An Unified Parametric-Nonparametric Uncertainty Quantification Approach for Linear Dynamical Systems
Adhikari, S.
48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics
& Materials Conference, Waikiki, Hawaii USA, April 2007.
Uncertainties need to be taken into account for credible
predictions of the dynamic response of complex aerospace
structural systems. Such uncertainties include uncertainties in
the system parameters (parametric uncertainty) and those arising
due to the modelling of a complex system (nonparametric
uncertainty). Over the past four decades distinct methods have
been developed to quantify these two types of uncertainties
seperately. In this paper we proposed an unified approach to model
both parametric and nonparametric uncertainties simultaneously.
The proposed approach is based on a noncentral Wishart
distribution whose parameters are obtained such that the
covariance matrices of the elements of the mass, stiffness and
damping matrices arising due to parametric uncertainties are
satisfied in a least-square sense. The existing nonparametric
distribution (a central Wishart distribution) can be obtained as a
special case of the proposed noncentral Wishart distribution. A
simple simulation algorithm is developed to implement the
noncentral Wishart random matrix model in conjunction with the
conventional finite element method. The method is applied to the
vibration of a cantilever plate with uncertainties. The dynamic
response obtained using the noncentral Wishart random matrix model
agrees well with the results obtained from the stochastic finite
element method.
BiBTeX Entry
@INPROCEEDINGS{cp30,
AUTHOR={S. Adhikari},
TITLE={An unified parametric-nonparametric uncertainty quantification approach for linear dynamical systems},
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