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Journal of Mechanical Design | Volume 131 | Issue 6 | Research Paper
Research Papers

Practical Implementation of Robust Design Assisted by Response Surface Approximation and Visual Data-Mining

[+] Author and Article Information
Koji Shimoyama1

Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japanshimoyama@edge.ifs.tohoku.ac.jp

Jin Ne Lim

Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japanlim@edge.ifs.tohoku.ac.jp

Shinkyu Jeong

Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japanjeong@edge.ifs.tohoku.ac.jp

Shigeru Obayashi

Institute of Fluid Science, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japanobayashi@ifs.tohoku.ac.jp

Masataka Koishi

CAE Laboratory, Yokohama Rubber Co., Ltd., 2-1 Oiwake, Hiratsuka, Kanagawa 254-8601, Japankoishi@hpt.yrc.co.jp

1

Corresponding author.

J. Mech. Des 131(6), 061007 (May 19, 2009) (11 pages) doi:10.1115/1.3125207 History: Received June 28, 2008; Revised March 02, 2009; Published May 19, 2009
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A new approach for multi-objective robust design optimization was proposed and applied to a practical design problem with a large number of objective functions. The present approach is assisted by response surface approximation and visual data-mining, and resulted in two major gains regarding computational time and data interpretation. The Kriging model for response surface approximation can markedly reduce the computational time for predictions of robustness. In addition, the use of self-organizing maps as a data-mining technique allows visualization of complicated design information between optimality and robustness in a comprehensible two-dimensional form. Therefore, the extraction and interpretation of trade-off relationships between optimality and robustness of design, and also the location of sweet spots in the design space, can be performed in a comprehensive manner.
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+Comparison between deterministic optimization and robust optimization (in minimization problem)
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Comparison between deterministic optimization and robust optimization (in minimization problem)
Figure 1

Comparison between deterministic optimization and robust optimization (in minimization problem)

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+Flowchart of multi-objective robust design optimization process
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Flowchart of multi-objective robust design optimization process
Figure 2

Flowchart of multi-objective robust design optimization process

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+Kriging model (in minimization problem)
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Kriging model (in minimization problem)
Figure 3

Kriging model (in minimization problem)

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+Self-organizing map
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Self-organizing map
Figure 4

Self-organizing map

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+Automobile tire structure
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Automobile tire structure
Figure 5

Automobile tire structure

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+Cross validation of Kriging-based RSs for tire stiffnesses: (a) Ex, (b) Ey, and (c) Ez
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Cross validation of Kriging-based RSs for tire stiffnesses: (a) Ex, (b) Ey, and (c) Ez
Figure 6

Cross validation of Kriging-based RSs for tire stiffnesses: (a) Ex, (b) Ey, and (c) Ez

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+Nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz
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Nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz
Figure 7

Nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz

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+Nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz
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Nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz
Figure 8

Nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) (σEy∕μEy) versus μEy and (b) (σEz∕μEz) versus μEz

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+SOMs of nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) Ex, (b) Ey, and (c) Ez
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SOMs of nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) Ex, (b) Ey, and (c) Ez
Figure 9

SOMs of nondominated solutions obtained through deterministic optimization (shown as values estimated by RSs): (a) Ex, (b) Ey, and (c) Ez

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+SOMs of nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) μEx, (b) μEy, (c) σEy∕μEy, (d) μEz, and (e) σEz∕μEz
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SOMs of nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) μEx, (b) μEy, (c) σEy∕μEy, (d) μEz, and (e) σEz∕μEz
Figure 10

SOMs of nondominated solutions obtained through robust optimization (shown as values estimated by RSs): (a) μEx, (b) μEy, (c) σEy∕μEy, (d) μEz, and (e) σEz∕μEz

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+Profiles of tire stiffness values against the variation of pint for nondominated solutions obtained through deterministic optimization and robust optimization (shown as real values calculated by ABAQUS ): (a) Ex versus pint, (b) Ey versus pint, and (c) Ez versus pint
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Profiles of tire stiffness values against the variation of pint for nondominated solutions obtained through deterministic optimization and robust optimization (shown as real values calculated by ABAQUS ): (a) Ex versus pint, (b) Ey versus pint, and (c) Ez versus pint
Figure 11

Profiles of tire stiffness values against the variation of pint for nondominated solutions obtained through deterministic optimization and robust optimization (shown as real values calculated by ABAQUS ): (a) Ex versus pint, (b) Ey versus pint, and (c) Ez versus pint

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