Random matrix theory and random uncertainties modeling

Christian Soize (1)

1 LaM - Laboratoire de Mécanique

Random matrix theory was intensively studied in the context of nuclear physics. For physical applications, the most important ensemble is the Gaussian Orthogonal Ensemble (GOE) whose elements are real symmetric random matrices with statistically independent entries and are invariant under orthogonal linear transformations. Recently, a new approach, called a nonparametric model of random uncertainties, has been introduced by the author for modeling random uncertainties in vibration analysis. This approach has been developed in introducing a new ensemble of random matrices constituted of symmetric positive-definite real random matrices, called the "positive-definite" ensemble, which differs from the GOE. The first objective of this paper is to compare the GOE with the "positive-definite" ensemble of random matrices in the context of the nonparametric approach of random uncertainties in dynamic systems for the low-frequency range. The second objective of this paper is to give a new validation for the nonparametric model of random uncertainties in dynamic systems in comparing, in the low-frequency range, the dynamical response of a simple system having random uncertainties modeled by the parametric and the nonparametric methods. It is proved that the "positive-definite" ensemble of random matrices, which has been introduced in the context of the development of this nonparametric approach, is well adapted to the low-frequency vibration analysis, while the use of the Gaussian orthogonal ensemble (GOE) is not.

Mots clés: uncertainty quantification; random matrix theory; random uncertainties; nonparametric probabilistic method; model uncertainties; modeling errors; random vibrations

Domaines: Probabilités [math.PR]; Mécanique [physics.med-ph]

Christian Soize. Random matrix theory and random uncertainties modeling. 4th International Conference on Computational Stochastic Mechanics, Sep 2002, Corfu, Greece. pp.575-581. ⟨hal-00686222⟩