Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics

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

1 Citation (Scopus)
67 Downloads (Pure)

Abstract

The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.

Original 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.
EditorsManoranjan Majji, James D. Turner, Geoff G. Wawrzyniak, William Todd Cerven
Place of PublicationSan Diego, California
Pages3979-3992
Number of pages14
Publication statusPublished - 9 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

orbital mechanics
mechanics
Mechanics
polynomials
Polynomials
propagation
expansion
space debris
Orbits
chaotic dynamics
kriging
orbits
Space debris
Chaos theory
embedding
Algebra
chaos
algebra
grids
costs

Keywords

  • space debris
  • orbit analysis
  • polynomial chaos expansion
  • sparse grids
  • uncertainty
  • non-intrusive
  • kriging model
  • Tchebycheff polynomials

Cite this

Tardioli, C., Kubicek, M., Vasile, M., Minisci, E., & Riccardi, A. (2015). Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics. In M. Majji, J. D. Turner, G. G. Wawrzyniak, & W. T. Cerven (Eds.), Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A. (pp. 3979-3992). [AAS 15-545] (Advances in Astrnautical Sciences; Vol. 156). San Diego, California.
Tardioli, Chiara ; Kubicek, Martin ; Vasile, Massimiliano ; Minisci, Edmondo ; Riccardi, Annalisa. / Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics. Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. editor / Manoranjan Majji ; James D. Turner ; Geoff G. Wawrzyniak ; William Todd Cerven. San Diego, California, 2015. pp. 3979-3992 (Advances in Astrnautical Sciences).
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abstract = "The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.",
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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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Tardioli, C, Kubicek, M, Vasile, M, Minisci, E & Riccardi, A 2015, Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics. in M Majji, JD Turner, GG Wawrzyniak & WT Cerven (eds), Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.., AAS 15-545, Advances in Astrnautical Sciences, vol. 156, San Diego, California, pp. 3979-3992, AAS/AIAA Astrodynamics Specialist Conference 2015, Vail, United States, 9/08/15.

Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics. / Tardioli, Chiara; Kubicek, Martin; Vasile, Massimiliano; Minisci, Edmondo; Riccardi, Annalisa.

Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.. ed. / Manoranjan Majji; James D. Turner; Geoff G. Wawrzyniak; William Todd Cerven. San Diego, California, 2015. p. 3979-3992 AAS 15-545 (Advances in Astrnautical Sciences; Vol. 156).

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

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T1 - Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics

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N2 - The paper presents four different non-intrusive approaches to the propagation of uncertainty in orbital dynamics with particular application to space debris orbit analysis. Intrusive approaches are generally understood as those methods that require a modification of the original problem by introducing a new algebra or by directly embedding high-order polynomial expansions of the uncertain quantities in the governing equations. Non-intrusive approaches are instead based on a polynomial representations built on sparse samples of the system response to the uncertain quantities. The paper will present a standard Polynomial Chaos Expansion, an Uncertain Quantification-High Dimensional Model Representation, a Generalised Kriging model and an expansion with Tchebycheff polynomials on sparse grids. The work will assess the computational cost and the suitability of these methods to propagate different type of orbits.

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KW - Tchebycheff polynomials

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Tardioli C, Kubicek M, Vasile M, Minisci E, Riccardi A. Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics. In Majji M, Turner JD, Wawrzyniak GG, Cerven WT, 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. 3979-3992. AAS 15-545. (Advances in Astrnautical Sciences).