An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis

Stefano Marelli (1) , Bruno Sudret (1, 2)

1 Chair of Risk, Safety and Uncertainty Quantification [ETH Zurich]
2 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques

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.

Mots clés: Polynomial Chaos Expansions; Adaptive Designs; Bootstrap; Structural Reliability; Active Learning

Domaines: Méthodologie [stat.ME]; Structures

Stefano Marelli, Bruno Sudret. An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis. Structural Safety, 2018, 75, pp.67-74. ⟨10.1016/j.strusafe.2018.06.003⟩. ⟨hal-01902018⟩