IDEAS home Printed from https://ideas.repec.org/a/gam/jstats/v5y2022i4p71-1211d977388.html
   My bibliography  Save this article

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. 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.
    2. 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.
    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. Jakub Bijak & Jason D. 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.
    4. 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.
    5. 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).
    6. 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.
    7. 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.
    8. 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.
    9. Drignei, Dorin, 2011. "A general statistical model for computer experiments with time series output," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 460-467.
    10. Yuan, Jun & Nian, Victor & Su, Bin & Meng, Qun, 2017. "A simultaneous calibration and parameter ranking method for building energy models," Applied Energy, Elsevier, vol. 206(C), pages 657-666.
    11. Gross, Eitan, 2015. "Effect of environmental stress on regulation of gene expression in the yeast," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 430(C), pages 224-235.
    12. Hwang, Youngdeok & Kim, Hang J. & Chang, Won & Yeo, Kyongmin & Kim, Yongku, 2019. "Bayesian pollution source identification via an inverse physics model," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 76-92.
    13. Choi, Wonjun & Menberg, Kathrin & Kikumoto, Hideki & Heo, Yeonsook & Choudhary, Ruchi & Ooka, Ryozo, 2018. "Bayesian inference of structural error in inverse models of thermal response tests," Applied Energy, Elsevier, vol. 228(C), pages 1473-1485.
    14. Yuan, Jun & Ng, Szu Hui, 2013. "A sequential approach for stochastic computer model calibration and prediction," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 273-286.
    15. Overstall, Antony M. & Woods, David C. & Martin, Kieran J., 2019. "Bayesian prediction for physical models with application to the optimization of the synthesis of pharmaceutical products using chemical kinetics," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 126-142.
    16. Abokersh, Mohamed Hany & Vallès, Manel & Cabeza, Luisa F. & Boer, Dieter, 2020. "A framework for the optimal integration of solar assisted district heating in different urban sized communities: A robust machine learning approach incorporating global sensitivity analysis," Applied Energy, Elsevier, vol. 267(C).
    17. Campbell, Katherine, 2006. "Statistical calibration of computer simulations," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1358-1363.
    18. Ioannis Andrianakis & Ian R Vernon & Nicky McCreesh & Trevelyan J McKinley & Jeremy E Oakley & Rebecca N Nsubuga & Michael Goldstein & Richard G White, 2015. "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-18, January.
    19. Park, Inseok & Amarchinta, Hemanth K. & Grandhi, Ramana V., 2010. "A Bayesian approach for quantification of model uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 95(7), pages 777-785.
    20. Marc Kennedy & Clive Anderson & Anthony O'Hagan & Mark Lomas & Ian Woodward & John Paul Gosling & Andreas Heinemeyer, 2008. "Quantifying uncertainty in the biospheric carbon flux for England and Wales," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 109-135, January.

    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 (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.