Directional subset simulation for reliability estimation

This study proposes a sequential multiple importance sampling (SeMIS) method for efficient estimation of rare event failure probability, which is typically represented by. Regarding () as a prior distribution and () as the likelihood function, the failure probability is equivalent to the evidence in Bayesian inference.Leveraged on this equivalence, the MIS used for Bayesian inference is adapted for failure probability estimation in this paper.In order to efficiently design the proposal distributions in MIS, we extend the idea of subset simulation (SuS) to adaptively define proposal distributions that propagate samples from both safe and failure domains to the limit state surface.In order to generate samples in the failure domain, an enlarged sampling parameter space is first designed by amplifying the standard deviation in "prior" distribution () from 1 to ( 1), i.e., to sample from ().A heuristic rule to determine the optimal is proposed, which is inversely proportional to the dimension of the problem and converge to 1 when the dimension becomes large enough.The performance of SeMIS algorithm is illustrated in various benchmark examples and compared with SuS.It shows that SeMIS yields an excellent estimation of failure probability in terms of estimation bias and statistical/computational efficiency.It is also robust to the pathological geometry of the limit state function, where SuS may fail.The SeMIS algorithm provides a competitive solution for failure probability estimation.