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子集模拟法是计算结构动力可靠度的新方法。该文在子集模拟法的基本思想上,适应性的选取子失效域的反应界限,合理的选取建议概率密度函数,应用修正的Metropolis算法产生计算条件失效概率时所需的随机变量样本,给出了所需样本的具体个数,并通过上述关键点总结给出了子集模拟法的具体计算步骤。最后应用子集模拟法首先计算了受平稳高斯白噪声作用的单自由度Duffing体系的失效概率,当确定落入失效域的样本时,需计算结构的非线性反应,该文采用迭代的数值逐步积分法进行计算;随后计算了受平稳高斯白噪声作用的采用三线型恢复力模型的三自由度结构的失效概率,结果表明:子集模拟法计算非线性结构动力可靠度时具有高效及高精度的特点,尤其适用于小失效概率的计算。
Subset simulation method is a new method to calculate structural dynamic reliability. In the basic idea of sub-set simulation method, this paper adaptively chooses the reaction limits of sub-failure domains, selects the recommended probability density function reasonably, and generates a sample of random variables needed to calculate the conditional failure probability using the modified Metropolis algorithm The specific number of the required samples out, and through the above key points to give a subset of simulation method of specific calculation steps. Finally, the sub-set simulation method is used to calculate the failure probability of the Duffing system with single degree-of-freedom affected by the stationary Gaussian white noise. When determining the sample falling into the failure zone, the nonlinear response of the structure needs to be calculated. Then the failure probabilities of the three-degree-of-freedom model with three-line restoring force model, which are affected by the stationary Gaussian white noise, are calculated. The results show that the subsets simulation method has high efficiency and high efficiency when calculating the dynamic reliability of nonlinear structures Accuracy characteristics, especially for small failure probability calculation.