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State Uncertainty Propagation in the Presence of Parametric Uncertainty and Additive White Noise
Authors
Konda, U., Singla, P., Singh, T., and Scott, P., D.,
Source
ASME Journal of Dynamic Systems, Measurement and Control,
133(5).
Abstract
The focus of this work is on the development of a framework permitting the unification of
generalized polynomial chaos (gPC) with the linear moment propagation equations, to
accurately characterize the state distribution for linear systems subject to initial condition
uncertainty, Gaussian white noise excitation and parametric uncertainty which is
not required to be Gaussian. For a fixed value of parameters, an ensemble of moment
propagation equations characterize the distribution of the state vector resulting from
Gaussian initial conditions and stochastic forcing, which is modeled as Gaussian white
noise. These moment equations exploit the gPC approach to describe the propagation of
a combination of uncertainties in model parameters, initial conditions and forcing terms.
Sampling the uncertain parameters according to the gPC approach, and integrating via
quadrature, the distribution for the state vector can be obtained. Similarly, for a fixed
realization of the stochastic forcing process, the gPC approach provides an output distribution
resulting from parametric uncertainty. This approach can be further combined
with moment propagation equations to describe the propagation of the state distribution,
which encapsulates uncertainties in model parameters, initial conditions and forcing
terms. The proposed techniques are illustrated on two benchmark problems to demonstrate
the technique's potential in characterizing the non-Gaussian distribution of the
state vector.
@article{Singh11_DSMC,
Author = {U. Konda, P. Singla, T. Singh, and P. D. Scott},
Journal = {ASME Journal for Dynamic Systems, Measurement and Control},
Month = {March},
Title = {Polynomial Chaos Based Design of Robust Input Shapers},
Volume = {133},
Number = {5},
Year = {2011}
}
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