Uncertainty Propagation in Linear Systems: An Exact Solution Using random Matrix Theory

Adhikari, S.
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference, Waikiki, Hawaii USA, April 2007.

In many stochastic mechanics problems the solution of a system of coupled linear random algebraic equations is needed. This problem in turn requires the calculation of the inverse of a random matrix. Over the past four decades several approximate analytical methods and simulation methods have been proposed for the solution of this problem in the context of probabilistic structural mechanics. In this paper, for the first time, we present an exact analytical method for the inverse of a real symmetric (in general non-Gaussian) random matrix of arbitrary dimension. The proposed method is based on random matrix theory and utilizes the Jacobian of the underlying nonlinear matrix transformation. Exact expressions for the mean and covariance of the response vector is obtained in closed-form. Numerical examples are given to illustrate the use of the expressions derived in the paper.
BiBTeX Entry
@INPROCEEDINGS{cp32,
    AUTHOR={S. Adhikari},
    TITLE={Uncertainty propagation in linear systems: \uppercase{a}n exact solution using random matrix theory},
    BOOKTITLE={48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics \& Materials Conference},
    YEAR={2007},
    Address={Waikiki, Hawaii, USA},
    Month={April},
    Organization={AIAA},
    Note={}
}

by Sondipon Adhikari