This paper proposes a shape parameterization method using a principal component analysis (PCA) for shape optimization. The proposed method is used as a preprocessing tool of parametric optimization algorithms, such as genetic algorithms (GAs) or response surface methods (RSMs). When these parametric optimization algorithms are used, the number of parameters should be small while the design space represented by the parameters should be able to represent a variety of shapes. In order to define the parameters, PCA is applied to shapes. In many industrial fields, a large amount of data of shapes and their performance is accumulated. By applying PCA to these shapes included in a database, important features of the shapes are extracted. A design space is defined by basis vectors which are generated from the extracted features. The number of dimensions of the design space is decreased without omitting important features. In this paper, each shape is discretized by a set of points and PCA is applied to it. A shape discretization method is also proposed and numerical examples are provided.

References

References
1.
Bendsoe
,
M. P.
, and
Kikuchi
,
N.
,
1988
, “
Generating Optimal Topologies in Structural Design Using a Homogenization Method
,”
Comput. Meth. Appl. Mech. Eng.
,
71
(
2
), pp.
197
224
.10.1016/0045-7825(88)90086-2
2.
Bendsoe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization
,
Springer-Verlag
,
Berlin
.
3.
Borrvall
,
T.
, and
Peterson
,
J.
,
2003
, “
Topology Optimization of Fluids in Stokes Flow
,”
Int. J. Numer. Methods Fluids
,
41
(1), pp.
77
107
.10.1002/fld.426
4.
Samareh
,
J. A.
,
1999
, “
A Survey of Shape Parameterization Techniques
,” CEAS/AIAA/ICASE/NASA Langley International Forum on Aeroelasticity and Structural Dynamics, NASA/CP-1999-209136, pp.
333
343
.
5.
Samareh
,
J. A.
,
2001
, “
A Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization
,”
AIAA J.
,
39
(
5
), pp.
877
884
.10.2514/2.1391
6.
Song
,
W.
, and
Keane
,
A. J.
,
2004
, “
A Study of Shape Parameterization Methods for Airfoil Optimization
,”
AIAA
Paper No. 2004–4482.10.2514/6.2004-4482
7.
Vucina
,
D.
,
Lozina
,
Z.
, and
Pehnec
,
I.
,
2008
, “
A Compact Parameterization for Shape Optimization of Aerofoils
,”
Proceedings of the World Congress on Engineering
, Vol.
1
, pp.
111
116
.
8.
Vanderplaats
,
G. N.
,
1979
, “
Approximation Concepts for Numerical Airfoil Optimization
,” NASA Technical Paper No. NASA TP-1370.
9.
Kulfan
,
B. M.
,
2007
, “
A Universal Parametric Geometry Representation Method–“CST”
,”
45th AIAA Aerospace Science Meeting and Exhibit
, AIAA–2007-0062.
10.
Berkhin
,
P.
,
2006
, “
A Survey of Clustering Data Mining Techniques
,”
Grouping Multidimensional Data
,
Springer
,
Berlin, Heidelberg
, pp.
25
71
.
11.
Oyama
,
A.
,
Nonomura
,
T.
, and
Hujii
,
K.
,
2010
, “
Data Mining of Parato-Optimal Transonic Airfoil Shapes Using Proper Orthogonal Decomposition
,”
J. Aircr.
,
47
(
5
), pp.
1756
1762
.10.2514/1.C000264
12.
Jeong
,
M.
,
Dennis
,
B. H.
, and
Yoshimura
,
S.
,
2005
, “
Multidimensional Clustering Interpretation and Its Application to Optimization of Coolant Passages of a Turbine Blade
,”
ASME J. Mech. Des.
,
127
(
2
), pp.
215
221
.10.1115/1.1830047
13.
Sirovich
,
L.
,
1987
, “
Turbulence and Dynamics of Coherent Structures Part 1: Coherent Structures
,”
Q. Appl. Math.
,
45
(
3
), pp.
561
571
.
14.
Drela
,
M.
,
1989
, “
XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils
,”
Lect. Notes Eng.
,
54
, pp.
1
12
.10.1007/978-3-642-84010-4
15.
Abbot
,
I. H.
, and
Von
Doenhoff
,
A. E.
,
1959
,
Theory of Wing Sections Including a Summary of Airfoil Data
,
Dover
,
New York
.
16.
Brittingham
,
R. A.
, and
Leylek
,
J. H.
,
2000
, “
A Detailed Analysis of Film Cooling Physics: Part IV–Compound-Angle Injection With Shaped Holes
,”
ASME J. Turbomach.
,
122
(1), pp.
133
145
.10.1115/1.555419
17.
Bunker
,
R. S.
,
2005
, “
A Review of Shaped Hole Turbine Film Cooling Technology
,”
ASME J. Heat Transfer
,
127
, pp.
441
453
.10.1115/1.1860562
18.
Heidmann
,
J. D.
,
2008
, “
A Numerical Study of Anti-Vortex Film Cooling Designs at High Blowing Ratio
,” NASA/TM-2008-215209, GT2008-50845.
19.
Lee
,
K. D.
, and
Kim
,
K. Y.
,
2010
, “
Shape Optimization of Fan-Shaped Hole to Enhance Film-Cooling Effectiveness
,” Int.
J. Heat Mass Transfer
,
53
(15–16), pp.
2996
3005
.10.1016/j.ijheatmasstransfer.2010.03.032
20.
Silieti
,
M.
,
Kassab
,
A. J.
, and
Divo
,
E.
,
2009
, “
Film Cooling Effectiveness: Comparison of Adiabatic and Conjugate Heat Transfer CFD Models
,” Int.
J. Transfer Sci.
,
48
, pp.
2237
2248
.10.1016/j.ijthermalsci.2009.04.007
21.
Okita
,
Y.
, and
Nishiura
,
M.
,
2007
, “
Film Effectiveness Performance of an Arrowhead-Shaped Film Cooling Hole Geometry
,”
ASME J. Turbomach.
,
129
(2), pp.
331
339
.10.1115/1.2437781
22.
Naik
,
S.
, and
Vogel
,
G.
,
2008
, “
Gas Turbine Airfoil With Leading Edge Cooling
,” U.S. Patent No. 7,997,866.
23.
Chatterjee
,
A.
,
2000
, “
An Introduction to the Proper Orthogonal Decomposition
,”
Curr. Sci.
,
78
(
7
), pp.
808
817
.
You do not currently have access to this content.