基于概率简单叠加法则的动力可靠度高效计算方法

EFFICIENT ESTIMATION OF DYNAMIC RELIABILITY BASED ON SIMPLE ADDITIVE RULES OF PROBABILITY

基于计算单元失效域的重要抽样法和区域分解法是计算高维输入随机变量条件下小失效概率的高效算法。该文在此基础上,首先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,其次利用区域分解法的思想,引入构成总失效域互斥的单元失效域,最后根据两种单元失效域的关系和概率简单叠加法则,即可计算总失效概率。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。算例部分对受高斯白噪声激励作用的单自由度线性体系和多自由度线性体系,分别应用该文方法、基于计算单元失效域的重要抽样法和区域分解法进行了计算,并用Monte-Carlo法进行了验证,结果表明计算动力可靠度,尤其是小失效概率时,该文方法对比Monte-Carlo法计算效率有明显提高,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。

Importance sampling technique based on elementary failure regions and domain decomposition method are efficient for dealing with problems with high-dimensional small failure probability. According to importance sampling technique, the identification of elementary failure regions is firstly proposed in this paper, which is corresponding to the failure of a particular output response at a particular instant. Then, according to domain decomposition method, mutual exclusive sets are proposed. According to the relation between elementary failure regions and mutual exclusive sets, and the simple additive rules of probability, the failure probability can be obtained. The key problems are the determination of unit impulse response function and the number of samples falling in the mutual exclusive sets. A single degree-of-freedom system and a two-degree-of-freedom system subjected to Gaussian white noise are analyzed numerically. Results show that the proposed method has higher efficiency than Monte Carlo method to estimate small failure probability, and similar efficiency to importance sampling based on elementary failure regions and domain decomposition method.