In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed framework, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

1.
Balling
,
R. J.
, and
Sobieszczanski-Sobieski
,
J.
,
1996
, “
Optimization of Coupled Systems: A Critical Overview of Approaches
,”
AIAA J.
,
34
(
1
), pp.
6
17
.
2.
Sobieszczanski-Sobieski
,
J.
, and
Haftka
,
R. T.
,
1997
, “
Multidisciplinary Aerospace Design Optimization: Survey of Recent Developments
,”
Structural Optimization
,
14
(
1
), pp.
1
23
.
3.
Lewis
,
K.
, and
Mistree
,
F.
,
1998
, “
Collaborative, Sequential, and Isolated Decisions in Design
,”
ASME J. Mech. Des.
,
120
(
4
), pp.
643
652
.
4.
Alexandrov
,
N. M.
, and
Lewis
,
R. M.
,
2002
, “
Analytical and Computational Aspects of Collaborative Optimization for Multidisciplinary Design
,”
AIAA J.
,
40
(
2
), pp.
301
309
.
5.
Rawlings, M. R., and Balling, R. J., 1998, September 2–4, “Collaborative Optimization with Disciplinary Conceptual Design,” 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, AIAA, 3, pp. 1580–1587. AIAA-98-4928.
6.
Braun
,
R. D.
,
Moore
,
A. A.
, and
Kroo
,
I. M.
,
1997
, “
Collaborative Architecture for Launch Vehicle Design
,”
J. Spacecr. Rockets
,
34
(
4
), pp.
478
486
.
7.
Kroo, I. M., Altus, S., Braun, R. D., Gage, P., and Sobieski, I. P., 1994, September 7–9, “Multidisciplinary Optimization Methods for Aircraft Preliminary Design,” 5th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Panama City, FL, AIAA, 1, pp. 697–707. AIAA-94-4325.
8.
Braun, R. D., and Kroo, I. M., 1993, August 11–13, “Post-optimality Analysis in Aerospace Vehicle Design,” AIAA Aircraft Design, Systems and Operations Meeting, Monterey, CA, AIAA. AIAA-93-3932.
9.
Rowell, L. F., Braun, R. D., Olds, J. R., and Unal, R., 1996, September 4–6, “Recent Experiences in Multidisciplinary Conceptual Design Optimization for Launch Vehicles,” 6th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Bellevue, WA, AIAA, 1, pp. 642–654. AIAA-96-4050.
10.
Tappeta
,
R. V.
, and
Renaud
,
J. E.
,
1997
, “
Multiobjective Collaborative Optimization
,”
ASME J. Mech. Des.
,
119
(
3
), pp.
403
411
.
11.
McAllister, C. D., Simpson, T. W., and Yukish, M., 2000, September 6–8, “Goal Programming Applications in Multidisciplinary Design Optimization,” 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, AIAA. AIAA-00-4717.
12.
Antonsson
,
E. K.
, and
Otto
,
K. N.
,
1995
, “
Imprecision in Engineering Design
,”
ASME J. Mech. Des.
,
17
(
2
), pp.
25
32
.
13.
Su
,
J.
, and
Renaud
,
J. E.
,
1997
, “
Automatic Differentiation in Robust Optimization
,”
AIAA J.
,
35
(
6
), pp.
1072
1079
.
14.
Du
,
X.
, and
Chen
,
W.
,
2000
, “
Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
385
394
.
15.
DeLaurentis, D. A., and Mavris, D. N., 2000, January 12–15, “Uncertainty Modeling and Management in Multidisciplinary Analysis and Synthesis,” 38th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA. AIAA-00-0422.
16.
Mavris, D. N., DeLaurentis, D. A., Bandte, O., and Hale, M. A., 1998, January 12–15, “A Stochastic Approach to Multi-disciplinary Aircraft Analysis and Design,” 36th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA. AIAA-98-0912.
17.
