非平稳随机激励下结构动力可靠度时域显式子集模拟法

基于动力响应显式表达式，时域显式随机模拟法可以通过减少单次样本计算时间有效提高动力可靠度的计算效率。然而，对于小失效概率问题，由于需要大量次样本计算，该法的计算量仍相当可观。为了克服上述困难，在时域显式随机模拟法基础上引入子集模拟法的基本思想，把小失效概率表示为一系列较大的条件概率的乘积，其中各条件概率采用时域显式随机模拟法计算，条件域内的样本采用Metropolis-Hastings抽样方法生成，从而实现了减少随机模拟所需的样本数，进一步提高了计算效率。算例结果表明改进的方法具有更高的计算效率，更适用于小失效概率和多自由度结构的动力可靠度问题。

TIME-DOMAIN EXPLICIT FORMULATION SUBSET SIMULATION METHOD FOR DYNAMIC RELIABILITY OF STRUCTURES SUBJECTED TO NON-STATIONARY RANDOM EXCITATIONS

Based on the explicit expressions of dynamic responses, a dime-domain explicit formulation random simulation method was developed to remarkably improve the efficiency of a dynamic reliability analysis by reducing single sample calculation time. However, for small failure probability events, the computational cost is still quite considerable because of the requirement of a large number of samples. To overcome above difficulty, a basic idea of subset simulation that expressing a small failure probability as a product of lager conditional probabilities is introduced to the dime-domain explicit formulation random simulation method to further lower the sample number. Among them, the conditional probabilities are obtained by the dime-domain explicit formulation random simulation method, and the samples required for obtaining the conditional probabilities are generated by Metropolis-Hastings algorithm. Numerical results show that the improved method has a higher computational efficiency and especially applicable for the dynamic reliability problems of small failure probability and for multi-degree-of-freedom structures.