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Research Papers

Maximizing Design Confidence in Sequential Simulation-Based Optimization

[+] Author and Article Information
Jing Li

e-mail: li2@oakland.edu

Zissimos P. Mourelatos

e-mail: mourelat@oakland.edu
Mechanical Engineering Department,
Oakland University,
Rochester, MI 48309

Michael Kokkolaras

Department of Mechanical Engineering
McGill University
Montreal, Quebec H3A oC3
e-mail: michael.kokkolaras@mcgill.ca

Panos Y. Papalambros

e-mail: pyp@umich.edu
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

David J. Gorsich

U.S. Army, TARDEC,
Warren, MI 48397
e-mail: david.j.gorsich.civ@mail.mil

The design space is defined by the bounds of the design optimization variables, while the feasible space is defined by the intersection of all design constraints.

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received June 24, 2012; final manuscript received March 12, 2013; published online June 10, 2013. Assoc. Editor: Timothy W. Simpson.

J. Mech. Des 135(8), 081004 (Jun 10, 2013) (8 pages) Paper No: MD-11-1285; doi: 10.1115/1.4024470 History: Received June 24, 2012; Revised March 12, 2013

Computational simulation models support a rapid design process. Given model approximation and operating conditions uncertainty, designers must have confidence that the designs obtained using simulations will perform as expected. The traditional approach to address this need consists of model validation efforts conducted predominantly prior to the optimization process. We argue that model validation is too daunting of a task to be conducted with meaningful success for design optimization problems associated with high-dimensional space and parameter spaces. In contrast, we propose a methodology for maximizing confidence in designs generated during the simulation-based optimization process. Specifically, we adopt a trust-region-like sequential optimization process and utilize a Bayesian hypothesis testing technique to quantify model confidence, which we maximize by calibrating the simulation model within local domains if and when necessary. This ensures that the design iterates generated during the sequential optimization process are associated with maximized confidence in the utilized simulation model. The proposed methodology is illustrated using a cantilever beam design subject to vibration.

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Figures

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Fig. 1

Notation and definition of local domains

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Fig. 2

Cantilever beam of rectangular cross-section with tip point load f(t)

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Fig. 3

Cantilever beam of rectangular cross-section for test and model (CAE) cases; the test uses a reduced cross-section close to the fixed end and the model assumes a pinned left end with a rotational spring constant kt

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Fig. 4

Confidence value as a function of design variables d1 and d2

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Fig. 5

Comparison of tip displacement between test and model at initial design before calibration

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Fig. 6

Comparison of tip displacement between test and model at initial design after calibration

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Fig. 7

Optimization process in the design space for noncalibrated and calibrated models

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Fig. 8

Design optimization history for noncalibrated and calibrated models

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