Bandte, O., Mavris, D. N., and DeLaurentis, D. A., 1999, October 19–21, “Viable Designs Through a Joint Probabilistic Estimation Technique,” AIAA/SAE World Aviation Congress, San Francisco, CA, AIAA. AIAA-99-01-5623.
18.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K.-L.
, and
Mistree
,
F.
,
1996
, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME J. Mech. Des.
,
118
(
4
), pp.
478
485
.
19.
Gu, X., Renaud, J. E., and Batill, S. M., 1998, September 2–4, “An Investigation of Multidisciplinary Design Subject to Uncertainty,” 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, MO, AIAA, 1, pp. 309–319. AIAA-98-4747.
20.
Gu
,
X.
,
Renaud
,
J. E.
,
Batill
,
S. M.
,
Brach
,
R. M.
, and
Budhiraja
,
A. S.
, 2000, “Worst Case Propagated Uncertainty of Multidisciplinary Systems in Robust Design Optimization,” Structural and Multidisciplinary Optimization, 20(3), pp. 190–213
21.
Gu
,
X.
,
Renaud
,
J. E.
,
Ashe
,
L. M.
,
Batill
,
S. M.
,
Budhiraja
,
A. S.
, and
Krajewski
,
L. J.
,
2002
, “
Decision-Based Collaborative Optimization
,”
ASME J. Mech. Des.
,
124
(
1
), pp.
1
13
.
22.
Hazelrigg
,
G. A.
,
1998
, “
A Framework for Decision-based Engineering Design
,”
ASME J. Mech. Des.
,
120
(
4
), pp.
653
658
.
23.
Du, X., and Chen, W., 2000, September 6–8, “Concurrent Subsystem Uncertainty Analysis in Multidisciplinary Design,” 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, AIAA. AIAA-00-4928.
24.
Venter, G., and Haftka, R. T., 1998, April 20–23, “Using Response Surface Methodology in Fuzzy Set Based Design Optimization,” 39th AIAA/ASME/ASCE/AHS/ASC Structures, Structural, Dynamics, and Materials Conference, Long Beach, CA, AIAA, 1, pp. 641–652. AIAA-98-1776.
25.
Lee, T. H., and Park, C., 2000, September 6–8, “Fuzzy Multi-objective Optimization of a Train Suspension Using Response Surface Model,” 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA. AIAA-00-4762.
26.
Mistree, F., Hughes, O. F., and Bras, B. A., 1993, “The Compromise Decision Support Problem and the Adaptive Linear Programming Algorithm,” Structural Optimization: Status and Promise, Kamat, M. P., ed., AIAA, Washington, D.C., pp. 247–289.
27.
Chen
,
W.
,
Wiecek
,
M.
, and
Zhang
,
J.
,
1998
, September 13–16, “
Quality Utility: A Compromise Programming Approach to Robust Design
,”
ASME J. Mech. Des.
,
121
(
2
), pp.
179
187
.
28.
Chen, W., Garimella, R., and Michelena, N., 1999, September 12–15, “Robust Design for Improved Vehicle Handling Under a Range of Maneuver Conditions,” ASME Design Automation Conference, Las Vegas, NV, ASME, Paper No. 99-DETC/DAC-8580.
29.
Papalambros, P. Y., and Wagner, T. C., 1991, “Optimal Engine Design Using Nonlinear Programming and the Engine Assessment Model,” Ford Motor Company Scientific Research Laboratories & University of Michigan Department of Mechanical Engineering.
30.
Papalambros, P. Y., and Wilde, D. J., 2000, Principles of Optimal Design: Modeling and Computation, Cambridge University Press, New York.
31.
Simpson
,
T. W.
,
Peplinski
,
J. D.
,
Koch
,
P. N.
, and
Allen
,
J. K.
,
2001
, “
Metamodels for Computer-Based Engineering Design: Survey and Recommendations
,”
Eng. Comput.
,
17
(
2
), pp.
129
150
.
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