Matrix Variate Distributions for Probabilistic Structural Dynamics

Abstract

Matrix variate distributions are proposed to quantify uncertainty in the mass, stiffness, and damping matrices arising in linear structural dynamics. The proposed approach is based on the so-called Wishart random matrices. It is assumed that the mean of the system matrices are known. A new optimal Wishart distribution is proposed to model the random system matrices. The optimal Wishart distribution is such that the mean of the matrix and its inverse produce minimum deviations from their respective deterministic values. The method proposed here gives a simple nonparametric approach for uncertainty quantification and propagation for complex aerospace structural systems. The new method is illustrated using a numerical example. It is shown that Wishart random matrices can be used to model uncertainty across a wide range of excitation frequencies.