A New Adaptive Importance Sampling using Subset Simulation to Estimate the Probability of Failure and the Most Probable Point

E Jahani, H. Ramroody


In this paper, to estimate the probability of failure and the most probable point (MPP), a new adaptive
Importance Sampling method based on Subset Simulation is presented. The MPP is a point in the failure
domain which has the most value of the joint probability density function among the other points in the
failure region. In the proposed method, Subset Simulation which is a robust method to estimate the failure
probability of rare events in high dimensional problems is adapted with the Importance Sampling. This
method is called the Subset-Importance Simulation (SIS). The SIS which contains the both advantages of
Subset Simulation and Importance Sampling in terms of computational effort, time and generating required
samples, can be led to considerably decrease the number of the generated samples in comparing with Subset
Simulation and Importance sampling separately. In order to examine the efficiency of the proposed method, it
has been applied to benchmark examples. The results confirm that the probability of the failure and the MPP
can be predicted with reasonable precision.

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