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Optimal uncertainty quantification with model uncertainty and legacy data
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Kamga, P-H. T., Li, B., McKerns, M., Nguyen, L. H., Ortiz, M., Owhadi, H. and Sullivan, T. J. (2014) Optimal uncertainty quantification with model uncertainty and legacy data. Journal of the Mechanics and Physics of Solids, 72 . pp. 1-19. doi:10.1016/j.jmps.2014.07.007
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Official URL: http://dx.doi.org/10.1016/j.jmps.2014.07.007
Abstract
We present an optimal uncertainty quantification (OUQ) protocol for systems that are characterized by an existing physics-based model and for which only legacy data is available, i.e., no additional experimental testing of the system is possible. Specifically, the OUQ strategy developed in this work consists of using the legacy data to establish, in a probabilistic sense, the level of error of the model, or modeling error, and to subsequently use the validated model as a basis for the determination of probabilities of outcomes. The quantification of modeling uncertainty specifically establishes, to a specified confidence, the probability that the actual response of the system lies within a certain distance of the model. Once the extent of model uncertainty has been established in this manner, the model can be conveniently used to stand in for the actual or empirical response of the system in order to compute probabilities of outcomes. To this end, we resort to the OUQ reduction theorem of Owhadi et al. (2013) in order to reduce the computation of optimal upper and lower bounds on probabilities of outcomes to a finite-dimensional optimization problem. We illustrate the resulting UQ protocol by means of an application concerned with the response to hypervelocity impact of 6061-T6 Aluminum plates by Nylon 6/6 impactors at impact velocities in the range of 5–7 km/s. The ability of the legacy OUQ protocol to process diverse information on the system and its ability to supply rigorous bounds on system performance under realistic—and less than ideal—scenarios demonstrated by the hypervelocity impact application is remarkable.
| Item Type: | Journal Article | ||||||
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| Divisions: | Faculty of Science > Engineering Faculty of Science > Mathematics |
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| Journal or Publication Title: | Journal of the Mechanics and Physics of Solids | ||||||
| Publisher: | Pergamon-Elsevier Science Ltd. | ||||||
| ISSN: | 0022-5096 | ||||||
| Official Date: | 1 December 2014 | ||||||
| Dates: |
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| Volume: | 72 | ||||||
| Page Range: | pp. 1-19 | ||||||
| DOI: | 10.1016/j.jmps.2014.07.007 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
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