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

Edward Boone, Jan Hannig, Ryad Ghanam, Sujit Ghosh, Fabrizio Ruggeri () and Serge Prudhomme
Additional contact information
Edward Boone: Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USA
Jan Hannig: Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USA
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

Stats, 2022, vol. 5, issue 4, 1-17

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.

Keywords: Bayesian updating; single degree-of-freedom oscillator; validation; modeling error (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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