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

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

doi:10.1109/acc.2010.5530816

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

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

Aerospace Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 Scopus citations

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 language	English (US)
Title of host publication	Proceedings of the 2010 American Control Conference, ACC 2010
Publisher	IEEE Computer Society
Pages	349-354
Number of pages	6
ISBN (Print)	9781424474264
DOIs	https://doi.org/10.1109/acc.2010.5530816
State	Published - 2010

Publication series

Name	Proceedings of the 2010 American Control Conference, ACC 2010

All Science Journal Classification (ASJC) codes

Control and Systems Engineering

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10.1109/acc.2010.5530816

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). Article 5530816 (Proceedings of the 2010 American Control Conference, ACC 2010). IEEE Computer Society. https://doi.org/10.1109/acc.2010.5530816

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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.",

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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, Proceedings of the 2010 American Control Conference, ACC 2010, IEEE Computer Society, pp. 349-354. https://doi.org/10.1109/acc.2010.5530816

Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory. / Terejanu, Gabriel; Singla, Puneet; Singh, Tarunraj et al.
Proceedings of the 2010 American Control Conference, ACC 2010. IEEE Computer Society, 2010. p. 349-354 5530816 (Proceedings of the 2010 American Control Conference, ACC 2010).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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T1 - Approximate interval method for epistemic uncertainty propagation using Polynomial Chaos and evidence theory

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AU - Singla, Puneet

AU - Singh, Tarunraj

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N2 - 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.

AB - 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.

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

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