An active learning reliability algorithm based on local spectral residual expansions of the limit state function

Abstract

The assessment of structural reliability under uncertainties is a common problem in structural engineering. In a probabilistic setting, it is formalized by determining the failure probability of a system defined as the probability that the so-called limit-state function takes non-positive values. In recent years, considerable efforts have been devoted to developing algorithms that efficiently determine the failure probability. A powerful class of algorithms for reliability problems involving computationally demanding limit-state functions is the class of active learning reliability methods. These methods adaptively enhance an approximation of the limit state function resulting in considerable performance increase compared to more traditional stochastic simulation techniques. We recently proposed a new active learning reliability method based on the stochastic spectral embedding surrogate modeling technique [1]. It is based on adaptively constructing residual local spectral expansions in partitions of the parameter space with an adaptively enriched experimental design. The partitioning and enrichment rules exploit information about the local approximation accuracy and proximity to the limit state surface. In this contribution, we apply this technique to a reliability problem of a five story structural frame with 21 uncertain and mutually dependent input parameters. The frame is analyzed with the finite element method and has a reference failure probability in the order of 1e-6. With our proposed method, we consistently compute this failure probability with less than 200 evaluations of the original forward model.