IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i4p71-1211d977388.html

Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study

Author

Listed:
  • Edward Boone

    (Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USA
    These authors contributed equally to this work.)

  • Jan Hannig

    (Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USA
    These authors contributed equally to this work.)

  • Ryad Ghanam

    (Department of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, Doha P.O. Box 8095, Qatar)

  • Sujit Ghosh

    (Department of Statistics, NC State University, Raleigh, NC 27695-8203, USA)

  • Fabrizio Ruggeri

    (Institute of Applied Mathematics and Information Technology, CNR-IMATI, Via Alfonso Corti 12, 20133 Milano, Italy)

  • Serge Prudhomme

    (Département de Mathématiques et de Génie Industriel, Polytechnique Montréal, Montréal, QC H3C 3A7, Canada)

Abstract

In this paper, we investigate a validation process in order to assess the predictive capabilities of a single degree-of-freedom oscillator. Model validation is understood here as the process of determining the accuracy with which a model can predict observed physical events or important features of the physical system. Therefore, assessment of the model needs to be performed with respect to the conditions under which the model is used in actual simulations of the system and to specific quantities of interest used for decision-making. Model validation also supposes that the model be trained and tested against experimental data. In this work, virtual data are produced from a non-linear single degree-of-freedom oscillator, the so-called oracle model, which is supposed to provide an accurate representation of reality. The mathematical model to be validated is derived from the oracle model by simply neglecting the non-linear term. The model parameters are identified via Bayesian updating. This calibration process also includes a modeling error due to model misspecification and modeled as a normal probability density function with zero mean and standard deviation to be calibrated.

Suggested Citation

  • Edward Boone & Jan Hannig & Ryad Ghanam & Sujit Ghosh & Fabrizio Ruggeri & Serge Prudhomme, 2022. "Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study," Stats, MDPI, vol. 5(4), pages 1-17, November.
    • Handle: RePEc:gam:jstats:v:5:y:2022:i:4:p:71-1211:d:977388
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2571-905X/5/4/71/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2571-905X/5/4/71/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    2. Yongjun Shen & Minghui Fan & Xianghong Li & Shaopu Yang & Haijun Xing, 2015. "Dynamical Analysis on Single Degree-of-Freedom Semiactive Control System by Using Fractional-Order Derivative," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, May.
    Full references (including those not matched with items on IDEAS)

    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. Vanslette, Kevin & Tohme, Tony & Youcef-Toumi, Kamal, 2020. "A general model validation and testing tool," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    2. Matthias Katzfuss & Joseph Guinness & Wenlong Gong & Daniel Zilber, 2020. "Vecchia Approximations of Gaussian-Process Predictions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(3), pages 383-414, September.
    3. McDonald, Cory P. & Urban, Noel R., 2010. "Using a model selection criterion to identify appropriate complexity in aquatic biogeochemical models," Ecological Modelling, Elsevier, vol. 221(3), pages 428-432.
    4. Jakub Bijak & Jason Hilton & Eric Silverman & Viet Dung Cao, 2013. "Reforging the Wedding Ring," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 29(27), pages 729-766.
    5. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    6. Hao Wu & Michael Browne, 2015. "Random Model Discrepancy: Interpretations and Technicalities (A Rejoinder)," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 619-624, September.
    7. Gholami, M. & Torreggiani, D. & Tassinari, P. & Barbaresi, A., 2021. "Narrowing uncertainties in forecasting urban building energy demand through an optimal archetyping method," Renewable and Sustainable Energy Reviews, Elsevier, vol. 148(C).
    8. Theresa Reiker & Monica Golumbeanu & Andrew Shattock & Lydia Burgert & Thomas A. Smith & Sarah Filippi & Ewan Cameron & Melissa A. Penny, 2021. "Emulator-based Bayesian optimization for efficient multi-objective calibration of an individual-based model of malaria," Nature Communications, Nature, vol. 12(1), pages 1-11, December.
    9. Li, Luyi & Lu, Zhenzhou, 2018. "A new method for model validation with multivariate output," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 579-592.
    10. Jakub Bijak & Eric Silverman, 2013. "Probability and Social Science. Methodological Relationships between the Two Approaches," Population Studies, Taylor & Francis Journals, vol. 67(1), pages 127-129, March.
    11. Shi, Lei & Lin, Shih-Po, 2016. "A new RBDO method using adaptive response surface and first-order score function for crashworthiness design," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 125-133.
    12. Villez, Kris & Del Giudice, Dario & Neumann, Marc B. & Rieckermann, Jörg, 2020. "Accounting for erroneous model structures in biokinetic process models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    13. Xiaoyu Xiong & Benjamin D. Youngman & Theodoros Economou, 2021. "Data fusion with Gaussian processes for estimation of environmental hazard events," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    14. Evan Baker & Peter Challenor & Matt Eames, 2021. "Future proofing a building design using history matching inspired level‐set techniques," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(2), pages 335-350, March.
    15. Petropoulos, G. & Wooster, M.J. & Carlson, T.N. & Kennedy, M.C. & Scholze, M., 2009. "A global Bayesian sensitivity analysis of the 1d SimSphere soil–vegetation–atmospheric transfer (SVAT) model using Gaussian model emulation," Ecological Modelling, Elsevier, vol. 220(19), pages 2427-2440.
    16. A. E. Ades & A. J. Sutton, 2006. "Multiparameter evidence synthesis in epidemiology and medical decision‐making: current approaches," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(1), pages 5-35, January.
    17. David Breitenmoser & Francesco Cerutti & Gernot Butterweck & Malgorzata Magdalena Kasprzak & Sabine Mayer, 2023. "Emulator-based Bayesian inference on non-proportional scintillation models by compton-edge probing," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    18. Chen, Jianli & Gao, Xinghua & Hu, Yuqing & Zeng, Zhaoyun & Liu, Yanan, 2019. "A meta-model-based optimization approach for fast and reliable calibration of building energy models," Energy, Elsevier, vol. 188(C).
    19. Kwag, Shinyoung & Gupta, Abhinav & Dinh, Nam, 2018. "Probabilistic risk assessment based model validation method using Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 380-393.
    20. Nagel, Joseph B. & Rieckermann, Jörg & Sudret, Bruno, 2020. "Principal component analysis and sparse polynomial chaos expansions for global sensitivity analysis and model calibration: Application to urban drainage simulation," Reliability Engineering and System Safety, Elsevier, vol. 195(C).

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:jstats:v:5:y:2022:i:4:p:71-1211:d:977388. 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 The email address of this maintainer does not seem to be valid anymore. Please ask MDPI Indexing Manager to update the entry or send us the correct address (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.