Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory

Gabriel Terejanu, Puneet Singla, Tarunraj Singh, Peter D. Scott

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

6 Citations (Scopus)

Abstract

The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probability distributions, the intuition is to quantify the uncertainty in the response using Polynomial Chaos expansion and discard all the information provided about the randomness of the output and extract only the bounds of its compact support. To solve for the bounding range of polynomials, we transform the Polynomial Chaos expansion in the Bernstein form, and use the range enclosure property of Bernstein polynomials to find the minimum and maximum value of the response. This procedure is used to propagate Dempster-Shafer structures on closed intervals through non-linear functions and it is applied on an algebraic challenge problem.

Original languageEnglish (US)
Title of host publicationProceedings of the 2010 American Control Conference, ACC 2010
Pages349-354
Number of pages6
StatePublished - Oct 15 2010
Event2010 American Control Conference, ACC 2010 - Baltimore, MD, United States
Duration: Jun 30 2010Jul 2 2010

Other

Other2010 American Control Conference, ACC 2010
CountryUnited States
CityBaltimore, MD
Period6/30/107/2/10

Fingerprint

Chaos theory
Polynomials
Enclosures
Random variables
Probability distributions
Uncertainty

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Cite this

Terejanu, G., Singla, P., Singh, T., & Scott, P. D. (2010). Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. In Proceedings of the 2010 American Control Conference, ACC 2010 (pp. 349-354). [5530816]
Terejanu, Gabriel ; Singla, Puneet ; Singh, Tarunraj ; Scott, Peter D. / Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. Proceedings of the 2010 American Control Conference, ACC 2010. 2010. pp. 349-354
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Terejanu, G, Singla, P, Singh, T & Scott, PD 2010, Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. in Proceedings of the 2010 American Control Conference, ACC 2010., 5530816, pp. 349-354, 2010 American Control Conference, ACC 2010, Baltimore, MD, United States, 6/30/10.

Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. / Terejanu, Gabriel; Singla, Puneet; Singh, Tarunraj; Scott, Peter D.

Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 349-354 5530816.

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

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Terejanu G, Singla P, Singh T, Scott PD. Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. In Proceedings of the 2010 American Control Conference, ACC 2010. 2010. p. 349-354. 5530816