一个重要优势是其方差优化任务可以分解到单个元件的层次上进行,从而避免了高维优化的难题.通过一个可解析求解的简单实例验证了似然比导数估计方法应用于可靠性灵敏度分析的有效性,以及所提出的偏倚技巧对于降低导数估计方差的有效性.对于所考虑的实例系统,提出的偏倚蒙特卡罗方法对各个感兴趣的量都给出了很好的估计,与原始蒙特卡罗方法相比,各个估计量的方差均降低了至少6个数量级.

Abstract: The likelihood ratio (LR) method was chosen as the basic derivative/gradient estimation method for reliability sensitivity analysis. The implementation of the LR method in crude component-based Monte Carlo (MC) and especially in the setting of classical reliability was first derived. To speed up the simulation, a biasing technique was then developed, which defines an unbiased importance sampling estimator based on system structure functions, and identifies the optimal set of biasing parameters via minimizing the variance of this estimator. One important advantage of this estimator is that, the task of minimizing its variance can be achieved by optimizing at the component level, thus avoiding the difficulty of high dimensional optimizations. A simple example with analytical solution available was studied to test the effectiveness of the LR method for reliability sensitivity analysis, and also the effectiveness of the proposed biasing technique for reducing the variance of LR derivative estimators. The results show that, the proposed biased MC method produced accurate estimates for all the quantities, and achieved at least six orders of magnitude of variance reduction for all of them, compared to crude MC.

中图分类号: 


版权所有 © 《北京航空航天大学学报》编辑部
通讯地址:北京市海淀区学院路37号 北京航空航天大学学报编辑部 邮编:100191 E-mail:jbuaa@buaa.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发