Uncertainty propagation in dynamic systems using polynomial chaos based multiresolution approach

Cheng Jin, Puneet Singla, Tarunraj Singh

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A multiresolution approach is presented to study the uncertainty propagation problem in dynamic systems. The proposed approach is an extension of the gener- alized polynomial chaos and involves a separation of random variables from deter- ministic ones in the solution algorithm for a stochastic differential equation. The random variables are expanded in various local polynomial expansions which are further blended together to obtain a global approximation for the random state variables. These polynomials are associated with the assumed probability density functions for the input variables. Galerkin projection is used to generate a system of deterministic differential equations for the expansion coeffIcients. We first present this method to linear systems with parametric uncertainties, and subsequently we generalize it to nonlinear systems with parametric and initial condition uncertain- ties. The effectiveness of the proposed method is demonstrated by considering different numerical examples.

Original languageEnglish (US)
Title of host publicationAIAA Guidance, Navigation, and Control Conference 2012
PublisherAmerican Institute of Aeronautics and Astronautics Inc.
ISBN (Print)9781600869389
DOIs
StatePublished - Jan 1 2012
EventAIAA Guidance, Navigation, and Control Conference 2012 - Minneapolis, MN, United States
Duration: Aug 13 2012Aug 16 2012

Publication series

NameAIAA Guidance, Navigation, and Control Conference 2012

Other

OtherAIAA Guidance, Navigation, and Control Conference 2012
CountryUnited States
CityMinneapolis, MN
Period8/13/128/16/12

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Uncertainty propagation in dynamic systems using polynomial chaos based multiresolution approach'. Together they form a unique fingerprint.

  • Cite this

    Jin, C., Singla, P., & Singh, T. (2012). Uncertainty propagation in dynamic systems using polynomial chaos based multiresolution approach. In AIAA Guidance, Navigation, and Control Conference 2012 (AIAA Guidance, Navigation, and Control Conference 2012). American Institute of Aeronautics and Astronautics Inc.. https://doi.org/10.2514/6.2012-4933