Title: An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis,
Abstract: Polynomial chaos expansions (PCE) have seen widespread use in the context of
uncertainty quantification. However, their application to structural
reliability problems has been hindered by the limited performance of PCE in the
tails of the model response and due to the lack of local metamodel error
estimates. We propose a new method to provide local metamodel error estimates
based on bootstrap resampling and sparse PCE. An initial experimental design is
iteratively updated based on the current estimation of the limit-state surface
in an active learning algorithm. The greedy algorithm uses the bootstrap-based
local error estimates for the polynomial chaos predictor to identify the best
candidate set of points to enrich the experimental design. We demonstrate the
effectiveness of this approach on a well-known analytical benchmark
representing a series system, on a truss structure and on a complex realistic
frame structure problem.