A maximum confidence enhancement (MCE)-based sequential sampling approach is developed for reliability-based design optimization (RBDO) using surrogate models. The developed approach employs the ordinary Kriging method for surrogate model development and defines a cumulative confidence level (CCL) measure to quantify the accuracy of reliability estimation when Monte Carlo simulation is used based on the developed surrogate model. To improve the computational efficiency, an MCE-based sequential sampling scheme is developed to successively select sample points for surrogate model updating based on the defined CCL measure, in which a sample point that produces the largest CCL improvement will be selected. To integrate the MCE-based sequential sampling approach with RBDO, a new sensitivity analysis approach is developed, enabling smooth design sensitivity information to be accurately estimated based upon the constructed surrogate model without incurring any extra computational costs, thus greatly enhancing the efficiency and robustness of the design process. Two case studies are used to demonstrate the efficacy of the developed approach.

References

References
1.
Youn
,
B. D.
,
Choi
,
K. K.
, and
Du
,
L.
,
2005
, “
Enriched Performance Measure Approach for Reliability-Based Design Optimization
,”
AIAA J.
,
43
(
4
), pp.
874
884
.10.2514/1.6648
2.
Youn
,
B. D.
,
Choi
,
K. K.
, and
Park
,
Y. H.
,
2003
, “
Hybrid Analysis Method for Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
125
(
2
), pp.
221
232
.10.1115/1.1561042
3.
Chen
,
X.
,
Hasselman
,
T. K.
, and
Neill
,
D. J.
,
1997
, “
Reliability Based Structural Design Optimization for Practical Applications
,”
Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, pp.
2724
2732
.
4.
Wang
,
P.
,
Hu
,
C.
, and
Youn
,
B. D.
,
2011
, “
A Generalized Complementary Intersection Method (Gcim) for System Reliability Analysis
,”
ASME J. Mech. Des.
,
133
(
7
), p.
071003
.10.1115/1.4004198
5.
Du
,
X.
, and
Chen
,
W.
,
2004
, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design
,”
ASME J. Mech. Des.
,
126
(
2
), pp.
225
233
.10.1115/1.1649968
6.
Kim
,
N. H.
,
Wang
,
H.
, and
Queipo
,
N. V.
,
2006
, “
Adaptive Reduction of Random Variables Using Global Sensitivity in Reliability-Based Optimization
,”
Int. J. Reliab. Saf.
,
1
(
1
), pp.
102
119
.10.1504/IJRS.2006.010692
7.
Lee
,
S. H.
,
Chen
,
W.
, and
Kwak
,
B. M.
,
2009
, “
Robust Design With Arbitrary Distributions Using Gauss-Type Quadrature Formula
,”
Struct. Multidiscip. Optim.
,
39
(
3
), pp.
227
243
.10.1007/s00158-008-0328-2
8.
Yu
,
X.
, and
Du
,
X.
,
2006
, “
Reliability-Based Multidisciplinary Optimization for Aircraft Wing Design
,”
Struct. Infrastruct. Eng.
,
2
(
3–4
), pp.
277
289
.10.1080/15732470600590333
9.
Youn
,
B. D.
,
Choi
,
K.
,
Yang
,
R.-J.
, and
Gu
,
L.
,
2004
, “
Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact
,”
Struct. Multidiscip. Optim.
,
26
(
3–4
), pp.
272
283
.10.1007/s00158-003-0345-0
10.
Youn
,
B. D.
,
Choi
,
K. K.
, and
Tang
,
J.
,
2005
, “
Structural Durability Design Optimization and Its Reliability Assessment
,”
Int. J. Prod. Dev.
,
1
(
3
), pp.
383
401
.10.1504/IJPD.2005.005948
11.
Yi
,
K.
,
Choi
,
K.
,
Kim
,
N. H.
, and
Botkin
,
M. E.
,
2007
, “
Design Sensitivity Analysis and Optimization for Minimizing Springback of Sheet
Formed Part
,”
Int. J. Numer. Methods Eng.
,
71
(
12
), pp.
1483
1511
.10.1002/nme.1994
12.
Youn
,
B. D.
,
Choi
,
K.
, and
Du
,
L.
,
2005
, “
Adaptive Probability Analysis Using an Enhanced Hybrid Mean Value Method
,”
Struct. Multidiscip. Optim.
,
29
(
2
), pp.
134
148
.10.1007/s00158-004-0452-6
13.
Most
,
T.
, and
Knabe
,
T.
,
2010
, “
Reliability Analysis of the Bearing Failure Problem Considering Uncertain Stochastic Parameters
,”
Comput. Geotech.
,
37
(
3
), pp.
299
310
.10.1016/j.compgeo.2009.11.003
14.
Youn
,
B. D.
,
Xi
,
Z.
, and
Wang
,
P.
,
2008
, “
Eigenvector Dimension Reduction (EDR) Method for Sensitivity-Free Probability Analysis
,”
Struct. Multidiscip. Optim.
,
37
(
1
), pp.
13
28
.10.1007/s00158-007-0210-7
15.
Rubino
,
G.
, and
Tuffin
,
B.
