A probabilistic hierarchical sub-modelling approach through a posteriori Bayesian state estimation of finite element error fields - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2021

A probabilistic hierarchical sub-modelling approach through a posteriori Bayesian state estimation of finite element error fields

J P Rouse
  • Fonction : Auteur
Pierre Kerfriden
M Hamadi
  • Fonction : Auteur

Résumé

The present work considers two challenges arising from common multiscale approaches and provides a non-intrusive solution for error estimation. Firstly, the quality of the global mesh/solution and its effect on state estimations at local features is considered. Zhu-Zienkiewicz goal oriented error estimates are used to approximate errors in global deformation fields. These are then propagated across region of interest boundaries to local models and distributions in key parameters are determined. The second challenge follows the observation that local models/features may well appear at several locations in a global model. Furthermore, these locations and the details of the local models may evolve during the design process. The global model remains applicable in all cases, however without some form of interpolation scheme it is not possible to use known error estimates to inform confidence bounds at new feature locations. Gaussian process models that make use of a stochastic differential equation interpretation of the Matérn prior are used to recover the full error field, thereby allowing movement of the local model at marginal expense. The application of goal orientated error estimates and Gaussian processes in multiscale problems of this kind is novel, general, and powerful.
Fichier principal
Vignette du fichier
MultiscaleErrorEstimation_pprint.pdf (10.89 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03462530 , version 1 (01-12-2021)

Identifiants

  • HAL Id : hal-03462530 , version 1

Citer

J P Rouse, Pierre Kerfriden, M Hamadi. A probabilistic hierarchical sub-modelling approach through a posteriori Bayesian state estimation of finite element error fields. 2021. ⟨hal-03462530⟩
64 Consultations
14 Téléchargements

Partager

Gmail Facebook X LinkedIn More