Research Papers: Design Automation

A Shape Parameterization Method Using Principal Component Analysis in Applications to Parametric Shape Optimization

[+] Author and Article Information
Kazuo Yonekura

Numerical Engineering Department,
R&D Technology Center,
IHI Corporation,
Yokohama 235-8501, Japan
e-mail: kazuo_yonekura@ihi.co.jp

Osamu Watanabe

Numerical Engineering Department,
R&D Technology Center,
IHI Corporation,
Yokohama 235-8501, Japan
e-mail: osamu_watanabe@ihi.co.jp

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 12, 2012; final manuscript received May 16, 2014; published online October 20, 2014. Assoc. Editor: Shinji Nishiwaki.

J. Mech. Des 136(12), 121401 (Oct 20, 2014) (7 pages) Paper No: MD-12-1607; doi: 10.1115/1.4028273 History: Received December 12, 2012; Revised May 16, 2014

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.

Copyright © 2014 by ASME
Topics: Shapes
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Fig. 1

The flow chart of the method

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Fig. 2

Discretization of a shape

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Fig. 3

Examples of grid on nonsimply connected shape. (a) Example of nonsimply connected shape. (b) Example of grid on surface (a)

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Fig. 4

Original geometries. (a) NACA2415, CL = 0.7022, CD = 0.00731, (b) NACA4415, CL = 0.9182, CD = 0.00919, (c) NACA23012, CL = 0.9011, CD = 0.00795, (d) NACA631-412, CL = 0.9681, CD = 0.0077, (e) NACA641-412, CL = 0.8755, CD = 0.008, and (f) NACA651-212, CL = 0.6989, CD = 0.00747.

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Fig. 5

Discretization of 2D-airfoil

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Fig. 6

Average vector and 1–4th basis vectors

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Fig. 7

Contribution ratio of basis vectors of airfoil shapes

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Fig. 8

The objective values CL and CD of original shapes and generated shapes

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Fig. 9

The selected optimal shape: (CL/CD = 181.9)

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Fig. 10

Reference shapes of a cooling hole problem

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Fig. 11

An example of structural grid on a cooling hole

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Fig. 12

An example of inserting additional surface on shape (m)

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Fig. 13

Contribution ratio of basis vectors of a cooling hole problem

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Fig. 14

Examples of generated holes

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Fig. 15

The objective values of a circular hole, generated shapes, and the selected shape

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Fig. 16

The selected optimal shape



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