,
2009
,
Rare Event Simulation Using Monte Carlo Methods
,
Wiley, Chichester, UK
.
16.
Lu
,
Z.
,
Song
,
S.
,
Yue
,
Z.
, and
Wang
,
J.
,
2008
, “
Reliability Sensitivity Method by Line Sampling
,”
Struct. Safety
,
30
(
6
), pp.
517
532
.10.1016/j.strusafe.2007.10.001
17.
Zio
,
E.
, and
Pedroni
,
N.
,
2010
, “
An Optimized Line Sampling Method for the Estimation of the Failure Probability of Nuclear Passive Systems
,”
Reliab. Eng. Syst. Saf.
,
95
(
12
), pp.
1300
1313
.10.1016/j.ress.2010.06.007
18.
Song
,
S.
,
Lu
,
Z.
, and
Qiao
,
H.
,
2009
, “
Subset Simulation for Structural Reliability Sensitivity Analysis
,”
Reliab. Eng. Syst. Saf.
,
94
(
2
), pp.
658
665
.10.1016/j.ress.2008.07.006
19.
Cheng
,
G.
,
Xu
,
L.
, and
Jiang
,
L.
,
2006
, “
A Sequential Approximate Programming Strategy for Reliability-Based Structural Optimization
,”
Comput. Struct.
,
84
(
21
), pp.
1353
1367
.10.1016/j.compstruc.2006.03.006
20.
Liang
,
J.
,
Mourelatos
,
Z. P.
, and
Nikolaidis
,
E.
,
2007
, “
A Single-Loop Approach for System Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
129
(
12
), pp.
1215
1224
.10.1115/1.2779884
21.
Royset
,
J.
,
Der Kiureghian
,
A.
, and
Polak
,
E.
,
2001
, “
Reliability-Based Optimal Structural Design by the Decoupling Approach
,”
Reliab. Eng. Syst. Saf.
,
73
(
3
), pp.
213
221
.10.1016/S0951-8320(01)00048-5
22.
Wang
,
P.
,
Youn
,
B. D.
,
Xi
,
Z.
, and
Kloess
,
A.
,
2009
, “
Bayesian Reliability Analysis With Evolving, Insufficient, and Subjective Data Sets
,”
ASME J. Mech. Des.
,
131
(
11
),
111008
.10.1115/1.4000251
23.
Youn
,
B. D.
, and
Wang
,
P.
,
2008
, “
Bayesian Reliability-Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method
,”
Struct. Multidiscip. Optim.
,
36
(
2
), pp.
107
123
.10.1007/s00158-007-0202-7
24.
Choi
,
J.
,
An
,
D.
, and
Won
,
J.
,
2010
, “
Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method
,”
ASME J. Mech. Des.
,
132
(
5
), p.
051003
.10.1115/1.4001377
25.
Currin
,
C.
,
Mitchell
,
T.
,
Morris
,
M.
, and
Ylvisaker
,
D.
,
1991
, “
Bayesian Prediction of Deterministic Functions, With Applications to the Design and Analysis of Computer Experiments
,”
J. Am. Stat. Assoc.
,
86
(
416
), pp.
953
963
.10.1080/01621459.1991.10475138
26.
Wang
,
Z.
, and
Wang
,
P.
,
2012
, “
A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
134
(
12
), p.
121007
.10.1115/1.4007931
27.
Li
,
J.
, and
Mourelatos
,
Z. P.
,
2009
, “
Time-Dependent Reliability Estimation for Dynamic Problems Using a Niching Genetic Algorithm
,”
ASME J. Mech. Des.
,
131
(
7
), p.
071009
.10.1115/1.3149842
28.
Sudret
,
B.
,
2008
, “
Analytical Derivation of the Outcrossing Rate in Time-Variant Reliability Problems
,”
Struct. Infrastruct. Eng.
,
4
(
5
), pp.
353
362
.10.1080/15732470701270058
29.
Baran
,
I.
,
Tutum
,
C. C.
, and
Hattel
,
J. H.
,
2012
, “
Reliability Estimation of the Pultrusion Process Using the First-Order Reliability Method (Form)
,”
Appl. Compos. Mater.
,
20
(
4
), pp.
639
653
.10.1007/s10443-012-9293-4
30.
Yang
,
D.
,
Li
,
G.
, and
Cheng
,
G.
,
2006
, “
Convergence Analysis of First Order Reliability Method Using Chaos Theory
,”
Comput. Struct.
,
84
(
8
), pp.
563
571
.10.1016/j.compstruc.2005.11.009
31.
Wang
,
L.
, and
Grandhi
,
R. V.
,
1996
, “
Safety Index Calculation Using Intervening Variables for Structural Reliability Analysis
,”
Comput. Struct.
,
59
(
6
), pp.
1139
1148
.10.1016/0045-7949(96)00291-X
32.
Do
,
M.
,
Sprooten
,
J.
,
Clenet
,
S.
, and
Robyns
,
B.
,
2011
, “
Reliability Evaluation of Power System With Large-Scale Wind Farm Integration Using First-Order Reliability Method
,”
Proceedings of the 2011-14th European Conference on Power Electronics and Applications (EPE 2011)
, pp.
