Abstract
Analytical target cascading (ATC) is a methodology for hierarchical multilevel system design optimization. In previous work, the deterministic ATC formulation was extended to account for random variables represented by expected values to be matched among subproblems and thus ensure design consistency. In this work, the probabilistic formulation is augmented to allow the introduction and matching of additional probabilistic characteristics. A particular probabilistic analytical target cascading (PATC) formulation is proposed that matches the first two moments of interrelated responses and linking variables. Several implementation issues are addressed, including representation of probabilistic design targets, matching responses and linking variables under uncertainty, and coordination strategies. Analytical and simulation-based optimal design examples are used to illustrate the new formulation. The accuracy of the proposed PATC formulation is demonstrated by comparing PATC results to those obtained using a probabilistic all-in-one formulation.
1.
Balling
, R.
J.
, and Sobieszczanski-Sobieski
,
J.
,
1996, “Optimization of
Coupled Systems: A Critical Overview of Approaches
,”
AIAA J.
0001-1452, 34
(1
), pp.
6
–17
.2.
Alexandrov
, N.
M.
, and Lewis
, R.
M.
, 1999,
“Comparative Properties of Collaborative Optimization and
Other Approaches to MDO
,” ICASE Report, No. 99-24,
NASA/CR-1999-209354.3.
Cramer
, E.
J.
, Dennis
, J.
E.
, Frank
, P.
D.
, Lewis
, R.
M.
, and Shubin
, G.
R.
, 1994,
“Problem Formulation for Multidisciplinary
Optimization
,” SIAM J. Optim.
1052-6234,
4
(4
), pp.
754
–776
.4.
Kroo
,
I.
,
Altus
,
S.
,
Braun
,
R.
,
Gage
,
P.
, and
Sobieski
,
I.
,
1994, ”Multidisciplinary
Optimization Methods for Aircraft Preliminary Design
,” 5th
AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization,
paper no. AIAA 94-4325, Panama City, Florida.5.
Braun
, R.
D.
, Kroo
, I.
M.
, and Moore
, A.
A.
, 1996,
“Use of the Collaborative Optimization Architecture for
Launch Vehicle Design
,” 6th AIAA/USAF/NASA/ISSMO Symposium
on Multidisciplinary Analysis and Optimization, paper no. AIAA 96-4018,
Bellevue, WA.6.
Kroo
,
I.
,
1997, “MDO Application
in Preliminary Design: Status and Directions,” AIAA
Pap.
0146-3705
97
–1408
.7.
Renaud
, J.
E.
, and Tappeta
, R.
V.
, 1997,
“Multiobjective Collaborative Optimization
,”
ASME J. Mech. Des.
1050-0472, 119
(3
), pp.
403
–411
.8.
Kim
,
H. M.
, Michelena
, N.
F.
, Papalambros
, P.
Y.
, and Jiang
,
T.
,
2000, “Target Cascading
in Optimal System Design
,” Proceedings of the ASME
Design Engineering Technical Conferences
, paper no. DETC
2000/DAC-14265, Baltimore, MD, September 10–13, 2000, 2, pp.
293
–302
; 9.
Kim
, H.
M.
, 2001,
Target Cascading in Optimal System Design, Ph.D. thesis, University of Michigan,
Ann Arbor, Michigan.10.
Kim
,
H. M.
, Rideout
, D.
G.
, Papalambros
, P.
Y.
, and Stein
, J.
L.
, 2001,
“Analytical Target Cascading in Automotive Vehicle
Design
,” Proceedings of the ASME Design Engineering
Technical Conferences
, paper no. DETC 2001/DAC-21079, Pittsburgh,
PA, 2, pp. 661
–670
; 11.
Kim
, H.
M.
, Kokkolaras
,
M.
,
Louca
, L.
S.
, Delagrammatikas
,
G. J.
, Michelena
, N.
F.
, Filipi
, Z.
S.
, Papalambros
, P.
Y.
, Stein
, J.
L.
, and Assanis
, D.
N.
, 2002,
“Target Cascading in Vehicle Redesign: A Class VI Truck
Study
,” Int. J. Veh. Des.
0143-3369, 29
(3
),
pp. 199
–225
.12.
Kokkolaras
,
M.
,
Fellini
,
R.
,
Kim
, H.
M.
, Michelena
, N.
F.
, and Papalambros
,
P. Y.
, 2002,
“Extension of the Target Cascading Formulation to the Design
of Product Families
,” Struct. Multidiscip.
Optim.
1615-147X, 24
(4
), pp.
293
–301
.13.
Kokkolaras
,
M.
,
Louca
, L.
S.
