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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
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    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.
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