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Random Matrix Models and Nonparametric Method for Uncertainty Quantification

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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.

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Authors and Affiliations

  1. Laboratoire Modélisation et Simulation Multi Echelle (MSME), Université Paris-Est, 5 bd Descartes, 77454, Marne-la-Vallee, France

    Christian Soize

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  1. Christian Soize
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Correspondence to Christian Soize .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, Virginia, USA

    David Higdon

  3. Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, USA

    Houman Owhadi

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© 2017 Springer International Publishing Switzerland

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Soize, C. (2017). Random Matrix Models and Nonparametric Method for Uncertainty Quantification. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-12385-1_5

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