Abstract

Robust design optimization (RDO) is a potent methodology that ensures stable performance in designed products during their operational phase. However, there remains a scarcity of robust design optimization methods that account for the intricacies of multidisciplinary coupling. In this article, we propose a multidisciplinary robust design optimization (MRDO) framework for physical systems under sparse samples containing the extreme scenario. The collaboration model is used to select samples that comply with multidisciplinary feasibility, avoiding time-consuming multidisciplinary decoupling analyses. To assess the robustness of sparse samples containing the extreme scenario, linear moment estimation is employed as the evaluation metric. The comparative analysis of MRDO results is conducted across various sample sizes, with and without the presence of the extreme scenario. The effectiveness and reliability of the proposed method are demonstrated through a mathematical case, a conceptual aircraft sizing design, and an energy efficiency optimization of a hobbing machine tool.

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References

1.
Wu
,
H.
, and
Du
,
X. P.
,
2023
, “
Time- and Space-Dependent Reliability-Based Design With Envelope Method
,”
ASME J. Mech. Des.
,
145
(
3
), p.
031708
.
2.
Zhang
,
D. Q.
,
Zhao
,
Z. D.
,
Ouyang
,
H.
,
Wu
,
Z. P.
, and
Han
,
X.
,
2023
, “
An Efficient Reliability Analysis Method Based on the Improved Radial Basis Function Neural Network
,”
ASME J. Mech. Des.
,
145
(
8
), p.
081705
.
3.
Beyer
,
H. G.
, and
Sendhoff
,
B.
,
2007
, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
(
33–34
), pp.
3190
3218
.
4.
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
.
5.
Shimoyama
,
K.
,
Lim
,
J. N.
,
Jeong
,
S.
,
Obayashi
,
S.
, and
Koishi
,
M.
,
2009
, “
Practical Implementation of Robust Design Assisted by Response Surface Approximation and Visual Data-Mining
,”
ASME J. Mech. Des.
,
131
(
6
), p.
061007
.
6.
Zhang
,
S. L.
,
Zhu
,
P.
,
Chen
,
W.
, and
Arendt
,
P.
,
2013
, “
Concurrent Treatment of Parametric Uncertainty and Metamodeling Uncertainty in Robust Design
,”
Struct. Multidiscip. Optim.
,
47
(
1
), pp.
63
76
.
7.
Rudnick-Cohen
,
E.
,
Herrmann
,
J. W.
, and
Azarm
,
S.
,
2020
, “
Non-Convex Feasibility Robust Optimization Via Scenario Generation and Local Refinement
,”
ASME J. Mech. Des.
,
142
(
5
), p.
051703
.
8.
Lei
,
G.
,
Bramerdorfer
,
G.
,
Ma
,
B.
,
Guo
,
Y. G.
, and
Zhu
,
J. G.
,
2021
, “
Robust Design Optimization of Electrical Machines: Multi-Objective Approach
,”
IEEE Trans. Energy Convers.
,
36
(
1
), pp.
390
401
.
9.
Jayaraman
,
D.
, and
Ramu
,
P.
,
2021
, “
L-Moments-Based Uncertainty Quantification for Scarce Samples Including Extremes
,”
Struct. Multidiscip. Optim.
,
64
(
2
), pp.
505
539
.
10.
Jayaraman
,
D.
,
Ramu
,
P.
,
Suresh
,
S. K.
, and
Ramanath
,
V.
,
2022
, “
A Dual Surrogate Driven L-Moments Based Robust Design With Scarce Samples in the Presence of Extremes
,”
Struct. Multidiscip. Optim.
,
65
(
3
), p.
74
.
11.
Sues
,
R.
, and
Cesare
,
M.
,
2000
, “
An Innovative Framework for Reliability-Based MDO
,”
41st Structures, Structural Dynamics, and Materials Conference and Exhibit
,
Atlanta, GA
,
Apr. 3–6
, p.
1509
.
12.
Du
,
X. P.
,
Guo
,
J.
, and
Beeram
,
H.
,
2008
, “
Sequential Optimization and Reliability Assessment for Multidisciplinary Systems Design
,”
Struct. Multidiscip. Optim.
,
35
(
2
), pp.
117
130
.
13.
Yao
,
W.
,
Chen
,
X. Q.
,
Ouyang
,
Q.
, and
van Tooren
,
M.
,
2013
, “
A Reliability-Based Multidisciplinary Design Optimization Procedure Based on Combined Probability and Evidence Theory
,”
Struct. Multidiscip. Optim.
,
48
(
2
), pp.
339
354
.
14.
