A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue International Journal for Numerical Methods in Engineering Année : 2022

A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling

James Paul Rouse
Pierre Kerfriden
Maxime Hamadi
  • Fonction : Auteur

Résumé

The present work proposes a computational approach that recovers full finite element error fields from a small number of estimates of errors in scalar quantities of interest. The approach is weakly intrusive and is motivated by large scale industrial applications wherein modifying the finite element models is undesirable and multiple regions of interest may exist in a single model. Error estimates are developed using a Zhu-Zienkiewicz estimator coupled with the adjoint methodology to deliver goal-oriented results. A Bayesian probabilistic estimation framework is deployed for full field estimation. An adaptive, radial basis function based reduced order modeling strategy is implemented to reduce the cost of calculating the posterior. The Bayesian reconstruction approach, accelerated by the proposed model reduction technology, is shown to yield good probabilistic estimates of full error fields, with a computational complexity that is acceptable compared to the evaluation of the goal-oriented error estimates. The novelty of the work is that a set of computed error estimates are considered as partial observations of an underlying error field, which is to be recovered. Future improvements of the method include the optimal selection of goal-oriented error measures to be acquired prior to the error field reconstruction.

Dates et versions

hal-03955941 , version 1 (25-01-2023)

Identifiants

Citer

James Paul Rouse, Pierre Kerfriden, Maxime Hamadi. A probabilistic data assimilation framework to reconstruct finite element error fields from sparse error estimates: Application to sub‐modeling. International Journal for Numerical Methods in Engineering, 2022, 123 (23), pp.5826-5853. ⟨10.1002/nme.7090⟩. ⟨hal-03955941⟩
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