Partial ring simulation: An efficient method identifying importance domain for structural reliability analysis

Abstract

Failure probability of a structure is dominated by the importance domain whose extent is much smaller than the whole random variable space. Once the importance domain is identified, the failure probability can be evaluated efficiently through compressing the sampling space into the importance domain. Recently, ring simulation has attempted to identify the importance interval in one dimension (i.e., the radius). To obtain a complete importance domain in all dimensions, a new simulation method, called “partial ring simulation”, is proposed for the efficient estimation of the failure probability. In the proposed method, the importance domain, consisting of importance radius and importance direction, is adaptively identified by a stepwise strategy utilizing the information from prior steps. For generating samples located in the importance domain, a Markov chain Monte Carlo sampling is then constructed. The effectiveness of the proposed method is validated by four examples involving parallel, series, and nonlinear limit state functions, small failure probabilities, and high-dimensional problems. The results indicate that the proposed method greatly improves the computational efficiency of ring simulation.