Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study
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...
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| Format: | Article |
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MDPI AG
2022-11-01
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| Series: | Stats |
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| Online Access: | https://www.mdpi.com/2571-905X/5/4/71 |
| _version_ | 1797455166272700416 |
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| author | Edward Boone Jan Hannig Ryad Ghanam Sujit Ghosh Fabrizio Ruggeri Serge Prudhomme |
| author_facet | Edward Boone Jan Hannig Ryad Ghanam Sujit Ghosh Fabrizio Ruggeri Serge Prudhomme |
| author_sort | Edward Boone |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T15:50:30Z |
| format | Article |
| id | doaj.art-52bc7b11065c4525918f64309ef3c7a9 |
| institution | Directory Open Access Journal |
| issn | 2571-905X |
| language | English |
| last_indexed | 2024-03-09T15:50:30Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Stats |
| spelling | doaj.art-52bc7b11065c4525918f64309ef3c7a92023-11-24T18:04:45ZengMDPI AGStats2571-905X2022-11-01541195121110.3390/stats5040071Model Validation of a Single Degree-of-Freedom Oscillator: A Case StudyEdward Boone0Jan Hannig1Ryad Ghanam2Sujit Ghosh3Fabrizio Ruggeri4Serge Prudhomme5Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USADepartment of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599-3260, USADepartment of Liberal Arts & Sciences, Virginia Commonwealth University in Qatar, Doha P.O. Box 8095, QatarDepartment of Statistics, NC State University, Raleigh, NC 27695-8203, USAInstitute of Applied Mathematics and Information Technology, CNR-IMATI, Via Alfonso Corti 12, 20133 Milano, ItalyDépartement de Mathématiques et de Génie Industriel, Polytechnique Montréal, Montréal, QC H3C 3A7, CanadaIn 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.https://www.mdpi.com/2571-905X/5/4/71Bayesian updatingsingle degree-of-freedom oscillatorvalidationmodeling error |
| spellingShingle | Edward Boone Jan Hannig Ryad Ghanam Sujit Ghosh Fabrizio Ruggeri Serge Prudhomme Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study Stats Bayesian updating single degree-of-freedom oscillator validation modeling error |
| title | Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study |
| title_full | Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study |
| title_fullStr | Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study |
| title_full_unstemmed | Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study |
| title_short | Model Validation of a Single Degree-of-Freedom Oscillator: A Case Study |
| title_sort | model validation of a single degree of freedom oscillator a case study |
| topic | Bayesian updating single degree-of-freedom oscillator validation modeling error |
| url | https://www.mdpi.com/2571-905X/5/4/71 |
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