IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v14y2021i20p6715-d657541.html
   My bibliography  Save this article

High-Order Deterministic Sensitivity Analysis and Uncertainty Quantification: Review and New Developments

Author

Listed:
  • Dan Gabriel Cacuci

    (Center for Nuclear Science and Energy, Department of Mechanical Engineering, University of South Carolina, Columbia, SC 29208, USA)

Abstract

This work reviews the state-of-the-art methodologies for the deterministic sensitivity analysis of nonlinear systems and deterministic quantification of uncertainties induced in model responses by uncertainties in the model parameters. The need for computing high-order sensitivities is underscored by presenting an analytically solvable model of neutron scattering in a hydrogenous medium, for which all of the response’s relative sensitivities have the same absolute value of unity. It is shown that the wider the distribution of model parameters, the higher the order of sensitivities needed to achieve a desired level of accuracy in representing the response and in computing the response’s expectation, variance, skewness and kurtosis. This work also presents new mathematical expressions that extend to the sixth-order of the current state-of-the-art fourth-order formulas for computing fourth-order correlations among computed model response and model parameters. Another novelty presented in this work is the mathematical framework of the 3rd-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (3rd-CASAM-N), which enables the most efficient computation of the exact expressions of the 1st-, 2nd- and 3rd-order functional derivatives (“sensitivities”) of a model’s response to the underlying model parameters, including imprecisely known initial, boundary and/or interface conditions. The 2nd- and 3rd-level adjoint functions are computed using the same forward and adjoint computer solvers as used for solving the original forward and adjoint systems. Comparisons between the CPU times are also presented for an OECD/NEA reactor physics benchmark, highlighting the fact that finite-difference schemes would not only provide approximate values for the respective sensitivities (in contradistinction to the 3rd-CASAM-N, which provides exact expressions for the sensitivities) but would simply be unfeasible for computing sensitivities of an order higher than first-order. Ongoing work will generalize the 3rd-CASAM-N to a higher order while aiming to overcome the curse of dimensionality.

Suggested Citation

  • Dan Gabriel Cacuci, 2021. "High-Order Deterministic Sensitivity Analysis and Uncertainty Quantification: Review and New Developments," Energies, MDPI, vol. 14(20), pages 1-53, October.
  • Handle: RePEc:gam:jeners:v:14:y:2021:i:20:p:6715-:d:657541
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/14/20/6715/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/1996-1073/14/20/6715/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities o," Energies, MDPI, vol. 13(7), pages 1-37, April.
    2. Dan Gabriel Cacuci, 2019. "Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantificat," Energies, MDPI, vol. 12(21), pages 1-34, November.
    3. Ruixian Fang & Dan Gabriel Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters," Energies, MDPI, vol. 13(6), pages 1-49, March.
    4. Ruixian Fang & Dan G. Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involvin," Energies, MDPI, vol. 13(10), pages 1-50, May.
    5. Dan Gabriel Cacuci, 2021. "Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework," Energies, MDPI, vol. 14(11), pages 1-45, June.
    6. D. G. Cacuci & R. Fang & J. A. Favorite & M. C. Badea & F. Di Rocco, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: III. Effects of Imprecisely Known Microscopic Fission Cr," Energies, MDPI, vol. 12(21), pages 1-67, October.
    7. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Ca," Energies, MDPI, vol. 12(21), pages 1-43, November.
    8. Ruixian Fang & Dan Gabriel Cacuci, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: II. Effects of Imprecisely Known Microscopic Scattering ," Energies, MDPI, vol. 12(21), pages 1-33, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Przemysław Stanisz & Mikołaj Oettingen & Jerzy Cetnar, 2022. "Development of a Trajectory Period Folding Method for Burnup Calculations," Energies, MDPI, vol. 15(6), pages 1-15, March.
    2. Dan Gabriel Cacuci, 2022. "Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems," Energies, MDPI, vol. 15(18), pages 1-44, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dan Gabriel Cacuci, 2022. "Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems," Energies, MDPI, vol. 15(17), pages 1-7, September.
    2. Dan Gabriel Cacuci, 2022. "Advances in High-Order Sensitivity Analysis for Uncertainty Quantification and Reduction in Nuclear Energy Systems," Energies, MDPI, vol. 15(17), pages 1-6, September.
    3. Dan Gabriel Cacuci, 2022. "Overview of Arbitrarily High-Order Adjoint Sensitivity and Uncertainty Quantification Methodology for Large-Scale Systems," Energies, MDPI, vol. 15(18), pages 1-44, September.
    4. Dan Gabriel Cacuci, 2021. "The n th -Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (n th -CASAM-L): I. Mathematical Framework," Energies, MDPI, vol. 14(24), pages 1-42, December.
    5. Dan Gabriel Cacuci, 2021. "On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions," Energies, MDPI, vol. 14(19), pages 1-38, October.
    6. Dan Gabriel Cacuci, 2021. "Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework," Energies, MDPI, vol. 14(11), pages 1-45, June.
    7. Ruixian Fang & Dan G. Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involvin," Energies, MDPI, vol. 13(10), pages 1-50, May.
    8. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities o," Energies, MDPI, vol. 13(7), pages 1-37, April.
    9. Andrew G. Buchan & Dan G. Cacuci & Steven Dargaville & Christopher C. Pain, 2022. "Optimised Adjoint Sensitivity Analysis Using Adjoint Guided Mesh Adaptivity Applied to Neutron Detector Response Calculations," Energies, MDPI, vol. 15(14), pages 1-11, July.
    10. Ruixian Fang & Dan Gabriel Cacuci, 2020. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters," Energies, MDPI, vol. 13(6), pages 1-49, March.
    11. Dan Gabriel Cacuci, 2019. "Towards Overcoming the Curse of Dimensionality: The Third-Order Adjoint Method for Sensitivity Analysis of Response-Coupled Linear Forward/Adjoint Systems, with Applications to Uncertainty Quantificat," Energies, MDPI, vol. 12(21), pages 1-34, November.
    12. Dan G. Cacuci & Ruixian Fang & Jeffrey A. Favorite, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: I. Effects of Imprecisely Known Microscopic Total and Ca," Energies, MDPI, vol. 12(21), pages 1-43, November.
    13. Ruixian Fang & Dan Gabriel Cacuci, 2019. "Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: II. Effects of Imprecisely Known Microscopic Scattering ," Energies, MDPI, vol. 12(21), pages 1-33, October.
    14. Jerzy Cetnar & Przemysław Stanisz & Mikołaj Oettingen, 2021. "Linear Chain Method for Numerical Modelling of Burnup Systems," Energies, MDPI, vol. 14(6), pages 1-19, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:14:y:2021:i:20:p:6715-:d:657541. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.