A new unequal-weighted sampling method for efficient reliability analysis

Highlights: • The failure probability is calculated based on a weighted summation over sub-spaces. • The random-variate space is partitioned via Voronoi cells to obtain the sub-spaces and their weights. • The failure probability of each sub-space is estimated by kernel density estimation, where the bandwidth is suggested. • Numerical examples are investigated to validate the proposed method. In this paper, a new method for efficient reliability analysis is proposed. The proposed method utilizes the Voronoi cells to partition the random-variate space into several sub-spaces and the kernel density estimation to approximate the failure probability in each sub-space. The optimal bandwidth for the kernel is also suggested. Then, the failure probability can be conveniently evaluated by a weighted summation over each sub-space (sampling point). Since the weight for each sub-space (sampling point) is not identical, this method is referred to as the unequal-weighted sampling method for reliability analysis. Numerical implementation procedure of the proposed method is also outlined. Several numerical examples are investigated to verify the proposed method, where the results are compared with those of Monte Carlo simulation and subset simulation methods. It is demonstrated that the proposed method can achieve the tradeoff of accuracy and efficiency for reliability analysis. Problems to be further studied are also pointed out.