Estimation of Small Failure Probabilities in High Dimensions by Adaptive Linked Importance Sampling
نویسنده
چکیده
Abstaract. A novel simulation approach, called Adaptive Linked Importance Sampling (ALIS), is proposed to compute small failure probabilities encountered in high-dimensional reliability analysis of engineering systems. It was shown by Au and Beck (2003) that Importance Sampling (IS) does generally not work in high dimensions. A geometric understanding of why this is true when one uses a fixed importance sampling density (ISD) was given in Katafygiotis and Zuev (2006). In this paper we introduce an algorithm referred to as Adaptive Linked Importance Sampling (ALIS). The basic idea of ALIS is instead of using a fixed ISD, as done in standard IS, to use a family of intermediate distributions that will converge to the target optimal ISD corresponding to the conditional probability given the failure event. We show that Subset Simulation (SS), which was introduced by Au and Beck (2001), does correspond to a special case of ALIS where the intermediate ISD’s are chosen to correspond to the conditional distributions given adaptively chosen intermediate nested failure events. However, the general formulation of ALIS allows for a much richer choice of intermediate ISD’s. As the concept of subsets is not a central feature of ALIS, the failure probability is not any longer expressed as a product of conditional failure probabilities as in the case of subset simulation. Starting with a one-dimensional example we demonstrate that ALIS can offer drastic improvements over subset simulation. In particular, we show that the choice of intermediate ISD’s prescribed by subset simulation is far from optimal. The generalization to high-dimensions is discussed. The accuracy and efficiency of the method is demonstrated with numerical examples.
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