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Optimal uncertainty quantification with model uncertainty and legacy data

Kamga, P.-H. T. and Li, B. and McKerns, M. and Nguyen, L. H. and Ortiz, M. and 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. ISSN 0022-5096.

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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:Article
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URLURL TypeDescription
Ortiz, M.0000-0001-5877-4824
Owhadi, H.0000-0002-5677-1600
Additional Information:© 2014 Elsevier Ltd. Received 19 July 2013, Revised 1 July 2014, Accepted 17 July 2014, Available online 2 August 2014. The authors gratefully acknowledge the support of the Department of Energy National Nuclear Security Administration under Award Number DE-FC52-08NA28613 through Caltech׳s ASC/PSAAP Center for the Predictive Modeling and Simulation of High Energy Density Dynamic Response of Materials.
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Subject Keywords:Hypervelocity impact; Uncertainty quantification; Optimal transportation; Meshfree interpolation; Particle erosion
Record Number:CaltechAUTHORS:20141201-081327318
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Official Citation:P.-H.T. Kamga, B. Li, M. McKerns, L.H. Nguyen, M. Ortiz, H. Owhadi, T.J. Sullivan, Optimal uncertainty quantification with model uncertainty and legacy data, Journal of the Mechanics and Physics of Solids, Volume 72, 1 December 2014, Pages 1-19, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:52194
Deposited By: Ruth Sustaita
Deposited On:01 Dec 2014 18:17
Last Modified:24 Feb 2020 10:30

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