Random Matrix Models and Nonparametric Method for Uncertainty Quantification

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

Chapter 8 in Handbook of Uncertainty Quantification, 2017, pp 219-287 from Springer

Abstract: 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.

Keywords: Random matrix; Symmetric random matrix; Positive-definite random matrix; Nonparametric uncertainty; Nonparametric method for uncertainty quantification; Random vector; Maximum entropy principle; Non-Gaussian; Generator; Random elastic medium; Uncertainty quantification in linear structural dynamics; Uncertainty quantification in nonlinear structural dynamics; Parametric-nonparametric uncertainties; Identification; Inverse problem; Statistical inverse problem (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-12385-1_5

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DOI: 10.1007/978-3-319-12385-1_5

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