Uncertainty Quantification and Propagation Using Matrix Variate Distributions
Adhikari, S.
1st International Conference on Uncertainty in Structural Dynamics,
University of Sheffield, Sheffield, UK, June 2007.
Uncertainties need to be taken into account for credible results
from high fidelity, physics and engineering-based numerical
simulations. As a result, the quantification and propagation of
uncertainties play a crucial role in today's predictive
engineering science. Uncertainties can be broadly divided into
parametric uncertainty (inherent variability/data uncertainty) and
nonparametric uncertainty (lack of knowledge/model uncertainty).
Within the past three decades the deterministic finite element
method has been generalized to consider parametric uncertainties
in a systematic manner by means of the Stochastic Finite Element
Method (SFEM). In the context structural dynamics, using SFEM one
usually obtains the random mass, stiffness and damping matrices.
More recently a systematic approach to model nonparametric
uncertainty is proposed. Using this method one can obtain the
probability density function of the system matrices. Therefore,
both parametric and nonparametric uncertainty modelling lead to
matrix variate distributions describing the system matrices of a
linear dynamic system. In this paper it is first proved that both
parametric and non-parametric uncertainty can be modelled using a
unified matrix variate distribution (similar to a noncentral
Wishart distribution). An information theoretic approach to obtain
the parameters of this distribution has been proposed. Parametric
and nonparametric uncertainty models can be identified as special
cases of this general distribution. Once the random system
matrices are 'known' via this distribution, exact analytical
methods have been proposed for the solution of the equation of
motion of linear dynamical systems using the random matrix theory.
BiBTeX Entry
@INPROCEEDINGS{cp40,
AUTHOR={S. Adhikari},
TITLE={Uncertainty quantification and propagation using matrix variate distributions},
BOOKTITLE={Proceedings of the 1st International Conference on Uncertainty in Structural Dynamics},
YEAR={2007},
Address={University of Sheffield, Sheffield, UK},
Month={June},
Note={}
}
by Sondipon Adhikari