An Unified Parametric-Nonparametric Uncertainty Quantification Approach for Linear Dynamical Systems

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. Nomenclature G mean of a system matri