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Pré-Publication, Document De Travail Année : 2024

A Fully Bayesian Extension to FEMU for Identification of Spatially Varying Elastic Properties from Digital Image and Volume Correlation Measurements

Identification de propriétés élastiques spatialement variables par une méthode FEMU bayésienne à partir de mesures DIC et DVC.

Résumé

We present a fully Bayesian framework for identifying spatially varying elastic parameters and their covariance properties using noisy displacement observations obtained with DIC or DVC trials. Our method is a generalization of identification procedures such as FEMU or I-DIC to materials with spatially varying properties and stochastic mesostructures. The identified variables can be used to generate new samples with similar covariance properties. We formulate the approach as a hierarchical Bayesian PDE-constrained inverse problem and MAP estimates are obtained through gradient based optimization. We resort to an adjoint based formulation and leverage automatic differentiation to derive the parameter sensitivities. We show how modelling unknown parameters with Gaussian Random Fields leads to a natural Bayesian regularization and develop the use of Whittle-Matérn priors. Hyperparameter estimation is discussed, and we propose an empirical Bayes approach to avoid numerical shortcomings related to a standard hierarchical model. A set of numerical examples is presented to assess the performance of the proposed method, based on synthetic data generated through Matérn Random fields. In particular, we show how data noise is naturally modelled by the Bayesian formulation and impacts spatial covariance of identified parameters.
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Dates et versions

hal-04587210 , version 1 (27-05-2024)

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Domaine public

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  • HAL Id : hal-04587210 , version 1

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Armand Touminet, Sabine Cantournet, Victor Fabre, Pierre Kerfriden. A Fully Bayesian Extension to FEMU for Identification of Spatially Varying Elastic Properties from Digital Image and Volume Correlation Measurements. 2024. ⟨hal-04587210⟩
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