An augmented weighted simulation method for high-dimensional reliability analysis

Abstract

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.