, Delagrammatikas
,
G. J.
, Michelena
, N.
F.
, Filipi
, Z.
S.
, Papalambros
, P.
Y.
, Stein
, J.
L.
, and Assanis
, D.
N.
, 2004,
“Simulation-Based Optimal Design of Heavy Trucks by
Model-Based Decomposition: An Extensive Analytical Target Cascading Case
Study
,” International Journal of Heavy Vehicle
Systems
, 11
(3,4
), pp.
402
–432
.14.
Wagner
, T.
C.
, 1993, A
General Decomposition Methodology for Optimal System Design, Ph.D. thesis,
University of Michigan, Ann Arbor, Michigan.15.
Cooper
,
A.
,
Georgiopoulos
,
P.
,
Kim
, H.
M.
, and Papalambros
,
P. Y.
, 2003,
“Analytical Target Setting: An Enterprise Context in Optimal
Product Design
,” Proceedings of the ASME Design
Engineering Technical Conferences
, paper no. DETC 2003/DAC-48734,
Chicago, IL.16.
Wassenaar
, H.
J.
, and Chen
,
W.
,
2003, “An Approach to
Decision-Based Design with Discrete Choice Analysis for Demand
Modeling
,” ASME J. Mech. Des.
1050-0472,
125
(3
), pp.
490
–497
.17.
Gu
,
X.
,
Renaud
, J.
E.
, and Batill
, S.
M.
, 1998,
“An Investigation of Multidisciplinary Design Subject to
Uncertainty
,” AIAA-1998-4747, 7th
AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis and Optimization
Symposium
, St. Louise
, Missouri,
1998, pp. 309
–319
.18.
Chen
,
W.
, and
Lewis
,
K.
,
1999, “Robust Design
Approach for Achieving Flexibility in Multidisciplinary
Design
,” AIAA J.
0001-1452, 37
(8
), pp.
982
–989
.19.
Du
,
X.
, and
Chen
,
W.
,
2002, “Efficient
Uncertainty Analysis Methods for Multidisciplinary Robust
Design
,” AIAA J.
0001-1452, 40
(3
), pp.
545
–552
.20.
Batill
,
S.
,
Renaud
, J.
E.
, and Gu
,
X.
,
2000, “Modeling and
Simulation Uncertainty in Multidisciplinary Design
Optimization
,” 8th AIAA/NASA/USAF/ISSMO Multidisciplinary
Analysis and Optimization Conference and Exhibit, paper no. AIAA 2000-4803, Long
Beach, California.21.
Padmanabhan
,
D.
, and
Batill
, S.
M.
, 2000,
“An Iterative Concurrent Subspace Robust Design
Framework
,” Proceedings of 8th AIAA/NASA/USAF/ISSMO
Multidisciplinary Analysis and Optimization Conference and Exhibit
,
paper no. AIAA-20002-0449, Long Beach
,
California
.22.
Gurnani
, A.
P.
, and Lewis
,
K.
,
2004, “An Approach to
Robust Decision Making in Multidisciplinary Selection Problems under
Uncertainty
,” Proceedings of 10th AIAA/ISSMO
Multidisciplinary Analysis and Optimization Conference
, August
30–September 1, 2004, Albany
,
New York
.23.
Sues
,
R.
,
Cesare
,
M.
,
Pageau
,
S.
, and
Wu
,
J.
,
2000, “Reliability Based
MDO for Aerospace Systems
,” 8th Symposium on
Multidisciplinary Analysis and Optimization, AIAA 2000-4804, Long Beach,
California.24.
Chiralaksanakul
,
A.
, and
Mahadevan
,
S.
,
2004, “Multidisciplinary
Design Optimization Under Uncertainty
,” 10th AIAA/ISSMO
Multidisciplinary Analysis and Optimization Conference, paper no.
AIAA-2004-4311, Albany, NY.25.
Kokkolaras
,
M.
,
Mourelatos
, Z.
P.
, and Papalambros
,
P. Y.
, 2006,
“Design Optimization of Hierarchically Decomposed Multilevel
System under Uncertainty
,” ASME J. Mech.
Des.
1050-0472,
128
(2
), pp.
503
–508
. An earlier version was presented at
the 2004 ASME Design Engineering Technical Conferences, paper no.
DETC2004/DAC-57357.26.
Phadke
, M.
S.
, 1989,
Quality Engineering Using Robust Design
,
Prentice Hall
, Englewood Cliffs, New
Jersey.27.
Kim
,
H.
,
Kumar
,
D.
,
Chen
,
W.
, and
Papalambros
, P.
Y.
