The response surface method (RSM) and the moving least squares method (MLSM) are extensively used due to their computational efficiency in solving reliability based design optimization (RBDO) problems. Since traditional RSM and MLSM are described by second-order polynomials, approximated constraints are sometimes unable to ensure feasibility when highly nonlinear and/or nonconvex constraint functions are approximated in RBDO. We explore the development of a new MLSM based meta-model that ensures the constraint feasibility of an optimal solution in RBDO. A constraint-feasible MLSM (CF-MLSM) is devised to realize feasibility regardless of the multimodality/nonlinearity of the constraint function in all approximation processes as well as the variation of random characteristics in RBDO. The usefulness of the proposed approach is verified by examining a nonlinear function problem and an actively controlled structure problem.

References

References
1.
Haftka
,
R. T.
, and
Gürdal
,
Z.
, 1991,
Elements of structural optimization
,
Kluwer Academic Publishers
,
Dordrecht
.
2.
Enevoldsen
,
I.
, and
Sorensen
,
J. D.
, 1994, “
Reliability-Based Optimization in Structural Engineering
,”
Struct. Saf.
,
15
(
3
), pp.
169
196
.
3.
Yu
,
X.
,
Choi
,
K. K.
, and
Chang
,
K. H.
,1997,
A Mixed Design Approach for Probabilistic Structural Durability
,”
Struct. Multidiscip. Optim.
,
14
(
2–3
), pp.
81
90
.
4.
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
.
5.
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
.
6.
Rais-Rohani
,
M.
, and
Singh
,
M. N.
, 2004, “
Comparison of Global and Local Response Surface Techniques in Reliability-Based Optimization of Composite Structures
,”
Struct. Multidiscip. Optim.
,
26
(
5
), pp.
333
345
.
7.
Youn
,
B. D.
, and
Choi
,
K. K.
, 2004, “
A New Response Surface Methodology for Reliability-Based Design Optimization, Computers, and Structures
,” 82(2), pp.
241
256
.
8.
Yeun
,
Y. S.
,
Kim
,
B. J.
,
Yang
,
Y. S.
, and
Ruy
,
W. S.
, 2005, “
Polynomial Genetic Programming for Response Surface Modeling Part 2: Adaptive Approximate Models With Probabilistic Optimization Problems
,”
Struct. Multidiscip. Optim.
,
29
(
1
), pp.
35
49
.
9.
Song
,
C. Y.
, and
Lee
,
J.
, 2009, “
Strength Design of Knuckle Component Using Moving Least Squares Response Surface Based Approximate Optimization Methods
,”
Proc. Inst. Mech. Eng., Part D (J. Automob. Eng.)
,
223
(
8
), pp.
1019
1032
.
10.
Song
,
C. Y.
, and
Lee
,
J.
, 2011, “
A Realization of Constraint Feasibility in a Moving Least Squares Response Surface Based Approximate Optimization
,”
Comput. Optim. Appl.
,
50
(
1
), pp.
163
188
.
11.
Picheny
,
V.
,
Kim
,
N. H.
, and
Haftka
,
R. T.
, 2008, “
Conservative Predictions Using Surrogate Modeling
,”
49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
, Schaumburg, AIAA–2008– 1716, IL.
12.
Kim
,
C.
, and
Choi
,
K. K.
, 2008, “
Reliability-Based Design Optimization Using Response Surface Method With Prediction Interval Estimation
,”
ASME J. Mech. Des.
,
130
(
12
),
121401
.
13.
Lancaster
,
P.
, and
Salkauskas
,
K.
, 1986,
Curve and Surface Fitting: An Introduction
,
Academic
,
New York
.
14.
Shewry
,
M.
, and
Wynn
,
H.
, 1987, “
Maximum Entropy Sampling
,”
J. Appl. Stat.
,
14
(
2
), pp.
165
170
.
15.
Sacks
,
J.
,
Schiller
,
S. B.
, and
Welch
,
W. J.
, 1989, “
Designs for Computer Experiments
,”
Statist. Sci.
,
4
(
4
), pp.
409
423
.
16.
Wolfe
,
P.
, 1961, “
A Duality Theorem for Nonlinear Programming
,”
Q. Appl. Math.
,
19
, pp.
239
244
.
17.
Mangasarian
,
O. L.
, 1969,
Nonlinear Programming
,
McGraw-Hill
,
New York
.
18.
Belegundu
,
A. D.
, and
Chandrupatla
,
T. R.
, 1999,
Optimization Concept and Applications in Engineering
,
Prentice-Hall
,
New Jersey
.
19.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
, 1986,
Methods of Structural Safety
,
Prentice-Hall
,
New Jersey
.
20.
Myers
,
R. H.
, and
Montgomery
,
D. C.
, 1995,
Response Surface Methodology: Process and Product Optimization Using Designed Experiments
,
Wiley
,
New York
.
21.
Sobieszczanski-Sobieski
,
J.
,
Bloebaum
,
C. L.
,
Hajela
,
P.
, 1991, “
Sensitivity of Control-Augmented Structures Obtained by a System Decomposition Method
,”
AIAA J.
,
29
(
2
), pp.
264
270
.
22.
Lee
,
J.
, and
Hajela
,
P.
, 1997, “
GA’s in Decomposition Based Design-Subsystem Interactions Through Immune Network Simulation
,”
Struct. Multidiscip. Optim.
,
14
(
4
), pp.
248
255
.
23.
Lawrence
,
C. T.
, and
Tits
,
A. L.
, 2001, “
A Computationally Efficient Feasible Sequential Quadratic Programming Algorithm
,”
SIAM J. Control Optim.
,
11
(
4
), pp.
1092
1118
.
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