Rare event estimation using Polynomial-Chaos-Kriging

Authors

Schöbi, R., Sudret, B. and Marelli, S.

Abstract

Structural reliability analysis aims at computing the probability of failure of systems whose performance may be assessed by using complex computational models (e.g. expensive-to-run finite element models). A direct use of Monte Carlo simulation is not feasible in practice, unless a surrogate model (such as Kriging, a.k.a Gaussian process modeling) is used. Such meta-models are often used in conjunction with adaptive experimental designs (i.e. design enrichment strategies), which allows one to iteratively increase the accuracy of the surrogate for the estimation of the failure probability while keeping low the overall number of runs of the costly original model.

In this paper we develop a new structural reliability method based on the recently developed Polynomial-Chaos Kriging (PC-Kriging) approach coupled with an active learning algorithm known as AK-MCS. We formulate the problem in such a way that the computation of both small probabilities of failure and extreme quantiles is unified. We discuss different convergence criteria for both types of analyses, and show in particular that the original AK-MCS stopping criterion may be over-conservative. We finally elaborate a multi-point enrichment algorithm which allows us to add several points in each iteration, thus fully exploiting high-performance computing architectures.

The proposed method is illustrated on three examples, namely a two-dimensional case which allows us to underline the advantages of our approach compared to standard AK-MCS. Then the quantiles of the 8-dimensional borehole function are estimated. Finally the reliability of a truss structure (10 random variables) is addressed. In all case, accurate results are obtained with about 100 runs of the original model.