Abstract

Most of the existing reliability-based design optimization (RBDO) are not capable of analyzing data from multifidelity sources to improve the confidence of optimal solution while maintaining computational efficiency. In this paper, we propose a novel reliability-based multifidelity optimization (RBMO) framework that adaptively integrates both low- and high-fidelity data for achieving reliable optimal designs. The Gaussian process (GP) modeling technique is first utilized to build a hybrid surrogate model by fusing data sources with different fidelity levels. To reduce the number of low- and high-fidelity data, an adaptive hybrid learning (AHL) algorithm is then developed to efficiently update the hybrid model. The updated hybrid surrogate model is used for reliability and sensitivity analyses in solving an RBDO problem, which provides a pseudo-optimal solution in the RBMO framework. An optimal solution that meets the reliability targets can be achieved by sequentially performing the adaptive hybrid learning at the iterative pseudo-optimal designs and solving RBDO problems. The effectiveness of the proposed framework is demonstrated through three case studies.

References

1.
Meng
,
Z.
,
Li
,
G.
,
Wang
,
B. P.
, and
Hao
,
P.
,
2015
, “
A Hybrid Chaos Control Approach of the Performance Measure Functions for Reliability-Based Design Optimization
,”
Comput. Struct.
,
146
, pp.
32
43
.10.1016/j.compstruc.2014.08.011
2.
Sun
,
G.
,
Zhang
,
H.
,
Fang
,
J.
,
Li
,
G.
, and
Li
,
Q.
,
2017
, “
Multi-Objective and Multi-Case Reliability-Based Design Optimization for Tailor Rolled Blank (TRB) Structures
,”
Struct. Multidiscip. Optim.
,
55
(
5
), pp.
1899
1916
.10.1007/s00158-016-1592-1
3.
Zhou
,
M.
,
Luo
,
Z.
,
Yi
,
P.
, and
Cheng
,
G.
,
2018
, “
A Two-Phase Approach Based on Sequential Approximation for Reliability-Based Design Optimization
,”
Struct. Multidiscip. Optim.
,
57
(
2
), pp.
489
508
.10.1007/s00158-017-1888-9
4.
Keshtegar
,
B.
, and
Chakraborty
,
S.
,
2018
, “
Dynamical Accelerated Performance Measure Approach for Efficient Reliability-Based Design Optimization With Highly Nonlinear Probabilistic Constraints
,”
Reliab. Eng. Syst. Saf.
, 178, pp. 69-83.https://www.sciencedirect.com/science/article/pii/S0951832018305611
5.
Liu
,
W.-S.
, and
Cheung
,
S. H.
,
2017
, “
Reliability Based Design Optimization With Approximate Failure Probability Function in Partitioned Design Space
,”
Reliab. Eng. Syst. Saf.
,
167
, pp.
602
611
.10.1016/j.ress.2017.07.007
6.
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
7.
Gunawan
,
S.
, and
Papalambros
,
P. Y.
,
2006
, “
A Bayesian Approach to Reliability-Based Optimization With Incomplete Information
,”
ASME J. Mech. Des.
, 128(4), pp.
909
918
.10.1115/1.2204969
8.
Youn
,
B.
, and
Wang
,
P.
,
2006
, “
Bayesian Reliability Based Design Optimization Under Both Aleatory and Epistemic Uncertainties
,”
AIAA
Paper No. 2006–6928.10.2514/6.2006-6928
9.
Zhuang
,
X.
,
Pan
,
R.
, and
Du
,
X.
,
2015
, “
Enhancing Product Robustness in Reliability-Based Design Optimization
,”
Reliab. Eng. Syst. Saf.
,
138
, pp.
145
153
.10.1016/j.ress.2015.01.026
10.
Shahraki
,
A. F.
, and
Noorossana
,
R.
,
2014
, “
Reliability-Based Robust Design Optimization: A General Methodology Using Genetic Algorithm
,”
Comput. Ind. Eng.
,
74
, pp.
199
207
.10.1016/j.cie.2014.05.013
11.
Lee
,
I.
