Abstract A multilevel moving particles method is developed for the estimation of failure probabilities that are computed from numerical approximations of the performance function. The algorithm balances the statistical error of the estimate and the approximation error. This is achieved by computing a telescoping sum of estimates for the difference in the number of moves at subsequent levels of the approximation error. The sample variance of these estimates decreases with decreasing approximation error. Thus, the number of samples that has to be evaluated with high accuracy is reduced compared to a single level computation. Therefore, the proposed algorithm is very efficient for structural reliability analysis problems, in which highly accurate evaluations of the performance function are necessary and require a huge computational effort.

中文翻译：

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一种用于可靠性估计的多级运动粒子方法

摘要 开发了一种多级运动粒子方法，用于估计从性能函数的数值近似计算的失效概率。该算法平衡了估计的统计误差和近似误差。这是通过计算近似误差的后续级别的移动次数差异的估计的伸缩和来实现的。这些估计的样本方差随着近似误差的减小而减小。因此，与单级计算相比，减少了必须以高精度评估的样本数量。因此，所提出的算法对于结构可靠性分析问题非常有效，其中需要对性能函数进行高度准确的评估，并且需要大量的计算工作。