0
Special section: Methods for Uncertainty Characterizations in Existing Models Through Uncertainly Quantification or Calibration

Concurrent Design Optimization and Calibration-Based Validation Using Local Domains Sized by Bootstrapping

[+] Author and Article Information
Dorin Drignei

 Mathematics and Statistics Department, Oakland University, Rochester, MI 48309

Zissimos P. Mourelatos1

 Mechanical Engineering Department, Oakland University, Rochester, MI 48309mourelat@oakland.edu

Vijitashwa Pandey

 Mechanical Engineering Department, Oakland University, Rochester, MI 48309

Michael Kokkolaras

 Mechanical Engineering Department, University of Michigan, Ann Arbor, MI 48109

1

Corresponding author.

J. Mech. Des 134(10), 100910 (Sep 28, 2012) (8 pages) doi:10.1115/1.4007572 History: Received February 25, 2012; Revised July 26, 2012; Published September 21, 2012; Online September 28, 2012

The design optimization process relies often on computational models for analysis or simulation. These models must be validated to quantify the expected accuracy of the obtained design solutions. It can be argued that validation of computational models in the entire design space is neither affordable nor required. In previous work, motivated by the fact that most numerical optimization algorithms generate a sequence of candidate designs, we proposed a new paradigm where design optimization and calibration-based model validation are performed concurrently in a sequence of variable-size local domains that are relatively small compared to the entire design space. A key element of this approach is how to account for variability in test data and model predictions in order to determine the size of the local domains at each stage of the sequential design optimization process. In this article, we discuss two alternative techniques for accomplishing this: parametric and nonparametric bootstrapping. The parametric bootstrapping assumes a Gaussian distribution for the error between test and model data and uses maximum likelihood estimation to calibrate the prediction model. The nonparametric bootstrapping does not rely on the Gaussian assumption providing; therefore, a more general way to size the local domains for applications where distributional assumptions are difficult to verify, or not met at all. If distribution assumptions are met, parametric methods are preferable over nonparametric methods. We use a validation literature benchmark problem to demonstrate the application of the two techniques. Which technique to use depends on whether the Gaussian distribution assumption is appropriate based on available information.

FIGURES IN THIS ARTICLE
<>
Copyright © 2012 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Simulated random numbers

Grahic Jump Location
Figure 2

Schematic of heat conduction problem

Grahic Jump Location
Figure 3

Simulated mixed random numbers

Grahic Jump Location
Figure 4

Test data (dashed-line) and calibrated approximate model data (solid-line) at the initial design point, for parametric (left) and nonparametric methods (right)

Grahic Jump Location
Figure 5

Optimization progress for variable local domain size (parametric bootstrap)

Grahic Jump Location
Figure 6

Optimization progress for variable local domain size (nonparametric bootstrap)

Grahic Jump Location
Figure 7

Test data (dashed-line) and calibrated approximate model data (solid-line) at the final design point, for parametric (left) and nonparametric methods (right)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In