关键词: 可靠性, 拟蒙特卡罗方法, 误差估计, 确定性点集, 低偏差抽样

Abstract: The Monte Carlo (MC) method has wide application in structural reliability problems not only for its simple program structure but also for the fact that its rate of convergence is completely independent of the number of dimensions of the problem under study. But, this method demonstrates poor computational efficiency in evaluating problems of small failure probability or problems that require a large amount of costly finite element analysis in each sampling cycle, and this disadvantage limits its application in structural reliability analysis. To overcome the deficiencies of the MC method, this article introduces and investigates various lowdiscrepancy sequences instead of pseudo random numbers to develop a quasiMonte Carlo (QMC) method for estimating the failure probability by combining these sequences with importance sampling. The proposed method exhibits advantages over the MC method in particular in that it is more accurate with the same number of samples and that it produces a deterministic estimate of errors. The accuracy and efficiency of the proposed method are shown by numerical examples. Therefore, the QMC method would seem to qualify as a comprehensive tool in structural reliability analysis.

Key words: reliability, quasi-Monte Carlo methods, error estimate, deterministic point set, low-discrepancy sampling