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Random Matrix Models and Nonparametric Method for Uncertainty Quantification

In: Handbook of Uncertainty Quantification

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  • Christian Soize

    (Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle (MSME))

Abstract

This chapter deals with the fundamental mathematical tools and the associated computational aspects for constructing the stochastic models of random matrices that appear in the nonparametric method of uncertainties and in the random constitutive equations for multiscale stochastic modeling of heterogeneous materials. The explicit construction of ensembles of random matrices but also the presentation of numerical tools for constructing general ensembles of random matrices are presented and can be used for high stochastic dimension. The developments presented are illustrated for the nonparametric method for multiscale stochastic modeling of heterogeneous linear elastic materials and for the nonparametric stochastic models of uncertainties in computational structural dynamics.

Suggested Citation

  • Christian Soize, 2017. "Random Matrix Models and Nonparametric Method for Uncertainty Quantification," Springer Books, in: Roger Ghanem & David Higdon & Houman Owhadi (ed.), Handbook of Uncertainty Quantification, chapter 8, pages 219-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-12385-1_5
    DOI: 10.1007/978-3-319-12385-1_5
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