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On moment estimation from polynomial chaos expansion models

Tom Lefebvre (UGent)
(2021) IEEE CONTROL SYSTEMS LETTERS. 5(5). p.1519-1524
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Abstract
Polynomial Chaos Expansions (PCEs) offer an efficient alternative to assess the statistical properties of a model output taking into account the statistical properties of several uncertain model inputs, particularly, under the restriction of probing the forward model as little as possible. The use of PCE knows a steady increase in recent literature with applications spanning from mere system analysis to robust control design and optimization. The principle idea is to model the output as a series expansion, with the expansion basis depending only on the stochastic variables. The basis is then chosen so that it is better suited to support the uncertainty propagation. Once the expansion coefficients have been identified, accessing the statistical moments benefits the linearity of the expansion and the properties of the moment operator. As a result, the first two statistical moments of the model output can be computed easily using well known analytical expressions. For high-order moments, analytical expressions also exist but are inefficient to evaluate. In this letter we present three strategies to efficiently calculate high-order moments from the expansion model and provide an empirical study of the associated computation time supporting any potential users in making an informed choice.
Keywords
Uncertainty, Computational modeling, Stochastic processes, Mathematical model, Estimation, Standards, Probability density function, Computational methods, numerical algorithms, uncertain systems, UNCERTAINTY QUANTIFICATION, DESIGN OPTIMIZATION, ROBUST OPTIMIZATION, PROPAGATION

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MLA
Lefebvre, Tom. “On Moment Estimation from Polynomial Chaos Expansion Models.” IEEE CONTROL SYSTEMS LETTERS, vol. 5, no. 5, 2021, pp. 1519–24, doi:10.1109/LCSYS.2020.3040851.
APA
Lefebvre, T. (2021). On moment estimation from polynomial chaos expansion models. IEEE CONTROL SYSTEMS LETTERS, 5(5), 1519–1524. https://doi.org/10.1109/LCSYS.2020.3040851
Chicago author-date
Lefebvre, Tom. 2021. “On Moment Estimation from Polynomial Chaos Expansion Models.” IEEE CONTROL SYSTEMS LETTERS 5 (5): 1519–24. https://doi.org/10.1109/LCSYS.2020.3040851.
Chicago author-date (all authors)
Lefebvre, Tom. 2021. “On Moment Estimation from Polynomial Chaos Expansion Models.” IEEE CONTROL SYSTEMS LETTERS 5 (5): 1519–1524. doi:10.1109/LCSYS.2020.3040851.
Vancouver
1.
Lefebvre T. On moment estimation from polynomial chaos expansion models. IEEE CONTROL SYSTEMS LETTERS. 2021;5(5):1519–24.
IEEE
[1]
T. Lefebvre, “On moment estimation from polynomial chaos expansion models,” IEEE CONTROL SYSTEMS LETTERS, vol. 5, no. 5, pp. 1519–1524, 2021.
@article{8685373,
  abstract     = {{Polynomial Chaos Expansions (PCEs) offer an efficient alternative to assess the statistical properties of a model output taking into account the statistical properties of several uncertain model inputs, particularly, under the restriction of probing the forward model as little as possible. The use of PCE knows a steady increase in recent literature with applications spanning from mere system analysis to robust control design and optimization. The principle idea is to model the output as a series expansion, with the expansion basis depending only on the stochastic variables. The basis is then chosen so that it is better suited to support the uncertainty propagation. Once the expansion coefficients have been identified, accessing the statistical moments benefits the linearity of the expansion and the properties of the moment operator. As a result, the first two statistical moments of the model output can be computed easily using well known analytical expressions. For high-order moments, analytical expressions also exist but are inefficient to evaluate. In this letter we present three strategies to efficiently calculate high-order moments from the expansion model and provide an empirical study of the associated computation time supporting any potential users in making an informed choice.}},
  author       = {{Lefebvre, Tom}},
  issn         = {{2475-1456}},
  journal      = {{IEEE CONTROL SYSTEMS LETTERS}},
  keywords     = {{Uncertainty,Computational modeling,Stochastic processes,Mathematical model,Estimation,Standards,Probability density function,Computational methods,numerical algorithms,uncertain systems,UNCERTAINTY QUANTIFICATION,DESIGN OPTIMIZATION,ROBUST OPTIMIZATION,PROPAGATION}},
  language     = {{eng}},
  number       = {{5}},
  pages        = {{1519--1524}},
  title        = {{On moment estimation from polynomial chaos expansion models}},
  url          = {{http://dx.doi.org/10.1109/LCSYS.2020.3040851}},
  volume       = {{5}},
  year         = {{2021}},
}

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