Special section: Methods for Uncertainty Characterizations in Existing Models Through Uncertainly Quantification or Calibration

Improving Identifiability in Model Calibration Using Multiple Responses

[+] Author and Article Information
Paul D. Arendt

 Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road Room B214, Evanston, IL 60208paularendt2012@u.northwestern.edu

Daniel W. Apley

 Department of Industrial Engineering and Management Sciences, Northwestern University, 2145 Sheridan Road Room C150, Evanston, IL 60208apley@northwestern.edu

Wei Chen1

 Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road Room A216, Evanston, IL 60208weichen@northwestern.edu

David Lamb, David Gorsich

 U.S. Army Tank-Automotive Research Development and Engineering Center, 6501 E. Eleven Mile Road, Warren, MI 48397


Corresponding author.

J. Mech. Des 134(10), 100909 (Sep 28, 2012) (9 pages) doi:10.1115/1.4007573 History: Received August 27, 2011; Revised July 03, 2012; Published September 21, 2012; Online September 28, 2012

In physics-based engineering modeling, the two primary sources of model uncertainty, which account for the differences between computer models and physical experiments, are parameter uncertainty and model discrepancy. Distinguishing the effects of the two sources of uncertainty can be challenging. For situations in which identifiability cannot be achieved using only a single response, we propose to improve identifiability by using multiple responses that share a mutual dependence on a common set of calibration parameters. To that end, we extend the single response modular Bayesian approach for calculating posterior distributions of the calibration parameters and the discrepancy function to multiple responses. Using an engineering example, we demonstrate that including multiple responses can improve identifiability (as measured by posterior standard deviations) by an amount that ranges from minimal to substantial, depending on the characteristics of the specific responses that are combined.

Copyright © 2012 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 2

Posterior distributions of the discrepancy function and the calibration parameter using a single response for (a) y1 , (b) y2 , (c) y3 , and (d) y4

Grahic Jump Location
Figure 3

Posterior distributions of the discrepancy functions and the calibration parameter using multiple responses for (a) y1 and y2 , (b) y2 and y3 , and (c) y3 and y4

Grahic Jump Location
Figure 1

Schematic showing the MRGP model’s covariance function represented by spatial correlation and nonspatial covariance for a fixed θ




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