Abstract

Reliability-based design (RBD) employs optimization to identify design variables that satisfy the reliability requirement. For many routine component design jobs that do not need optimization, however, RBD may not be applicable, especially for those design jobs which are performed manually or with a spreadsheet. This work develops a modified RBD approach to component design so that the reliability target can be achieved by conducting traditional component design repeatedly using a deterministic safety factor. The new component design is based on the first-order reliability method (FORM), which iteratively assigns the safety factor during the design process until the reliability requirement is satisfied. In addition to several iterations of deterministic component design, the other additional work is the calculation of the derivatives of the design margin with respect to the random input variables. The proposed method can be used for a wide range of component design applications. For example, if a deterministic component design is performed manually or with a spreadsheet, so is the reliability-based component design. Three examples are used to demonstrate the practicality of the new design method.

References

1.
Ramu
,
P.
,
Qu
,
X.
,
Youn
,
B.
,
Haftka
,
R.
, and
Choi
,
K.
,
2004
, “
Safety Factor and Inverse Reliability Measures
,”
Proceedings of the 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference
,
Palm Springs, CA
,
Apr. 19–22
, p.
1670
.
2.
Wu
,
Y. T.
,
Shin
,
Y.
,
Sues
,
R.
, and
Cesare
,
M.
,
2001
, “
Safety-Factor Based Approach for Probability-Based Design Optimization
,”
Proceedings of the 19th AIAA Applied Aerodynamics Conference
,
Anaheim, CA
,
June 11–14
, p.
1522
.
3.
Stahl
,
B.
, and
Banon
,
H.
,
2002
, “
Fatigue Safety Factors for Deepwater Risers
,”
Proceedings of the ASME 21st International Conference on Offshore Mechanics and Arctic Engineering
,
Oslo, Norway
,
June 23–28
,
American Society of Mechanical Engineers Digital Collection
, pp.
349
355
.
4.
Mischke
,
C.
,
1970
, “
A Method of Relating Factor of Safety and Reliability
,”
ASME J. Eng. Ind.
,
92
(
3
), pp.
537
541
. 10.1115/1.3427803
5.
Qu
,
X.
, and
Haftka
,
R.
,
2003
, “
Reliability-Based Design Optimization Using Probabilistic Safety Factor
,”
Proceedings of the 44th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
,
Norfolk, VA
,
Apr. 7–10
, p.
1657
.
6.
Bilionis
,
I.
, and
Zabaras
,
N.
,
2012
, “
Multi-Output Local Gaussian Process Regression: Applications to Uncertainty Quantification
,”
J. Comput. Phys.
,
231
(
17
), pp.
5718
5746
. 10.1016/j.jcp.2012.04.047
7.
Allen
,
M.
, and
Maute
,
K.
,
2004
, “
Reliability-Based Design Optimization of Aeroelastic Structures
,”
Struct. Multidiscipl. Optim.
,
27
(
4
), pp.
228
242
. 10.1007/s00158-004-0384-1
8.
Du
,
X.
,
Guo
,
J.
, and
Beeram
,
H.
,
2008
, “
Sequential Optimization and Reliability Assessment for Multidisciplinary Systems Design
,”
Struct. Multidiscipl. Optim.
,
35
(
2
), pp.
117
130
. 10.1007/s00158-007-0121-7
9.
Du
,
X.
,
Sudjianto
,
A.
, and
Huang
,
B.
,
2005
, “
Reliability-Based Design With the Mixture of Random and Interval Variables
,”
ASME J. Mech. Des.
,
127
(
6
), pp.
1068
1076
. 10.1115/1.1992510
10.
Chen
,
X.
,
Hasselman
,
T.
,
Neill
,
D.
,
Chen
,
X.
,
Hasselman
,
T.
, and
Neill
,
D.
,
1997
, “
Reliability Based Structural Design Optimization for Practical Applications
,”
Proceedings of the 38th Structures, Structural Dynamics, and Materials Conference
,
Kissimmee, FL
,
Apr. 7–10
, p.
1403
.
11.
Agarwal
,
H.
,
2004
,
Reliability Based Design Optimization: Formulations and Methodologies
,
Doctoral dissertation
,
University of Notre Dame
.
12.
Youn
,
B. D.
, and
Wang
,
P.
,
2008
, “
Bayesian Reliability-Based Design Optimization Using Eigenvector Dimension Reduction (Edr) Method
,”
Struct. Multidiscipl. Optim.
,
36
(
2
), pp.
107
123
. 10.1007/s00158-007-0202-7
13.
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
14.
Huang
,
H. Z.
,
Zhang
,
X.
,
Liu
,
Y.
,
Meng
,
D.
, and
Wang
,
Z.