Meng
,
D. B.
,
Li
,
Y. F.
,
Huang
,
H. Z.
,
Wang
,
Z. L.
, and
Liu
,
Y.
,
2015
, “
Reliability-Based Multidisciplinary Design Optimization Using Subset Simulation Analysis and Its Application in the Hydraulic Transmission Mechanism Design
,”
ASME J. Mech. Des.
,
137
(
5
), p.
051402
.
15.
Wang
,
L.
,
Xiong
,
C.
,
Hu
,
J. X.
,
Wang
,
X. J.
, and
Qiu
,
Z. P.
,
2018
, “
Sequential Multidisciplinary Design Optimization and Reliability Analysis Under Interval Uncertainty
,”
Aerosp. Sci. Technol.
,
80
, pp.
508
519
.
16.
Du
,
X. P.
, and
Chen
,
W.
,
2002
, “
Efficient Uncertainty Analysis Methods for Multidisciplinary Robust Design
,”
AIAA J.
,
40
(
3
), pp.
545
552
.
17.
Li
,
M.
, and
Azarm
,
S.
,
2008
, “
Multiobjective Collaborative Robust Optimization With Interval Uncertainty and Interdisciplinary Uncertainty Propagation
,”
ASME J. Mech. Des.
,
130
(
8
), p.
081402
.
18.
Xia
,
T. T.
,
Li
,
M.
, and
Zhou
,
J. H.
,
2016
, “
A Sequential Robust Approach for Multi-Disciplinary Design Optimization With Uncertainty
,”
Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2016, Vol 2b
,
Charlotte, NC
,
Aug. 21–24
, pp.
549
559
.
19.
Zaman
,
K.
, and
Mahadevan
,
S.
,
2013
, “
Robustness-Based Design Optimization of Multidisciplinary System Under Epistemic Uncertainty
,”
AIAA J.
,
51
(
5
), pp.
1021
1031
.
20.
Xu
,
H. W.
,
Li
,
W.
,
Li
,
M. F.
,
Hu
,
C.
,
Zhang
,
S. C.
, and
Wang
,
X.
,
2018
, “
Multidisciplinary Robust Design Optimization Based on Time-Varying Sensitivity Analysis
,”
J. Mech. Sci. Technol.
,
32
(
3
), pp.
1195
1207
.
21.
Li
,
W.
,
Xiao
,
M.
,
Yi
,
Y. S.
, and
Gao
,
L.
,
2019
, “
Maximum Variation Analysis Based Analytical Target Cascading for Multidisciplinary Robust Design Optimization Under Interval Uncertainty
,”
Adv. Eng. Inform.
,
40
, pp.
81
92
.
22.
McAllister
,
C. D.
, and
Simpson
,
T. W.
,
2003
, “
Multidisciplinary Robust Design Optimization of an Internal Combustion Engine
,”
ASME J. Mech. Des.
,
125
(
1
), pp.
124
130
.
23.
Wang
,
X. J.
,
Wang
,
R. X.
,
Chen
,
X. J.
,
Wang
,
L.
,
Geng
,
X. Y.
, and
Fan
,
W. C.
,
2017
, “
Interval Prediction of Responses for Uncertain Multidisciplinary System
,”
Struct. Multidiscip. Optim.
,
55
(
6
), pp.
1945
1964
.
24.
Hou
,
L. Q.
,
Cai
,
Y. L.
, and
Li
,
J. S.
,
2017
, “
Evidence-Based Multi-Disciplinary Robust Optimization for Mars Microentry Probe Design
,”
Stud. Comput. Intell.
,
662
, pp.
135
155
.
25.
Lei
,
G.
,
Liu
,
C. C.
,
Guo
,
Y. G.
, and
Zhu
,
J. G.
,
2016
, “
Robust Multidisciplinary Design Optimization of PM Machines With Soft Magnetic Composite Cores for Batch Production
,”
IEEE Trans. Magn.
,
52
(
3
), p.
8101304
.
26.
Xia
,
T.
,
Li
,
M.
, and
Zhou
,
J.
,
2016
, “
A Sequential Robust Optimization Approach for Multidisciplinary Design Optimization With Uncertainty
,”
ASME J. Mech. Des.
,
138
(
11
), p.
111406
.
27.
Li
,
W.
,
Xiao
,
M.
, and
Gao
,
L.
,
2019
, “
Improved Collaboration Pursuing Method for Multidisciplinary Robust Design Optimization
,”
Struct. Multidiscip. Optim.
,
59
(
6
), pp.
1949
1968
.
28.
Li
,
W.
,
Xiao
,
M.
,
Garg
,
A.
, and
Gao
,
L.
