Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies

M. P. Mignolet (1) , Christian Soize (2)

1 Fac Mech & Aerosp Engn
2 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

A complete probabilistic model of random positive definite matrices is developed that incorporates constraints on the standard deviations of a set of its eigenvalues. The model is, in particular, applicable to the representation of the mass and stiffness matrices of random dynamic systems of which certain natural frequencies are observed. The model development is based on the maximization of the entropy under a set of constraints representing the prescribed eigenvalue standard deviations, the mean matrix being given, and the existence of the mean Frobenius norm of the inverse of the random matrix. The efficient simulation of samples of random matrices according to the proposed model is discussed in detail. Finally, examples of application validate the above concepts and demonstrate the usefulness of the proposed model.

Mots clés: uncertainty quantification; random uncertainties; nonparametric probabilistic method; modeling errors; model uncertainties; random matrix; information theory; maximum entropy; structural dynamics; random system; probabilistic model; stochastic model

Domaines: Mécanique [physics.med-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Vibrations [physics.class-ph]

M. P. Mignolet, Christian Soize. Nonparametric stochastic modeling of linear systems with prescribed variance of several natural frequencies. Probabilistic Engineering Mechanics, 2008, 23 (2-3), pp.267-278. ⟨10.1016/j.probengmech.2007.12.027⟩. ⟨hal-00685147⟩