In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

References

References
1.
Schuëller
,
G.
, and
Jensen
,
H.
, 2008, “
Computational Methods in Optimization Considering Uncertainties—An Overview
,”
Comput. Methods Appl. Mech. Eng.
,
198
, pp.
2
13
.
2.
Nilsena
,
T.
, and
Aven
,
T.
, 2003, “
Models and Model Uncertainty in the Context of Risk Analysis
,”
Reliab. Eng. Syst. Saf.
,
79
, pp.
309
17
.
3.
Byeng
,
D.
,
Kyung
,
K.
,
Liu
,
D.
, and
David
,
G.
, 2007, “
Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty
,”
ASME J. Mech. Des.
,
129
, pp.
876
882
.
4.
Bae
,
H.
,
Grandhi
,
R.
, and
Canfield
,
R.
, 2004, “
Epistemic Uncertainty Quantification Techniques Including Evidence Theory for Large-Scale Structures
,”
Comput. Struct.
,
82
, pp.
1101
1112
.
5.
Ben-Haim
,
Y.
, 2004, “
Uncertainty, Probability and Information-Gaps
,”
Reliab. Eng. Syst. Saf.
,
85
, pp.
249
266
.
6.
Ben-Haim
,
Y.
, 2006,
Info-Gap Decision Theory: Decisions Under Severe Uncertainty
,
2nd ed.
,
Academic Press
,
London
.
7.
Klir
,
G.
, 2004, “
Generalized Information Theory: Aims, Results, and Open Problems
,”
Reliab. Eng. Syst. Saf.
,
85
, pp.
21
38
.
8.
Klir
,
G.
, 2006,
Uncertainty and Information: Foundations of Generalized Information Theory
,
John Wiley and Sons
,
New Jersey
.
9.
Rackwitz
,
R.
, 2001, “
Reliability Analysis—A Review and Some Perspectives
,”
Struct. Safety
,
23
, pp.
365
95
.
10.
Chiralaksanakul
,
A.
, and
Mahadevan
,
S.
, 2005, “
First-Order Approximation Methods in Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
127
, pp.
851
857
.
11.
Tu
,
J.
,
Choi
,
K.
, and
Park
,
Y.
, 2001, “
Design Potential Method for Robust System Parameter Design
,”
AIAA J.
,
39
, pp.
667
677
.
12.
Huang
,
B.
, and
Du
,
X.
, 2008, “
Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation
,”
Reliab. Eng. Syst. Saf.
,
93
, pp.
325
336
.
13.
Li
,
H.
, and
Foschi
,
R.
, 1998, “
An Inverse Reliability Method and Its Application
,”
Struct. Safety
,
20
, pp.
257
270
.
14.
Tu
,
J
,
Choi
,
K.
, and
Young
,
H.
, 1999, “
A New Study on Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
121
, pp.
557
564
.
15.
Lombardi
,
M.
, and
Haftka
,
R.
, 1998, “
Anti-Optimization Technique for Structural Design Under Load Uncertainties
,”
Comput. Methods Appl. Mech. Eng.
,
157
, pp.
19
31
.
16.
Wu
,
Y.
,
Shin
,
Y.
,
Sues
,
R.
, and
Cesare
,
M.
, 2001, “
Safety-Factor Based Approach for Probability-Based Design Optimization
,”
Proceedings of the 42nd AIAA/ASME/ASC/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit
, Seattle, Washington.
17.
Nguyen
,
T.
,
Song
,
J.
, and
Paulino
,
G.
, 2010, “
Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications
,”
ASME J. Mech. Des.
,
132
, pp.
1
11
.
18.
Du
,
X.
,
Sudjianto
,
A.
, and
Huang
,
B.
, 2005, “
Reliability-Based Design With the Mixture of Random and Interval Variables
,”
ASME J. Mech. Des.
,
127
, pp.
1068
1076
.
19.
Ge
,
R.
,
Chen
,
J.
, and
Wei
,
J.
, 2008, “
Reliability–Based Design of Composites Under the Mixed Uncertainties and the Optimization Algorithm
,”
Acta Mech Solida Sinica
,
21
, pp.
19
27
.
20.
Beyer
,
H.
, and
Sendhoff
,
B.
, 2007, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
3190
3218
.
21.
Au
,
F.
,
Cheng
,
Y.
,
Tham
,
L.
, and
Zeng
,
G.
, 2003, “
Robust Design of Structures Using Convex Models
,”
Comput. Struct.
,
81
, pp.
2611
2619
.
22.
Wei
,
J.
, and
Chen
,
J.
, 2008, “
Fuzzy Robust Design of FRP Laminates
,”
J. Compos. Mater.
,
42
, pp.
211
23
.
23.
Parkinson
,
A.
,
Sorensen
,
C.
, and
Pourhassan
,
N.
, 1993, “
A General Approach for Robust Optimal Design
,”
ASME J. Mech. Des.
,
115
, pp.
74
80
.
24.
Du
,
X.
, and
Chen
,
W.
, 2000, “
Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design
,”
ASME J. Mech. Des.
,
122
, pp.
385
394
.
25.
Sundaresan
,
S.
,
Ishii
,
K.
, and
Houser
,
D.
, 1993, “
A Robust Optimization Procedure With Variations on Design Variables and Constraints
,”
Adv. Des. Autom.
,
69
, pp.
379
86
.
26.
Yu
,
J.
, and
Ishii
,
K.
, 1998, “
Design for Robustness Based on Manufacturing Variation Patterns
,”
ASME J. Mech. Des.
,
120
, pp.
196
202
.
27.
Mourelatos
,
Z.
, and
Liang
,
J.
, 2006, “
A Methodology for Trading-Off Performance and Robustness Under Uncertainty
,”
ASME J. Mech. Des.
,
128
, pp.
856
863
.
28.
Du
,
X.
,
Sudjianto
,
A.
, and
Chen
,
W.
, 2004, “
An Integrated Framework for Optimization Under Uncertainty Using Inverse Reliability Strategy
,”
ASME J. Mech. Des.
,
126
, pp.
562
570
.
29.
Du
,
X.
, and
Chen
,
W.
, 2004, “
Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design
,”
ASME J. Mech. Des.
,
126
, pp.
225
33
.
30.
Zhou
,
J.
, and
Mourelatos
,
Z.
, 2008, “
A Sequential Algorithm for Possibility-Based Design Optimization
,”
ASME J. Mech. Des.
,
130
, pp.
1
10
.
31.
Takewaki
,
I.
, and
Ben-Haim
,
Y.
, 2005, “
Info-Gap robust Design With Load and Model Uncertainties
,”
J. Sound Vib.
,
288
, pp.
551
570
.
32.
Yang
,
D.
, and
Yi
,
P.
, 2009, “
Chaos Control of Performance Measure Approach for Evaluation of Probabilistic Constraints
,”
Struct. Multidiscip. Optim.
,
38
, pp.
83
92
.
33.
Aoues
,
Y.
, and
Chateauneuf
,
A.
, 2010, “
Benchmark Study of Numerical Methods for Reliability-Based Design Optimization
,”
Struct. Multidiscip. Optim.
,
41
, pp.
277
294
.
You do not currently have access to this content.