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