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

Rouse, James Paul, Kerfriden, Pierre ORCID: https://orcid.org/0000-0002-7749-3996 and Hamadi, Maxime 2022. 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 123 (23) , pp. 5826-5853. 10.1002/nme.7090

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Abstract

Abstract: 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Advanced Research Computing @ Cardiff (ARCCA) Engineering
Additional Information:	License information from Publisher: LICENSE 1: URL: http://creativecommons.org/licenses/by/4.0/
Publisher:	Wiley
ISSN:	0029-5981
Date of First Compliant Deposit:	25 August 2022
Date of Acceptance:	26 July 2022
Last Modified:	01 Aug 2024 13:07
URI:	https://orca.cardiff.ac.uk/id/eprint/152146

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