Optimal Adaptive Importance Sampling for Reliability Analysis

Resumo

Reliability Analysis play a central role in Structural Safety. For this reason, several methods have been proposed and adapted to solve this problem over the years. In this work we focus on a family of sampling-based schemes called Adaptive Importance Sampling (AIS). The idea of AIS is to take an initial sampling distribution, draw a sample, evaluate the required statistical moments and then update the sampling distribution using some rule in order to make it closer to the target distribution. The procedure is then repeated iteratively until a good representation of the target distribution is obtained. In the context of Reliability Analysis, this idea can be employed to represent the optimal sampling distribution of IS and thus allow an accurate estimate of the probability of failure. There exist several variants of AIS, but all of them provide a sequence of samples obtained with a sequence of sampling distributions. If employed to evaluated statistical moments, as is the case of Reliability Analysis, it is then necessary to combine the estimates obtained at each iteration to get a final result. Generally, this is done by taking the average value among all iterations. However, in this work we reflect on better ways to combine these estimates in order to obtain the final result.