Stochastic representations and statistical inverse identification for uncertainty quantification in computational mechanics

Christian Soize 1, * Christophe Desceliers 1 Johann Guilleminot 1 Thinh-Tien Le 1 Manh-Tu Nguyen 1 Guillaume Perrin 1, 2, 3, 4 Jean-Marc Allain 5 H. Gharbi 5 Denis Duhamel 4, 3 Christine Funfschilling 2
* Corresponding author
1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 SNCF : Innovation & Recherche
3 NAVIER UMR 8205 - Laboratoire Navier
4 Dynamique des structures et identification
NAVIER UMR 8205 - Laboratoire Navier
5 LMS - Laboratoire de mécanique des solides
Abstract : The paper deals with the statistical inverse problem for the identification of a non-Gaussian tensor-valued random field in high stochastic dimension. Such a random field can represent the parameter of a boundary value problem (BVP). The available experimental data, which correspond to observations, can be partial and limited. A general methodology and some algorithms are presented including some adapted stochastic representations for the non-Gaussian tensor-valued random fields and some ensembles of prior algebraic stochastic models for such random fields and the corresponding generators. Three illustrations are presented: (i) the stochastic modeling and the identification of track irregularities for dynamics of high-speed trains, (ii) a stochastic continuum modeling of random interphases from atomistic simulations for a polymer nanocomposite, and (iii) a multiscale experimental identification of the stochastic model of a heterogeneous random medium at mesoscale for mechanical characterization of a human cortical bone.
Keywords : Polynomial Chaos Multiscale analysis Random fields Stochastic modeling Statistical inverse problems Uncertainty quantification
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Conference papers
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Christian Soize, Christophe Desceliers, Johann Guilleminot, Thinh-Tien Le, Manh-Tu Nguyen, et al.. Stochastic representations and statistical inverse identification for uncertainty quantification in computational mechanics. (Plenary Lecture) UNCECOMP 2015, 1st ECCOMAS Thematic International Conference on Uncertainty Quantification in Computational Sciences and Engineering, M. Papadrakakis, May 2015, The Island of Crete, Greece. pp.1-26. ⟨hal-01158252⟩

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