Investigation of random matrix applications on structural dynamics using a tensor decomposition

Abstract

Random matrix ensembles can be applied to rigid body and structural dynamics to model epistemic uncertainties, that is, modeling errors. In this paper, random matrices are investigated in terms of a tensor decomposition. This decomposition yields a parallel (or coaxial) component and an orthogonal component. Then, a metric is defined to measure the deviation of both components with respect to the nominal matrix. This approach allows for better understanding of the choice of the random ensembles, i.e., the stochastic model of a given mechanical system. Three symmetric matrix ensembles are analyzed: Gaussian orthogonal ensemble, symmetric positive-definite ensemble, and proportional ensemble. It is shown that these symmetric ensembles yield quite different results, and the applied metric can clearly distinguish the matrix ensembles.