Multifidelity adaptive kriging metamodel based on discretization error bounds

Abstract

Summary This article presents an approach to build a multifidelity kriging metamodel from finite element computations on different meshes for stuctural reliability assessment. The proposed method takes advantage of the computation of bounds on the discretization error, which enables to guarantee the state (safe or failure) of each computation of the performance function. An algorithm to build the metamodel from the different levels of fidelity and estimate the failure probability is provided. Illustrations are presented on a two dimensional mechanical crack opening problem. Bounds on the failure probability are also post‐processed.

Two multifidelity kriging-based strategies to control discretization error in reliability analysis exploiting a priori and a posteriori error estimators

“…Choosing a sufficiently converged mesh (that is to say the highest fidelity level) is usually done prior to the computation of the probability of failure. However, it is shown in [38,22] that a small error on the value of the performance function may lead to a large error on the probability of failure. Several recent works propose to estimate and control the discretization error on the probability of failure.…”

“…In [18], this discretization error estimator is used with FORM to compute bounds on the probability of failure. In [38], a kriging metamodel is built using points that are guaranteed to be rightly classified by the discretization error bounds. Bounds on the probability of failure are also obtained when the performance function is monotonic against random variables on a numerical example with a unique random variable.…”

“…Note that, it may not be the case for non-linear mechanics, non-linear quantities of interest and/or with industrial finite element softwares in which the error estimators is not available. This method is an adaptation of the method presented in [38]. The novelties to this method presented in this paper are the extension to multiple random variables and the derivation of bounds on the probability of failure.…”

Uncertainty Propagation of Structural Computation for Fatigue Assessment

“…Furthermore, the mesh is generaly chosen prior to fatigue analysis. Yet, it was proved in Ghavidel et al (2018); Mell et al (2020) that a small error on the local quantity of interest (i.e. local stress) can lead to a large error on the probability of failure.…”

“…Second, it is possible to use discretization error estimators that are available as a post-process of the finite element solution Zienkiewicz & Zhu (1987); Ainsworth & Oden (1997). Such techniques have been coupled with metamodeling techniques in Gallimard (2011); Mell et al (2020). However, it was not applied to fatigue analysis.…”