Wishart random matrices for uncertainty quantification of complex dynamical systems
Adhikari, S.
International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA 2008),
Genoa, Italy, June 2008.
Precise mathematical description of complex systems such as aircrafts and spacecrafts is extremely difficult to implement in practice. As a result, there is always some amount of uncertainty in the mathematical and numerical models of such systems. Such uncertainties need to be taken into account for credible predictions of the dynamic response of complex structural systems. These uncertainties include uncertainties in the system parameters and those arising due to the modelling of a complex system. For most practical systems, the detailed and complete information regarding these two types of uncertainties is not available. In this paper the Wishart random matrix model is used to quantify the total uncertainty in the mass, stiffness and damping matrices when such detailed information regarding uncertainty is unavailable. Four possible approaches to obtain the parameters of Wishart random matrix model are investigated. Using numerical examples and analytical approaches, the optimal set of parameters to be used in conjunction with Wishart random matrices is obtained. The method is applied to high and medium frequency vibration of a cantilever plate with uncertainties. The dynamic response obtained using the Wishart random matrix model agree well with the results obtained from the stochastic finite element method and laboratory based experimental results.
BiBTeX Entry
@INPROCEEDINGS{cp50,
AUTHOR={S. Adhikari},
TITLE={Wishart random matrices for uncertainty quantification of complex dynamical systems},
BOOKTITLE={International Conference on Mathematical Problems in Engineering ,Aerospace and Sciences (ICNPAA 2008)},
YEAR={2008},
Address={Genoa, Italy},
Month={June}
}
by Sondipon Adhikari