State uncertainty propagation in the presence of parametric uncertainty and additive white noise

Umamaheswara Konda, Puneet Singla, Tarunraj Singh, Peter D. Scott

Research output: Contribution to journalArticle

9 Scopus citations

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 techniques' potential in characterizing the non-Gaussian distribution of the state vector.

Original languageEnglish (US)
Article number051009
JournalJournal of Dynamic Systems, Measurement and Control, Transactions of the ASME
Volume133
Issue number5
DOIs
StatePublished - Sep 2 2011

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Information Systems
  • Instrumentation
  • Mechanical Engineering
  • Computer Science Applications

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