,
2012
, “
Enhanced Sequential Optimization and Reliability Assessment for Reliability-Based Design Optimization
,”
J. Mech. Sci. Technol.
,
26
(
7
), pp.
2039
2043
. 10.1007/s12206-012-0511-7
15.
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
16.
Tu
,
J.
,
Choi
,
K. K.
, and
Park
,
Y. H.
,
1999
, “
A New Study on Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
121
(
4
), pp.
557
564
. 10.1115/1.2829499
17.
Hu
,
Z.
, and
Du
,
X.
,
2019
, “
Efficient Reliability-Based Design With Second Order Approximations
,”
Eng. Optim.
,
51
(
1
), pp.
101
119
. 10.1080/0305215X.2018.1440292
18.
Moustapha
,
M.
, and
Sudret
,
B.
,
2019
, “
Surrogate-Assisted Reliability-Based Design Optimization: A Survey and a Unified Modular Framework
,”
Struct. Multidiscipl. Optim.
,
60
, pp.
2157
2176
. 10.1007/s00158-019-02290-y
19.
Rocchetta
,
R.
,
Crespo
,
L. G.
, and
Kenny
,
S. P.
,
2020
, “
A Scenario Optimization Approach to Reliability-Based Design
,”
Reliab. Eng. Syst. Saf.
,
196
, p.
106755
. 10.1016/j.ress.2019.106755
20.
Chaudhuri
,
A.
,
Kramer
,
B.
, and
Willcox
,
K. E.
,
2020
, “
Information Reuse for Importance Sampling in Reliability-Based Design Optimization
,”
Reliab. Eng. Syst. Saf.
,
201
, p.
106853
. 10.1016/j.ress.2020.106853
21.
Cui
,
T.
,
Allison
,
J. T.
, and
Wang
,
P.
,
2020
, “
A Comparative Study of Formulations and Algorithms for Reliability-Based Co-Design Problems
,”
ASME J. Mech. Des.
,
142
(
3
), p.
031104
. 10.1115/1.4045299
22.
Zang
,
T. A.
,
2002
,
Needs and Opportunities for Uncertainty-Based Multidisciplinary Design Methods for Aerospace Vehicles
,
National Aeronautics and Space Administration, Langley Research Center
,
Hampton, VA
.
23.
Du
,
X.
,
2008
, “
Unified Uncertainty Analysis by the First Order Reliability Method
,”
ASME J. Mech. Des.
,
130
(
9
), p.
091401
. 10.1115/1.2943295
24.
Zhao
,
Y. G.
, and
Ono
,
T.
,
1999
, “
A General Procedure for First/Second-Order Reliabilitymethod (Form/Sorm)
,”
Struct. Saf.
,
21
(
2
), pp.
95
112
. 10.1016/S0167-4730(99)00008-9
25.
Maier
,
H. R.
,
Lence
,
B. J.
,
Tolson
,
B. A.
, and
Foschi
,
R. O.
,
2001
, “
First-Order Reliability Method for Estimating Reliability, Vulnerability, and Resilience
,”
Water Resour. Res.
,
37
(
3
), pp.
779
790
. 10.1029/2000WR900329
26.
Abumeri
,
G.
,
Abdi
,
F.
,
Baker
,
M.
,
Triplet
,
M.
, and
Griffin
,
J.
,
2007
, “
Reliability Based Design of Composite Over-Wrapped Tanks
,”
No. 0148-7191, SAE Technical Paper
.
27.
Cao
,
L.
,
Yao
,
C.
, and
Wu
,
H.
,
2016
, “
Reliability Optimal Design of B-Pillar in Side Impact
,”
No. 0148-7191, SAE Technical Paper
.
28.
Youn
,
B. D.
,
Choi
,
K.
,
Yang
,
R. J.
, and
Gu
,
L.
,
2004
, “
Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact
,”
Struct. Multidiscipl. Optim.
,
26
(
3–4
), pp.
272
283
. 10.1007/s00158-003-0345-0
29.
Hoffman
,
R. M.
,
Sudjianto
,
A.
,
Du
,
X.
, and
Stout
,
J.
,
2003
, “
Robust Piston Design and Optimization Using Piston Secondary Motion Analysis
,”
No. 0148-7191, SAE Technical Paper
.
30.
Yi
,
P.
,
Zhu
,
Z.
, and
Gong
,
J.
,
2016
, “
An Approximate Sequential Optimization and Reliability Assessment Method for Reliability-Based Design Optimization
,”
Struct. Multidiscipl. Optim.
,
54
(
6
), pp.
1367
1378
. 10.1007/s00158-016-1478-2
31.
Li
,
F.
,
Wu
,
T.
,
Badiru
,
A.
,
Hu
,
M.
, and
Soni
,
S.