,
Choi
,
K.
,
Du
,
L.
, and
Gorsich
,
D.
,
2008
, “
Dimension Reduction Method for Reliability-Based Robust Design Optimization
,”
Comput. Struct.
,
86
(
13–14
), pp.
1550
1562
.10.1016/j.compstruc.2007.05.020
12.
Hu
,
Z.
, and
Du
,
X.
,
2016
, “
Reliability-Based Design Optimization Under Stationary Stochastic Process Loads
,”
Eng. Optim.
,
48
(
8
), pp.
1296
1312
.10.1080/0305215X.2015.1100956
13.
Yu
,
S.
, and
Wang
,
Z.
,
2018
, “
Time-Dependent Reliability-Based Robust Design Optimization Via Extreme Value Moment Method
,”
ASME
Paper No. DETC2018-85718.10.1115/DETC2018-85718
14.
Li
,
M.
, and
Wang
,
Z.
,
2017
, “
Sequential Kriging Optimization for Time-Variant Reliability-Based Design Involving Stochastic Processes
,”
ASME
Paper No. DETC2017-67426.10.1115/DETC2017-67426
15.
Zhao
,
W.
,
Fan
,
F.
, and
Wang
,
W.
,
2017
, “
Non-Linear Partial Least Squares Response Surface Method for Structural Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
161
, pp.
69
77
.10.1016/j.ress.2017.01.004
16.
Goswami
,
S.
,
Ghosh
,
S.
, and
Chakraborty
,
S.
,
2016
, “
Reliability Analysis of Structures by Iterative Improved Response Surface Method
,”
Struct. Saf.
,
60
, pp.
56
66
.10.1016/j.strusafe.2016.02.002
17.
Hadidi
,
A.
,
Azar
,
B. F.
, and
Rafiee
,
A.
,
2017
, “
Efficient Response Surface Method for High-Dimensional Structural Reliability Analysis
,”
Struct. Saf.
,
68
, pp.
15
27
.10.1016/j.strusafe.2017.03.006
18.
Huang
,
X.
,
Liu
,
Y.
,
Zhang
,
Y.
, and
Zhang
,
X.
,
2017
, “
Reliability Analysis of Structures Using Stochastic Response Surface Method and Saddlepoint Approximation
,”
Struct. Multidiscip. Optim.
,
55
(
6
), pp.
2003
2012
.10.1007/s00158-016-1617-9
19.
Schueremans
,
L.
, and
Van Gemert
,
D.
,
2005
, “
Benefit of Splines and Neural Networks in Simulation Based Structural Reliability Analysis
,”
Struct. Saf.
,
27
(
3
), pp.
246
261
.10.1016/j.strusafe.2004.11.001
20.
Chojaczyk
,
A.
,
Teixeira
,
A.
,
Neves
,
L. C.
,
Cardoso
,
J.
, and
Soares
,
C. G.
,
2015
, “
Review and Application of Artificial Neural Networks Models in Reliability Analysis of Steel Structures
,”
Struct. Saf.
,
52
, pp.
78
89
.10.1016/j.strusafe.2014.09.002
21.
Dai
,
H.
, and
Cao
,
Z.
,
2017
, “
A Wavelet Support Vector Machine‐Based Neural Network Metamodel for Structural Reliability Assessment
,”
Comput.‐Aided Civ. Infrastruct. Eng.
,
32
(
4
), pp.
344
357
.10.1111/mice.12257
22.
Deng
,
J.
,
Gu
,
D.
,
Li
,
X.
, and
Yue
,
Z. Q.
,
2005
, “
Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network
,”
Struct. Saf.
,
27
(
1
), pp.
25
48
.10.1016/j.strusafe.2004.03.004
23.
Zhang
,
L.
,
Lu
,
Z.
, and
Wang
,
P.
,
2015
, “
Efficient Structural Reliability Analysis Method Based on Advanced Kriging Model
,”
Appl. Math. Modell.
,
39
(
2
), pp.
781
793
.10.1016/j.apm.2014.07.008
24.
Sun
,
Z.
