动力可靠度计算的概率简单叠加法则法

Method based on simple additive rules of probability for dynamic reliability calculations

首先给出了基于计算单元失效域的重要抽样法和区域分解法的计算步骤,随后利用基于计算单元失效域的重要抽样法的思想,引入构成总失效域的由持时内的时间点划分出的单元失效域;利用区域分解法的思想,引入构成总失效域的互斥的单元失效域,最后根据两种单元失效域的关系和概率简单叠加法则计算总失效概率。其中关键问题是计算结构反应时单位脉冲响应函数的确定和落入各个互斥单元失效域的样本数的确定。算例的计算结果表明计算动力可靠度,尤其是高维输入随机变量条件下小失效概率时,概率简单叠加法则法对比Monte-Carlo法计算效率有显著提高,并同基于计算单元失效域的重要抽样法和区域分解法一样高效。

In this paper,computational procedures of importance sampling method based on elementary failure events and domain decomposition method are presented first.In the following steps,firstly according to importance sampling method,elementary failure regions corresponding to the failure of a particular output response at a particular instant are proposed.Secondly according to domain decomposition method,mutual exclusive sets are proposed.Finally according to the relation between elementary failure regions and mutual exclusive sets,and simple additive rules of probability,the failure probability can be expressed.The key problems are the determination of unit impulse response function and the number of samples which fall into the mutual exclusive sets.Results of numerical examples show that for estimation of dynamic reliability,especially small failure probability in high dimensions,the efficiency of the method proposed in this paper is increased obviously compared with Monte-Carlo method,and is as high as the efficiency of importance sampling method based on elementary failure regions and that of domain decomposition method.