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

Annalisa Riccardi; Chiara Tardioli; Massimiliano Vasile

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

Annalisa Riccardi, Chiara Tardioli, Massimiliano Vasile

Mechanical And Aerospace Engineering

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

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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.

Original language	English
Title of host publication	Astrodynamics 2015
Subtitle of host publication	Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.
Editors	J. D. Turner, G. G. Wawrzyniak, W. T. Cerven , M. Majji
Place of Publication	San Diego, California
Pages	707-722
Number of pages	16
Publication status	Published - 13 Aug 2015
Event	AAS/AIAA Astrodynamics Specialist Conference 2015 - Colorado, Vail, United States Duration: 9 Aug 2015 → 13 Aug 2015

Publication series

Name	Advances in Astrnautical Sciences
Publisher	American Astronautical Society
Volume	156
ISSN (Print)	0065-3438

Conference

Conference	AAS/AIAA Astrodynamics Specialist Conference 2015
Country/Territory	United States
City	Vail
Period	9/08/15 → 13/08/15

Keywords

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

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Riccardi-etal-AAS-2015-Uncertainty-propagation-in-orbital-mechanics-based-on-Tchebycheff-polynomial-algebraAccepted author manuscript, 13.2 MB

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)..

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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title = "An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra",

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.",

keywords = "algebra, uncertainty analysis, mechanics, astrophysics, approximation accuracy, uniform convergence, uncertainty propagation, series expansion, polynomial algebra, orbital mechanics, non-intrusive, model uncertainties",

author = "Annalisa Riccardi and Chiara Tardioli and Massimiliano Vasile",

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 {\textcopyright} 2016 by American Astronautical Society Publications Office, P.O. Box 28130, San Diego, CA 92198, U.S.A.; Web Site: http://www.univelt.com; AAS/AIAA Astrodynamics Specialist Conference 2015 ; Conference date: 09-08-2015 Through 13-08-2015",

year = "2015",

month = aug,

day = "13",

language = "English",

isbn = "9780877036296",

series = "Advances in Astrnautical Sciences",

publisher = "American Astronautical Society",

pages = "707--722",

editor = "Turner, \{J. D.\} and Wawrzyniak, \{G. G.\} and \{Cerven \}, \{W. T.\} and M. Majji",

booktitle = "Astrodynamics 2015",

}

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 proceeding › Conference contribution book

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AU - Riccardi, Annalisa

AU - Tardioli, Chiara

AU - Vasile, Massimiliano

N1 - 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 © 2016 by American Astronautical Society Publications Office, P.O. Box 28130, San Diego, CA 92198, U.S.A.; Web Site: http://www.univelt.com

PY - 2015/8/13

Y1 - 2015/8/13

N2 - 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.

AB - 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.

KW - algebra

KW - uncertainty analysis

KW - mechanics

KW - astrophysics

KW - approximation accuracy

KW - uniform convergence

KW - uncertainty propagation

KW - series expansion

KW - polynomial algebra

KW - orbital mechanics

KW - non-intrusive

KW - model uncertainties

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UR - http://www.univelt.com/book=5315

M3 - Conference contribution book

SN - 9780877036296

T3 - Advances in Astrnautical Sciences

SP - 707

EP - 722

BT - Astrodynamics 2015

A2 - Turner, J. D.

A2 - Wawrzyniak, G. G.

A2 - Cerven , W. T.

A2 - Majji, M.

CY - San Diego, California

T2 - AAS/AIAA Astrodynamics Specialist Conference 2015

Y2 - 9 August 2015 through 13 August 2015

ER -

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).

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

Abstract

Publication series

Conference

Keywords

Access to Document

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Marie Curie ITN (Stardust)

Cite this

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

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

Marie Curie ITN (Stardust)

Cite this