,
Wang
,
J.
,
Li
,
R.
, and
Tong
,
C.
,
2017
, “
LIF: A New Kriging Based Learning Function and Its Application to Structural Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
157
, pp.
152
165
.10.1016/j.ress.2016.09.003
25.
Iooss
,
B.
, and
Le Gratiet
,
L.
,
2017
, “
Uncertainty and Sensitivity Analysis of Functional Risk Curves Based on Gaussian Processes
,”
Reliab. Eng. Syst. Saf.
, 187, pp.
58
66
.10.1016/j.ress.2017.11.022
26.
Li
,
M.
, and
Wang
,
Z.
,
2019
, “
Surrogate Model Uncertainty Quantification for Reliability-Based Design Optimization
,”
Reliab. Eng. Syst. Saf.
, in press.10.1016/j.ress.2019.03.039
27.
Pan
,
Q.
, and
Dias
,
D.
,
2017
, “
An Efficient Reliability Method Combining Adaptive Support Vector Machine and Monte Carlo Simulation
,”
Struct. Saf.
,
67
, pp.
85
95
.10.1016/j.strusafe.2017.04.006
28.
Stern
,
R. E.
,
Song
,
J.
, and
Work
,
D. B.
,
2017
, “
Accelerated Monte Carlo System Reliability Analysis Through Machine-Learning-Based Surrogate Models of Network Connectivity
,”
Reliab. Eng. Syst. Saf.
,
164
, pp.
1
9
.10.1016/j.ress.2017.01.021
29.
das Chagas Moura
,
M.
,
Zio
,
E.
,
Lins
,
I. D.
, and
Droguett
,
E.
,
2011
, “
Failure and Reliability Prediction by Support Vector Machines Regression of Time Series Data
,”
Reliab. Eng. Syst. Saf.
,
96
(
11
), pp.
1527
1534
.10.1016/j.ress.2011.06.006
30.
Ji
,
J.
,
Zhang
,
C.
,
Gui
,
Y.
,
,
Q.
, and
Kodikara
,
J.
,
2017
, “
New Observations on the Application of LS-SVM in Slope System Reliability Analysis
,”
J. Comput. Civ. Eng.
,
31
(
2
), p.
06016002
.10.1061/(ASCE)CP.1943-5487.0000620
31.
Xiao
,
N.-C.
,
Zuo
,
M. J.
, and
Zhou
,
C.
,
2018
, “
A New Adaptive Sequential Sampling Method to Construct Surrogate Models for Efficient Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
169
, pp.
330
338
.10.1016/j.ress.2017.09.008
32.
Roussouly
,
N.
,
Petitjean
,
F.
, and
Salaun
,
M.
,
2013
, “
A New Adaptive Response Surface Method for Reliability Analysis
,”
Probab. Eng. Mech.
,
32
, pp.
103
115
.10.1016/j.probengmech.2012.10.001
33.
Song
,
H.
,
Choi
,
K. K.
,
Lee
,
I.
,
Zhao
,
L.
, and
Lamb
,
D.
,
2013
, “
Adaptive Virtual Support Vector Machine for Reliability Analysis of High-Dimensional Problems
,”
Struct. Multidiscip. Optim.
,
47
(
4
), pp.
479
491
.10.1007/s00158-012-0857-6
34.
Bect
,
J.
,
Ginsbourger
,
D.
,
Li
,
L.
,
Picheny
,
V.
, and
Vazquez
,
E.
,
2012
, “
Sequential Design of Computer Experiments for the Estimation of a Probability of Failure
,”
Stat. Comput.
,
22
(
3
), pp.
773
793
.10.1007/s11222-011-9241-4
35.
Zhan
,
Z.
,
Fu
,
Y.
, and
Yang
,
R.-J.
,
2014
, “
A Stochastic Bias Corrected Response Surface Method and Its Application to Reliability-Based Design Optimization
,”
SAE Int. J. Mater. Manuf.
,
7
(
2
), pp.
262
268
.10.4271/2014-01-0731
36.
