To use predictive models in engineering design of physical systems, one should first quantify the model uncertainty via model updating techniques employing both simulation and experimental data. While calibration is often used to tune unknown calibration parameters of a computer model, the addition of a discrepancy function has been used to capture model discrepancy due to underlying missing physics, numerical approximations, and other inaccuracies of the computer model that would exist even if all calibration parameters are known. One of the main challenges in model updating is the difficulty in distinguishing between the effects of calibration parameters versus model discrepancy. We illustrate this identifiability problem with several examples, explain the mechanisms behind it, and attempt to shed light on when a system may or may not be identifiable. In some instances, identifiability is achievable under mild assumptions, whereas in other instances, it is virtually impossible. In a companion paper, we demonstrate that using multiple responses, each of which depends on a common set of calibration parameters, can substantially enhance identifiability.
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e-mail: paularendt2012@u.northwestern.edu
e-mail: apley@northwestern.edu
e-mail: weichen@northwestern.edu
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October 2012
Special Section: Methods For Uncertainty Characterizations In Existing Models Through Uncertainly Quantification Or Calibration
Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability
Paul D. Arendt,
e-mail: paularendt2012@u.northwestern.edu
Paul D. Arendt
Department of Mechanical Engineering, Northwestern University
, 2145 Sheridan Road Room B214, Evanston, IL
, 60208
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Daniel W. Apley,
e-mail: apley@northwestern.edu
Daniel W. Apley
Department of Industrial Engineering and Management Sciences, Northwestern University
, 2145 Sheridan Road Room C150, Evanston, IL
, 60208
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Wei Chen
e-mail: weichen@northwestern.edu
Wei Chen
Department of Mechanical Engineering, Northwestern University
, 2145 Sheridan Road Room A216, Evanston, IL
, 60208
Search for other works by this author on:
Paul D. Arendt
Department of Mechanical Engineering, Northwestern University
, 2145 Sheridan Road Room B214, Evanston, IL
, 60208e-mail: paularendt2012@u.northwestern.edu
Daniel W. Apley
Department of Industrial Engineering and Management Sciences, Northwestern University
, 2145 Sheridan Road Room C150, Evanston, IL
, 60208e-mail: apley@northwestern.edu
Wei Chen
Department of Mechanical Engineering, Northwestern University
, 2145 Sheridan Road Room A216, Evanston, IL
, 60208e-mail: weichen@northwestern.edu
J. Mech. Des. Oct 2012, 134(10): 100908 (12 pages)
Published Online: September 28, 2012
Article history
Received:
August 27, 2011
Revised:
July 3, 2012
Published:
September 21, 2012
Online:
September 28, 2012
Citation
Arendt, P. D., Apley, D. W., and Chen, W. (September 28, 2012). "Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability." ASME. J. Mech. Des. October 2012; 134(10): 100908. https://doi.org/10.1115/1.4007390
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