重要性抽样法研究

A Review of Importance Sampling

重要性抽样法是一种最重要的提高抽样效率的方法,由于其适用范围广,容易实现,在通信网、航空航天、自动控制等系统的可靠性安全性仿真中得到广泛研究和应用。本文从计算复杂性的角度提出了极小概率事件发生概率估计的困难,简单介绍了重要性抽样的基本原理,综述了基于随机优化和大偏差原理的技术、加速失效法、分裂法等几种最优抽样分布构造技术的实现及其适用范围,在此基础上提出基于知识的重要性抽样思想,有助于解决目前数字仿真特别是高可靠度系统可靠性仿真中的抽样效率问题。

Importance sampling is one of the most important methods of improving sampling efficiency. It has been widely studied and applied in the analysis of communication networks, aviation and spacecraft systems, automatic control system, etc., because of its applicability and facilitation. This paper describes the difficulty of rare-event probability estimation using digital simulation method in the view of computation complexity, and focuses on the principles and construction methods of importance sampling plan. Realization and applicability of some optimized sampling distribution construction techniques such as stochastic optimization method, large deviation principle based techniques, failure biasing method and splitting method are summarized. Based on the discussion a knowledge based sampling distribution construction methodology is established. This will help to solve the sampling efficiency in digital simulation especially for high dependent system reliability analysis.