结构动力可靠度的重要抽样法

重要抽样法是蒙特卡洛数值模拟方法中的一种重要的方差缩减技术，目前重要抽样法在工程结构可靠度计算中的应用主要集中于静力问题。本文分析了动力可靠度蒙特卡洛方法的特点，提出了在结构动力可靠度问题中应用重要抽样法的方法，并针对白噪声荷载，给出了选择重要抽样函数的方法和重要抽样函数的具体表达式。理论和数值分析表明，本文所提出的重要抽样法应用于结构动力可靠度计算是可行的。

Importance sampling techniques in dynamical structural reliability

The possibility of importance sampling technique applied to dynamical structural reliability problems is explored, and then the procedures of calculating dynamical structural reliability under white noise excitation with importance sampling technique is presented. The white noise is modeled as independent normal random variable series. The scheme of amplifying the intensity of white noise, i.e., the variance of the normal random variables, is adopted to increase the chances of response samples falling in the failure domain. The joint probability density function of the normal random series with amplified variance is chosen as the importance sampling function. The influence of different amplifying ratios of variance on calculation precision is compared through a numerical example. It is indicated from the calculation that there exists an optimal value of amplifying ratios of variance that makes the calculation most efficient. Theoretical and numerical analyses show that the important sampling method presented herein is suitable to be applied to the calculation of dynamical failure probability of structures.