A generalized Bayesian approach to model calibration
In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian m...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2020
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| Online Access: | https://hdl.handle.net/1721.1/128133 |
| _version_ | 1811073417376432128 |
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| author | Tohme, Tony. Vanslette, Kevin Youcef-Toumi, Kamal |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Tohme, Tony. Vanslette, Kevin Youcef-Toumi, Kamal |
| author_sort | Tohme, Tony. |
| collection | MIT |
| description | In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user's definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that “fail” in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase. ©2020 Elsevier Ltd |
| first_indexed | 2024-09-23T09:32:44Z |
| format | Article |
| id | mit-1721.1/128133 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:32:44Z |
| publishDate | 2020 |
| publisher | Elsevier BV |
| record_format | dspace |
| spelling | mit-1721.1/1281332022-09-26T12:10:07Z A generalized Bayesian approach to model calibration Tohme, Tony. Vanslette, Kevin Youcef-Toumi, Kamal Massachusetts Institute of Technology. Department of Mechanical Engineering In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user's definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that “fail” in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase. ©2020 Elsevier Ltd 2020-10-19T22:35:43Z 2020-10-19T22:35:43Z 2020-07 2020-07 2020-08-14T14:39:56Z Article http://purl.org/eprint/type/JournalArticle 1879-0836 https://hdl.handle.net/1721.1/128133 Tohme, Tony et al., "A generalized Bayesian approach to model calibration." Reliability Engineering & System Safety 204 (December 2020): 107141 doi. 10.1016/j.ress.2020.107141 ©2020 Authors en https://dx.doi.org/10.1016/j.ress.2020.107141 Reliability Engineering and System Safety Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier BV arXiv |
| spellingShingle | Tohme, Tony. Vanslette, Kevin Youcef-Toumi, Kamal A generalized Bayesian approach to model calibration |
| title | A generalized Bayesian approach to model calibration |
| title_full | A generalized Bayesian approach to model calibration |
| title_fullStr | A generalized Bayesian approach to model calibration |
| title_full_unstemmed | A generalized Bayesian approach to model calibration |
| title_short | A generalized Bayesian approach to model calibration |
| title_sort | generalized bayesian approach to model calibration |
| url | https://hdl.handle.net/1721.1/128133 |
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