In the reliability analysis of mechanical systems, sampling method is widely used due to the universality and practicability. However, the computation of high-dimensional problems encounters tremendous numerical difficulties, especially when the performance function is highly nonlinear. In this study, an augmented weighted simulation method (AWSM) is proposed in order to tackle this difficulty. The basic idea of AWSM is introducing a series of intermediate events into weighted simulation method (WSM), in which a new optimization method is constructed to reasonably determine each intermediate event. In this way, the failure event is divided to a sequence of conditional events, and the failure probability is accordingly converted to the product of conditional probabilities. Furthermore, a space reduction strategy is proposed to increase the probability of the samples generated in each conditional event, which greatly improves the sampling efficiency. Also, the coefficient of variation of AWSM is derived. Two mathematical examples and four engineering examples are tested, and the results demonstrate the efficiency and accuracy of the proposed method for high-dimensional problems.

在机械系统的可靠性分析中，抽样方法因其普遍性和实用性而被广泛使用。然而，高维问题的计算遇到了巨大的数值困难，尤其是当性能函数高度非线性时。在这项研究中，为了解决这个困难，提出了一种增强加权模拟方法（AWSM）。AWSM 的基本思想是将一系列中间事件引入加权模拟方法（WSM）中，其中构造了一种新的优化方法来合理地确定每个中间事件。这样，故障事件就被划分为一系列条件事件，故障概率也相应地转化为条件概率的乘积。此外，提出了空间缩减策略，以增加每个条件事件中产生样本的概率，大大提高了采样效率。此外，还导出了 AWSM 的变异系数。测试了两个数学实例和四个工程实例，结果证明了所提出的方法对高维问题的有效性和准确性。