Research Papers

Constraint Management of Reduced Representation Variables in Decomposition-Based Design Optimization

[+] Author and Article Information
Michael J. Alexander

 Propulsion Systems Research Lab, General Motors Technical Center, 330500 Mound Road, Warren, MI 48090michael.j.alexander@gm.com

James T. Allison

Department of Industrial and Enterprise Systems Engineering,  University of Illinois at Urbana-Champaign, 117 Transportation Building MC-238, 104 S. Mathews Avenue, Urbana, IL 61801jtalliso@illinois.edu

Panos Y. Papalambros

Department of Mechanical Engineering,  University of Michigan, 3200 EECS c/o 2250 G.G. Brown, 2350 Hayward Street, Ann Arbor, MI 48104pyp@umich.edu

David J. Gorsich

Chief Scientist for Ground Vehicle Systems,  U.S. Army TARDEC, 6501 E. 11 Mile Road, Warren, MI 48397david.j.gorsich.civ@mail.mil

J. Mech. Des 133(10), 101014 (Oct 28, 2011) (10 pages) doi:10.1115/1.4004976 History: Received February 02, 2011; Revised August 24, 2011; Published October 28, 2011; Online October 28, 2011

In decomposition-based design optimization strategies such as analytical target cascading (ATC), it is sometimes necessary to use reduced representations of highly discretized functional data exchanged among subproblems to enable efficient design optimization. However, the variables used by such reduced representation methods are often abstract, making it difficult to constrain them directly beyond simple bounds. This problem is usually addressed by implementing a penalty value-based heuristic that indirectly constrains the reduced representation variables. Although this approach is effective, it leads to many ATC iterations, which in turn yields an ill-conditioned optimization problem and an extensive runtime. To address these issues, this paper introduces a direct constraint management technique that augments the penalty value-based heuristic with constraints generated by support vector domain description (SVDD). A comparative ATC study between the existing and proposed constraint management methods involving electric vehicle design indicates that the SVDD augmentation is the most appropriate within decomposition-based design optimization.

Copyright © 2011 by American Society of Mechanical Engineers
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Figure 1

ATC information flow [23]

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Figure 2

General plan view of electric vehicle [23]

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Figure 3

Penalty value-based heuristic: MATLAB ® try-catch statement

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Figure 4

Optimal motor map, PVBH

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Figure 5

Partial SVDD boundary, max-torque POD model validity region

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Figure 6

Partial SVDD boundary, min-torque POD model validity region

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Figure 7

Partial SVDD boundary, power loss POD model validity region

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Figure 8

Optimal motor map, SVDD augmentation

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Figure 9

Closed-curve shape for SVDD comparison

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Figure 10

SVDD boundary approximation for closed-curve shape

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Figure 11

Torque curve comparison for AiO optimal motor map

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Figure 12

Power loss map relative error for AiO optimal motor map



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