,
2021
, “
A New Approach to Solve Uncertain Multidisciplinary Design Optimization Based on Conditional Value at Risk
,”
IEEE Trans. Autom. Sci. Eng.
,
18
(
1
), pp.
356
368
.
29.
Saporito
,
M.
,
Da Ronch
,
A.
,
Bartoli
,
N.
, and
Defoort
,
S.
,
2023
, “
Robust Multidisciplinary Analysis and Optimization for Conceptual Design of Flexible Aircraft Under Dynamic Aeroelastic Constraints
,”
Aerosp. Sci. Technol.
,
138
, p.
108349
.
30.
Kania
,
R. J.
, and
Azarm
,
S.
,
2023
, “
Bi-Objective Surrogate Feasibility Robust Design Optimization Utilizing Expected Non-Dominated Improvement With Relaxation
,”
ASME J. Mech. Des.
,
145
(
3
), p.
031703
.
31.
Kim
,
S.
,
Jwa
,
M.
,
Lee
,
S.
,
Park
,
S.
, and
Kang
,
N.
,
2022
, “
Deep Learning-Based Inverse Design for Engineering Systems: Multidisciplinary Design Optimization of Automotive Brakes
,”
Struct. Multidiscip. Optim.
,
65
(
11
), p.
323
.
32.
Dubreuil
,
S.
,
Bartoli
,
N.
,
Gogu
,
C.
, and
Lefebvre
,
T.
,
2020
, “
Towards an Efficient Global Multidisciplinary Design Optimization Algorithm
,”
Struct. Multidiscip. Optim.
,
62
(
4
), pp.
1739
1765
.
33.
Ghoreishi
,
S. F.
, and
Imani
,
M.
,
2021
, “
Bayesian Surrogate Learning for Uncertainty Analysis of Coupled Multidisciplinary Systems
,”
ASME J. Comput. Inf. Sci. Eng.
,
21
(
4
), p.
041009
.
34.
Abarbanel
,
H.
,
Koonin
,
S.
,
Levine
,
H.
,
MacDonald
,
G.
, and
Rothaus
,
O.
,
1992
,
Statistics of Extreme Events with Application to Climate
,
MITRE Corp Mclean Va Jason Program Office, JSR-90-305
,
Mclean, Vaginia
, pp.
1
79
.
35.
Moon
,
M. Y.
,
Kim
,
H. S.
,
Lee
,
K. S.
,
Park
,
B.
, and
Choi
,
K. K.
,
2020
, “
Uncertainty Quantification and Statistical Model Validation for an Offshore Jacket Structure Panel Given Limited Test Data and Simulation Model
,”
Struct. Multidiscip. Optim.
,
61
(
6
), pp.
2305
2318
.
36.
Li
,
W.
,
Gao
,
L.
, and
Xiao
,
M.
,
2020
, “
Multidisciplinary Robust Design Optimization Under Parameter and Model Uncertainties
,”
Eng. Optim.
,
52
(
3
), pp.
426
445
.
37.
Wang
,
D. P.
,
Wang
,
G. G.
, and
Naterer
,
G. F.
,
2007
, “
Collaboration Pursuing Method for Multidisciplinary Design Optimization Problems
,”
AIAA J.
,
45
(
5
), pp.
1091
1103
.
38.
Wang
,
D. P.
,
Wang
,
G. G.
, and
Naterer
,
G. F.
,
2007
, “
Extended Collaboration Pursuing Method for Solving Larger Multidisciplinary Design Optimization Problems
,”
AIAA J.
,
45
(
6
), pp.
1208
1221
.
39.
Hosking
,
J. R.
,
1990
, “
L-Moments: Analysis and Estimation of Distributions Using Linear Combinations of Order Statistics
,”
J. R. Statist. Soc. Ser. B: Statist. Methodol.
,
52
(
1
), pp.
105
124
.
40.
Wujek
,
B.
,
Renaud
,
J.
,
Batill
,
S.
,
Johnson
,
E.
, and
Brockman
,
J.
,
1996
, “
Design Flow Management and Multidisciplinary Design Optimization in Application to Aircraft Concept Sizing
,”
34th Aerospace Sciences Meeting and Exhibit
,
Reno, NV
,
Jan. 15–18
, p.
713
.
41.
Li
,
W.
,
Li
,
C. B.
,
Wang
,
N. B.
,
Li
,
J.
, and
Zhang
,
J. W.
,
2022
, “
Energy Saving Design Optimization of CNC Machine Tool Feed System: A Data-Model Hybrid Driven Approach
,”
IEEE Trans. Autom. Sci. Eng.
,
19
(
4
), pp.
3809
3820
.
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