Meta-models for structural reliability and uncertainty quantification

Bruno Sudret (1, 2)

1 GdR MASCOT-NUM - Méthodes d'Analyse Stochastique des Codes et Traitements Numériques
2 msa - Matériaux et Structures Architecturés

A meta-model (or a surrogate model) is the modern name for what was traditionally called a response surface. It is intended to mimic the behaviour of a computational model M (e.g. a finite element model in mechanics) while being inexpensive to evaluate, in contrast to the original model M which may take hours or even days of computer processing time. In this paper various types of meta-models that have been used in the last decade in the context of structural reliability are reviewed. More specifically classical polynomial response surfaces, polynomial chaos expansions and kriging are addressed. It is shown how the need for error estimates and adaptivity in their construction has brought this type of approaches to a high level of efficiency. A new technique that solves the problem of the potential biasedness in the estimation of a probability of failure through the use of meta-models is finally presented.

Mots clés: Structural reliability; uncertainty quantification; meta-models; surrogate models; polynomial chaos expansions; kriging; importance sampling

Domaines: Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Physique [physics]; Mécanique [physics]; Mécanique des structures [physics.class-ph]; Mathématiques [math]; Statistiques [math.ST]; Statistiques [stat]; Théorie [stat.TH]

Bruno Sudret. Meta-models for structural reliability and uncertainty quantification. "Asian-Pacific Symposium on Structural Reliability and its Applications", May 2012, Singapore, Singapore. pp.1-24. ⟨hal-00683179⟩