### 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 |

Pages | 349-354 |

Number of pages | 6 |

State | Published - Oct 15 2010 |

Event | 2010 American Control Conference, ACC 2010 - Baltimore, MD, United States Duration: Jun 30 2010 → Jul 2 2010 |

### Other

Other | 2010 American Control Conference, ACC 2010 |
---|---|

Country | United States |

City | Baltimore, MD |

Period | 6/30/10 → 7/2/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering

### Cite this

*Proceedings of the 2010 American Control Conference, ACC 2010*(pp. 349-354). [5530816]

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*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.

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

TY - GEN

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

AU - Terejanu, Gabriel

AU - Singla, Puneet

AU - Singh, Tarunraj

AU - Scott, Peter D.

PY - 2010/10/15

Y1 - 2010/10/15

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.

UR - http://www.scopus.com/inward/record.url?scp=77957778549&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77957778549&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781424474264

SP - 349

EP - 354

BT - Proceedings of the 2010 American Control Conference, ACC 2010

ER -