An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra

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

Abstract

The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra.
Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost.
LanguageEnglish
Title of host publicationAstrodynamics 2015
Subtitle of host publicationProceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.
EditorsJ. D. Turner, G. G. Wawrzyniak, W. T. Cerven , M. Majji
Place of PublicationSan Diego, California
Pages707-722
Number of pages16
Publication statusPublished - 13 Aug 2015
EventAAS/AIAA Astrodynamics Specialist Conference 2015 - Colorado, Vail, United States
Duration: 9 Aug 201513 Aug 2015

Publication series

NameAdvances in Astrnautical Sciences
PublisherAmerican Astronautical Society
Volume156
ISSN (Print)0065-3438

Conference

ConferenceAAS/AIAA Astrodynamics Specialist Conference 2015
CountryUnited States
CityVail
Period9/08/1513/08/15

Fingerprint

Algebra
Mechanics
Polynomials
Costs
Uncertainty

Keywords

  • algebra
  • uncertainty analysis
  • mechanics
  • astrophysics
  • approximation accuracy
  • uniform convergence
  • uncertainty propagation
  • series expansion
  • polynomial algebra
  • orbital mechanics
  • non-intrusive
  • model uncertainties

Cite this

Riccardi, A., Tardioli, C., & Vasile, M. (2015). An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. In J. D. Turner, G. G. Wawrzyniak, W. T. Cerven , & M. Majji (Eds.), Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A. (pp. 707-722). (Advances in Astrnautical Sciences; Vol. 156). San Diego, California.
Riccardi, Annalisa ; Tardioli, Chiara ; Vasile, Massimiliano. / An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. editor / J. D. Turner ; G. G. Wawrzyniak ; W. T. Cerven ; M. Majji. San Diego, California, 2015. pp. 707-722 (Advances in Astrnautical Sciences).
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abstract = "The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra. Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost.",
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note = "This paper was originally presented at the AAS/AIAA Astrodynamics Specialist Conference held August 9-13, 2015, Vail, Colorado, U.S.A., and was originally published in the American Astronautical Society (AAS) publication Astrodynamics 2015, edited by Manoranjan Majji, James D. Turner, Geoff G. Wawrzyniak and William Todd Cerven, American Astronautical Society (AAS) Advances in the Astronautical Sciences, Volume 156, 2016, pp. 4205-4220 (Copyright {\circledC} 2016 by American Astronautical Society Publications Office, P.O. Box 28130, San Diego, CA 92198, U.S.A.; Web Site: http://www.univelt.com",
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Riccardi, A, Tardioli, C & Vasile, M 2015, An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. in JD Turner, GG Wawrzyniak, WT Cerven & M Majji (eds), Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. Advances in Astrnautical Sciences, vol. 156, San Diego, California, pp. 707-722, AAS/AIAA Astrodynamics Specialist Conference 2015, Vail, United States, 9/08/15.

An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. / Riccardi, Annalisa; Tardioli, Chiara; Vasile, Massimiliano.

Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. ed. / J. D. Turner; G. G. Wawrzyniak; W. T. Cerven ; M. Majji. San Diego, California, 2015. p. 707-722 (Advances in Astrnautical Sciences; Vol. 156).

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

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Riccardi A, Tardioli C, Vasile M. An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. In Turner JD, Wawrzyniak GG, Cerven WT, Majji M, editors, Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. San Diego, California. 2015. p. 707-722. (Advances in Astrnautical Sciences).