Comptes Rendus
no. 11
Real-time Bayesian data assimilation with data selection, correction of model bias, and on-the-fly uncertainty propagation
Paul-Baptiste Rubio1 ; Ludovic Chamoin1, 2  ; François Louf1
1 LMT (ENS Paris-Saclay, CNRS, Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan, France
2 Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France
Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 762-779.

The work introduces new advanced numerical tools for data assimilation in structural mechanics. Considering the general Bayesian inference context, the proposed approach performs real-time and robust sequential updating of selected parameters of a numerical model from noisy measurements, so that accurate predictions on outputs of interest can be made from the numerical simulator. The approach leans on the joint use of Transport Map sampling and PGD model reduction into the Bayesian framework. In addition, a procedure for the dynamical and data-based correction of model bias during the sequential Bayesian inference is set up, and a procedure based on sensitivity analysis is proposed for the selection of the most relevant data among a large set of data, as encountered for instance with full-field measurements coming from digital image/volume correlation (DIC/DVC) technologies. The performance of the overall numerical strategy is illustrated on a specific example addressing structural integrity on damageable concrete structures, and dealing with the prediction of crack propagation from a damage model and DIC experimental data.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2019.11.004
Mots clés : Data assimilation, Bayesian inference, Model reduction, Modeling error, Real-time simulations, Full-field measurements, Uncertainty quantification
Paul-Baptiste Rubio 1 ; Ludovic Chamoin 1, 2 ; François Louf 1

1 LMT (ENS Paris-Saclay, CNRS, Université Paris-Saclay), 61, avenue du Président-Wilson, 94235 Cachan, France
2 Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France 
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     title = {Real-time {Bayesian} data assimilation with data selection, correction of model bias, and on-the-fly uncertainty propagation},
     journal = {Comptes Rendus. M\'ecanique},
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Paul-Baptiste Rubio; Ludovic Chamoin; François Louf. Real-time Bayesian data assimilation with data selection, correction of model bias, and on-the-fly uncertainty propagation. Comptes Rendus. Mécanique, Volume 347 (2019) no. 11, pp. 762-779. doi : 10.1016/j.crme.2019.11.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.11.004/

[1] F. Darema Dynamic data driven applications systems: a new paradigm for application simulations and measurements, Computational Science - ICCS, 2004, pp. 662-669

[2] J. Kaipio; E. Somersalo Statistical and Computational Inverse Problems, Springer-Verlag, New York, 2004

[3] A. Tarantola Inverse Problem Theory and Methods for Model Parameter Estimation, Society for Industrial and Applied Mathematics, 2005

[4] A.M. Stuart Inverse problems: a Bayesian perspective, Acta Numer., Volume 19 (2010), pp. 451-559

[5] M.S. Arulampalam; S. Maskell; N. Gordon; T. Clapp A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking, IEEE Trans. Signal Process., Volume 50 (2002) no. 2, pp. 174-188

[6] C.P. Robert; G. Casella Monte Carlo Statistical Methods, Springer Texts in Statistics, Springer, New York, 2004

[7] T.A. El Moselhy; Y. Marzouk Bayesian inference with optimal maps, J. Comput. Phys., Volume 231 (2012) no. 23, pp. 7815-7850

[8] Y. Marzouk; T. Moselhy; M. Parno; A. Spantini Sampling via measure transport: an introduction, Handbook of Uncertainty Quantification, 2016, pp. 1-41

[9] A. Spantini; D. Bigoni; Y. Marzouk Inference via low-dimensional couplings, J. Mach. Learn. Res., Volume 19 (2018), pp. 1-71

[10] F. Chinesta; R. Keunings; A. Leygue The Proper Generalized Decomposition for Advanced Numerical Simulations: A Primer, SpringerBriefs in Applied Sciences and Technology, 2014

[11] J. Berger; H.R.B. Orlande; N. Mendes Proper generalized decomposition model reduction in the Bayesian framework for solving inverse heat transfer problems, Inverse Probl. Sci. Eng., Volume 25 (2017) no. 2, pp. 260-278

[12] P.B. Rubio; F. Louf; L. Chamoin Fast model updating coupling Bayesian inference and PGD model reduction, Comput. Mech., Volume 62 (2018) no. 6, pp. 1485-1509

[13] P.B. Rubio; F. Louf; L. Chamoin Transport map sampling with PGD model reduction for fast dynamical Bayesian data assimilation, Int. J. Numer. Methods Eng., Volume 120 (2019) no. 4, pp. 447-472

[14] Y. Maday; A.T. Patera; J.D. Penn; M. Yano A parametrized-background data-weak approach to variational data assimilation: formulation, analysis, and application to acoustics, Int. J. Numer. Methods Eng., Volume 102 (2014) no. 5, pp. 933-965

[15] F. Chinesta; E. Cueto; E. Abisset-Chavanne; J-L. Duval; F.E. Khaldi Virtual, digital and hybrid twins: a new paradigm in data-based engineering and engineered data, Arch. Comput. Methods Eng. (2018) (online)

[16] C. Villani Optimal Transport: Old and New, Springer, 2008

[17] D. Calvetti; M. Dunlop; E. Somersalo; A. Stuart Iterative updating of model error for Bayesian inversion, Inverse Probl., Volume 34 (2018) no. 2

[18] D.A. Ross; J. Lim; R.S. Lin; M.H. Yang Incremental learning for robust visual tracking, Int. J. Comput. Vis., Volume 77 (2008) no. 1–3, pp. 125-141

[19] H. Jeffreys Theory of Probability, Clarendon Press, Oxford, 1961

[20] F. Hild; S. Roux Digital image correlation: from displacement measurement to identification of elastic properties - a review, Strain, Volume 42 (2006) no. 2, pp. 69-80

[21] H. Leclerc; J. Neggers; F. Matthieu; F. Hild; S. Roux Correli 3.0, IDDN.FR.001.520008.000.S.P.2015.000.31500, Agence pour la Protection des Programmes, Paris, 2015

[22] B. Richard; F. Ragueneau Continuum damage mechanics based model for quasi brittle materials subjected to cyclic loadings: formulation, numerical implementation and applications, Eng. Fract. Mech., Volume 98 (2013), pp. 383-406

[23] M. Vitse; D. Néron; P.-A. Boucard Dealing with a nonlinear material behavior and its variability through PGD models: application to reinforced concrete structures, Finite Elem. Anal. Des., Volume 153 (2019), pp. 22-37

[24] P. Ladevèze On reduced models in nonlinear solid mechanics, Eur. J. Mech. A, Solids, Volume 60 (2016), pp. 227-237

[25] M.D. Parno; Y.M. Marzouk Transport map accelerated Markov Chain Monte-Carlo, SIAM/ASA J. Uncertain. Quantificat., Volume 6 (2018) no. 2, pp. 645-682

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