New bubble sampling method for reliability analysis

In recent years, the safety of engineering systems is seriously threatened by increasingly complex and uncertain engineering environment, and the reliability analysis of engineering structure has attracted increasing attention. The sampling methods are widely used because of its simplicity and universality. However, their applications are limited by the expensive computational cost. To ease the computation burden, a new bubble sampling method (BSM) is proposed in this study. Its core idea is to generate several bubbles in the safe and failure domains, in which the performance function signs of samples located in these bubbles can be directly determined and are unnecessary to be computed. In this way, the number of function calls is greatly reduced. Moreover, a new bubble optimization model is developed, in which the uniform sampling strategy is adopted. Several numerical and engineering applications are validated to demonstrate the performances of the proposed BSM, which confirms its computational efficiency and accuracy.