Oberkampf
,
W. L.
, and
Barone
,
M. F.
,
2006
, “
Measures of Agreement Between Computation and Experiment: Validation Metrics
,”
J. Comput. Phys.
,
217
(
1
), pp.
5
36
.10.1016/j.jcp.2006.03.037
37.
Kennedy
,
M. C.
, and
O'Hagan
,
A.
,
2001
, “
Bayesian Calibration of Computer Models
,”
J. R. Stat. Soc.
,
63
(
3
), pp.
425
464
.10.1111/1467-9868.00294
38.
Xi
,
Z.
,
Fu
,
Y.
, and
Yang
,
R.
,
2013
, “
Model Bias Characterization in the Design Space Under Uncertainty
,”
Int. J. Performability Eng.
,
9
(
4
), pp.
433
444
.https://www.researchgate.net/publication/257992790_Model_bias_characterization_in_the_design_space_under_uncertainty
39.
Roy
,
C. J.
, and
Oberkampf
,
W. L.
,
2011
, “
A Comprehensive Framework for Verification, Validation, and Uncertainty Quantification in Scientific Computing
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
25–28
), pp.
2131
2144
.10.1016/j.cma.2011.03.016
40.
Wang
,
S.
,
Chen
,
W.
, and
Tsui
,
K.-L.
,
2009
, “
Bayesian Validation of Computer Models
,”
Technometrics
,
51
(
4
), pp.
439
451
.10.1198/TECH.2009.07011
41.
Shi
,
L.
, and
Lin
,
S.-P.
,
2016
, “
A New RBDO Method Using Adaptive Response Surface and First-Order Score Function for Crashworthiness Design
,”
Reliab. Eng. Syst. Saf.
,
156
, pp.
125
133
.10.1016/j.ress.2016.07.007
42.
Moon
,
M.-Y.
,
Choi
,
K.
,
Cho
,
H.
,
Gaul
,
N.
,
Lamb
,
D.
, and
Gorsich
,
D.
,
2017
, “
Reliability-Based Design Optimization Using Confidence-Based Model Validation for Insufficient Experimental Data
,”
ASME J. Mech. Des.
,
139
(
3
), p.
031404
.10.1115/1.4035679
43.
Jiang
,
Z.
,
Chen
,
W.
,
Fu
,
Y.
, and
Yang
,
R.-J.
,
2013
, “
Reliability-Based Design Optimization With Model Bias and Data Uncertainty
,”
SAE Int. J. Mater. Manuf.
,
6
(
3
), pp.
502
516
.10.4271/2013-01-1384
44.
Pan
,
H.
,
Xi
,
Z.
, and
Yang
,
R.-J.
,
2016
, “
Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization
,”
Struct. Multidiscip. Optim.
,
54
(
6
), pp.
1543
1556
.10.1007/s00158-016-1530-2
45.
Wang
,
Z.
, and
Wang
,
P.
,
2014
, “
A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design
,”
ASME J. Mech. Des.
,
136
(
2
), p.
021006
.10.1115/1.4026033
46.
Lee
,
I.
,
Choi
,
K. K.
,
Noh
,
Y.
,
Zhao
,
L.
, and
Gorsich
,
D.
,
2011
, “
Sampling-Based Stochastic Sensitivity Analysis Using Score Functions for RBDO Problems With Correlated Random Variables
,”
ASME J. Mech. Des.
,
133
(
2
), p.
021003
.10.1115/1.4003186
47.
Li
,
M.
, and
Wang
,
Z.
,
2018
, “
Confidence-Driven Design Optimization Using Gaussian Process Metamodeling With Insufficient Data
,”
ASME J. Mech. Des.
,
140
(
12
), p.
121405
.10.1115/1.4040985
48.
Xia
,
B.
,
,
H.
,
Yu
,
D.
, and
Jiang
,
C.
,
2015
, “
Reliability-Based Design Optimization of Structural Systems Under Hybrid Probabilistic and Interval Model
,”
Comput. Struct.
,
160
, pp.
126
134
.10.1016/j.compstruc.2015.08.009
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