Meta-models for structural reliability and uncertainty quantification

TL;DR

This paper reviews various meta-models used in structural reliability, highlighting their efficiency improvements and introducing a new technique to reduce bias in failure probability estimation.

Contribution

It provides a comprehensive review of classical and modern meta-models and introduces a novel method to address bias in failure probability estimation.

Findings

Polynomial chaos expansions improve accuracy

Kriging offers flexible surrogate modeling

New technique reduces bias in failure probability estimates

Abstract

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 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.