基于子集模拟法的非线性结构动力可靠度计算

DYNAMIC RELIABILITY COMPUTATION FOR NON-LINEAR STRUCTURES BASED ON SUBSET SIMULATION METHOD

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 for dynamic reliability calculations.Based on the original method,the proposal probability density function is selected in this paper,and the intermediate response threshold values are chosen adaptively.The conditional probabilities are evaluated by modified Metropolis algorithm.The detailed numbers of samples for calculating conditional probabilities are determined.Then calculation procedures for subset simulation method are presented.The efficiency of subset simulation method is demonstrated by calculating the first excursion probabilities of two examples.One is a Duffing system with single degree-of-freedom,the other is a three degree-of-freedom structure with three lines restoring model.The two structures are both subjected to stationary white noise excitation.For the Duffing system,when determining the samples that fall in the failure domains,responses of the non-linear structure need to be calculated,and iterative numerical step-by-step integration method is adopted.Results show that the proposed method can be applied in the dynamic reliability calculation for non-linear structures.It is accurate and efficient especially for computing small probabilities.