,
2013
, “
A Single-Loop Deterministic Method for Reliability-Based Design Optimization
,”
Eng. Optim.
,
45
(
4
), pp.
435
458
. 10.1080/0305215X.2012.685071
32.
Lim
,
J.
, and
Lee
,
B.
,
2016
, “
A Semi-Single-Loop Method Using Approximation of Most Probable Point for Reliability-Based Design Optimization
,”
Struct. Multidiscipl. Optim.
,
53
(
4
), pp.
745
757
. 10.1007/s00158-015-1351-8
33.
Jeong
,
S. B.
, and
Park
,
G. J.
,
2017
, “
Single Loop Single Vector Approach Using the Conjugate Gradient in Reliability Based Design Optimization
,”
Struct. Multidiscipl. Optim.
,
55
(
4
), pp.
1329
1344
. 10.1007/s00158-016-1580-5
34.
Choi
,
S. H.
,
Lee
,
G.
, and
Lee
,
I.
,
2018
, “
Adaptive Single-Loop Reliability-Based Design Optimization and Post Optimization Using Constraint Boundary Sampling
,”
J. Mech. Sci. Technol.
,
32
(
7
), pp.
3249
3262
. 10.1007/s12206-018-0627-5
35.
Rao
,
S. S.
,
1992
,
Reliability-Based Design
,
McGraw-Hill Companies
,
New York
.
36.
Dolinski
,
K.
,
1982
, “
First-Order Second-Moment Approximation in Reliability of Structural Systems: Critical Review and Alternative Approach
,”
Struct. Saf.
,
1
(
3
), pp.
211
231
. 10.1016/0167-4730(82)90027-3
37.
Elishakoff
,
I.
,
Van Manen
,
S.
, and
Arbocz
,
J.
,
1987
, “
First-Order Second-Moment Analysis of the Buckling of Shells With Random Imperfections
,”
AIAA J.
,
25
(
8
), pp.
1113
1117
. 10.2514/3.9751
38.
Lee
,
T. W.
, and
Kwak
,
B. M.
,
1987
, “
A Reliability-Based Optimal Design Using Advanced First Order Second Moment Method
,”
J. Struct. Mech.
,
15
(
4
), pp.
523
542
. 10.1080/08905458708905132
39.
Cederbaum
,
G.
,
Elishakoff
,
I.
, and
Librescu
,
L.
,
1990
, “
Reliability of Laminated Plates Via the First-Order Second-Moment Method
,”
Compos. Struct.
,
15
(
2
), pp.
161
167
. 10.1016/0263-8223(90)90005-Y
40.
Lin
,
S.
, and
Kam
,
T.
,
2000
, “
Probabilistic Failure Analysis of Transversely Loaded Laminated Composite Plates Using First-Order Second Moment Method
,”
J. Eng. Mech.
,
126
(
8
), pp.
812
820
. 10.1061/(ASCE)0733-9399(2000)126:8(812)
41.
Hasofer
,
A. M.
, and
Lind
,
N. C.
,
1974
, “
Exact and Invariant Second-Moment Code Format
,”
J. Eng. Mech. Div.
,
100
(
1
), pp.
111
121
.
42.
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
43.
Cornell
,
C. A.
,
1969
, “
A Probability-Based Structural Code
,”
Proc. J. Proc.
,
66
(
12
), pp.
974
985
.
44.
Du
,
X.
, and
Chen
,
W.
,
2001
, “
A Most Probable Point-Based Method for Efficient Uncertainty Analysis
,”
J. Des. Manuf. Autom.
,
4
(
1
), pp.
47
66
. 10.1080/15320370108500218
45.
Echard
,
B.
,
Gayton
,
N.
, and
Lemaire
,
M.
,
2011
, “
AK-MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation
,”
Struct. Saf.
,
33
(
2
), pp.
145
154
. 10.1016/j.strusafe.2011.01.002
46.
Zhu
,
Z.
, and
Du
,
X.
,
2016
, “
Reliability Analysis With Monte Carlo Simulation and Dependent Kriging Predictions
,”
ASME J. Mech. Des.
,
138
(
12
), p.
121403
. 10.1115/1.4034219
47.
Isukapalli
,
S.
,
Roy
,
A.
, and
Georgopoulos
,
P.
,
1998
, “
Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems
,”
Risk Anal.
,
18
(
3
), pp.
351
363
. 10.1111/j.1539-6924.1998.tb01301.x
48.
Wu
,
H.
,
Zhu
,
Z.
, and
Du
,
X.
,
2020
, “
System Reliability Analysis With Autocorrelated Kriging Predictions
,”
ASME J. Mech. Des.
,
142
(
10
), p.
101702
. 10.1115/1.4046648
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