, 2004,
“Target Feasibility Achievement in Enterprise-Driven
Hierarchical Multidisciplinary Design
,” 10th AIAA/ISSMO
Multidisciplinary Analysis and Optimization Conference, paper no.
AIAA-2004-4546, Albany, NY.28.
Allison
,
J.
,
2004, Complex System Optimization: A
Comparison of Analytical Target Cascading, Collaborative Optimization, and Other
Formulations, MS thesis, University of Michigan, Ann Arbor,
Michigan.29.
Michalek
, J.
J.
, and Papalambros
,
P. Y.
, 2005,
“Technical Brief: Weights, Norms, and Notation in Analytical
Target Cascading
,” ASME J. Mech. Des.
1050-0472,
127
(3
), pp.
499
–501
.30.
Ang
,
A.H.-S.
, and
Tang
, W.
H.
, 1975,
Probability Concepts in Engineering Planning and Design, Volume
I–Basic Principles
, Wiley
, New
York.31.
Du
,
X.
, and
Chen
,
W.
,
2000, “Towards a Better
Understanding of Modeling Feasibility Robustness in
Engineering
,” ASME J. Mech. Des.
1050-0472,
122
(4
), pp.
385
–394
.32.
Kalsi
,
M.
,
Hacker
,
K.
, and
Kemper
,
L.
,
2001, “A Comprehensive
Robust Design Approach for Decision Trade-Offs in Complex Systems
Design
,” ASME J. Mech. Des.
1050-0472,
123
, pp.
1
–10
.33.
McAllister
, C.
D.
, and Simpson
, T.
W.
, 2003,
“Multidisciplinary Robust Design Optimization of an Internal
Combustion Engine
,” ASME J. Mech. Des.
1050-0472,
125
, pp.
124
–130
.34.
Du
,
X.
,
Sudjianto
,
A.
, and
Chen
,
W.
,
2004, “An Integrated
Framework for Optimization Using Inverse Reliability
Strategy
,” ASME J. Mech. Des.
1050-0472,
126
(4
), pp.
562
–570
.35.
Wassenaar
, H.
J.
, Chen
,
W.
,
Cheng
,
J.
, and
Sudjianto
,
A.
,
2003, “Enhancing
Discrete Choice Demand Modeling for Decision-Based Design
,”
ASME J. Mech. Des.
1050-0472,
127
(4
), pp.
514
–523
.36.
Wassenaar
, H.
J.
, Chen
,
W.
,
Cheng
,
J.
, and
Sudjianto
,
A.
,
2004, “An Integrated
Latent Variable Choice Modeling Approach to Enhancing Product Demand
Modeling
,” Proceedings of the ASME Design
Engineering Technical Conference
, paper no. DETC2004-57487, Salt
Lake City, UT.37.
Michelena
,
N.
,
Park
,
H.
, and
Papalambros
,
P.
,
2002, “Convergence
Properties of Analytical Target Cascading
,”
Proceedings of the 9th AIAA/ISSMO Symposium on Multidisciplinary
Analysis and Optimization
, paper no. AIAA-2002-5506, Atlanta, GA; 38.
Haftka
, R.
T.
, and Watson
, L.
T.
, 2005,
“Multidisciplinary Design Optimization with Quasiseparable
Subsystems
,” Opt. Eng.
0091-3286, 6
, pp.
9
–20
.39.
Beightler
, C.
S.
, and Phillips
,
D. T.
, 1976,
Applied Geometric Programming
,
Wiley
, New York.40.
Tamhane
, A.
C.
, and Dunlop
, D.
D.
, 2000,
Statistics and Data Analysis from Elementary to
Intermediate
, Prentice Hall
, New
Jersey.41.
Tosserams
,
S.
,
Etman
, L. F.
P.
, Papalambros
, P.
Y.
, and Rooda
, J.
E.
, 2005,
“An Augmented Lagrangian Relaxation for Analytical Target
Cascading using the Alternating Directions Method of
Multipliers
,” Proceedings of the 6th World
Conference on Structural and Multidisciplinary Optimization
,
Rio de Janeiro
,
Brazil
.42.
Kim
, H.
M.
, Chen
,
W.
, and
Wiecek
,
M.
,
2005, “Lagrangian
Coordination for Enhancing the Convergence of Analytical Target
Cascading
,” Proceedings of the IFORS
,
Honolulu
, Hawaii,
USA
.43.
Du
,
X.
, and
Chen
,
W.
,
2004, “Sequential
Optimization and Reliability Assessment Method for Efficient Probabilistic
Design
,” ASME J. Mech. Des.
1050-0472,
126
(2
), pp.
225
–233
.Copyright © 2006
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