1
10
.
33.
Du
,
X.
, and
Hu
,
Z.
,
2012
, “
First Order Reliability Method With Truncated Random Variables
,”
ASME J. Mech. Des.
,
134
(
9
), p.
091005
.10.1115/1.4007150
34.
Rahman
,
S.
, and
Xu
,
H.
,
2004
, “
A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics
,”
Probab. Eng. Mech.
,
19
(
4
), pp.
393
408
.10.1016/j.probengmech.2004.04.003
35.
Lee
,
I.
,
Choi
,
K.
,
Du
,
L.
, and
Gorsich
,
D.
,
2008
, “
Dimension Reduction Method for Reliability-Based Robust Design Optimization
,”
Comput. Struct.
,
86
(
13
), pp.
1550
1562
.10.1016/j.compstruc.2007.05.020
36.
Xu
,
H.
, and
Rahman
,
S.
,
2004
, “
A Generalized Dimension
Reduction Method for Multidimensional Integration in Stochastic Mechanics
,”
Int. J. Numer. Methods Eng.
,
61
(
12
), pp.
1992
2019
.10.1002/nme.1135
37.
Ghanem
,
R.
, and
Spanos
,
P. D.
,
2003
,
Stochastic Finite Elements: A Spectral Approach
,
Dover Publications
. Com.
38.
Paffrath
,
M.
, and
Wever
,
U.
,
2007
, “
Adapted Polynomial Chaos Expansion for Failure Detection
,”
J. Comput. Phys.
,
226
(
1
), pp.
263
281
.10.1016/j.jcp.2007.04.011
39.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2002
, “
The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(
2
), pp.
619
644
.10.1137/S1064827501387826
40.
Simpson
,
T. W.
,
Mauery
,
T. M.
,
Korte
,
J. J.
, and
Mistree
,
F.
,
1998
, “
Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization
,”
7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA Paper No. 98-4758
.
41.
Xiong
,
Y.
,
Chen
,
W.
, and
Tsui
,
K.-L.
,
2008
, “
A New Variable-Fidelity Optimization Framework Based on Model Fusion and Objective-Oriented Sequential Sampling
,”
ASME J. Mech. Des.
,
130
(
11
), p.
111401
.10.1115/1.2976449
42.
Queipo
,
N. V.
,
Haftka
,
R. T.
,
Shyy
,
W.
,
Goel
,
T.
,
Vaidyanathan
,
R.
, and
Kevin Tucker
,
P.
,
2005
, “
Surrogate-Based Analysis and Optimization
,”
Prog. Aerosp. Sci.
,
41
(
1
), pp.
1
28
.10.1016/j.paerosci.2005.02.001
43.
Lee
,
T. H.
, and
Jung
,
J. J.
,
2008
, “
A Sampling Technique Enhancing Accuracy and Efficiency of Metamodel-Based Rbdo: Constraint Boundary Sampling
,”
Comput. Struct.
,
86
(
13
), pp.
1463
1476
.10.1016/j.compstruc.2007.05.023
44.
Zhao
,
L.
,
Choi
,
K.
, and
Lee
,
I.
,
2011
, “
Metamodeling Method Using Dynamic Kriging for Design Optimization
,”
AIAA J.
,
49
(
9
), pp.
2034
2046
.10.2514/1.J051017
45.
Zhuang
,
X.
, and
Pan
,
R.
,
2012
, “
A Sequential Sampling Strategy to Improve Reliability-Based Design Optimization with Implicit Constraint Functions
,”
ASME J. Mech. Des.
,
134
(
2
), p.
021002
.10.1115/1.4005597
46.
Jones
,
D. R.
,
Schonlau
,
M.
, and
Welch
,
W. J.
,
1998
, “
Efficient Global Optimization of Expensive Black-Box Functions
,”
J. Global Optim.
,
13
(
4
), pp.
455
492
.10.1023/A:1008306431147
47.
Lee
,
I.
,
Choi
,
K.
, and
Zhao
,
L.
,
2011
, “
Sampling-Based RBDO Using the Stochastic Sensitivity Analysis and Dynamic Kriging Method
,”
Struct. Multidiscip. Optim.
,
44
(
3
), pp.
299
317
.10.1007/s00158-011-0659-2
48.
Žilinskas
,
A.
,
1992
, “
A Review of Statistical Models for Global Optimization
,”
J. Global Optim.
,
2
(
2
), pp.
145
153
.10.1007/BF00122051
49.
Keane
,
A.
, and
Nair
,
P.
,
2005
,
Computational Approaches for Aerospace Design: The Pursuit of Excellence
,
John Wiley & Sons
, Chap. 5.
50.
Rahman
,
S.
,
2009
, “
Stochastic Sensitivity Analysis by Dimensional Decomposition and Score Functions
,”
Probab. Eng. Mech.
,
24
(
3
), pp.
278
287
.10.1016/j.probengmech.2008.07.004
51.
Rao
,
S. S.
, and
Rao
,
S.
,
2009
,
Engineering Optimization: Theory and Practice
,
John Wiley & Sons
, Chap. 7.
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