DOI: 10.1115/1.4028273. A Shape Parameterization Method Using Principal Component Analysis in Applications to Parametric Shape Optimization

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

10.1115/1.4028273

Crossref journal-article

ASME International

Journal of Mechanical Design (33)

Abstract

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.

Bibliography

Yonekura, K., & Watanabe, O. (2014). A Shape Parameterization Method Using Principal Component Analysis in Applications to Parametric Shape Optimization. Journal of Mechanical Design, 136(12).

Authors 2

Kazuo Yonekura (first)
Osamu Watanabe (additional)

References 23 Referenced 19

10.1016/0045-7825(88)90086-2 / Comput. Meth. Appl. Mech. Eng. / Generating Optimal Topologies in Structural Design Using a Homogenization Method (1988)
{'volume-title': 'Topology Optimization', 'year': '2003', 'key': '2019100615160377700_B2'} / Topology Optimization (2003)
10.1002/fld.426 / Int. J. Numer. Methods Fluids / Topology Optimization of Fluids in Stokes Flow (2003)
{'first-page': '333', 'article-title': 'A Survey of Shape Parameterization Techniques', 'year': '1999', 'key': '2019100615160377700_B4'} / A Survey of Shape Parameterization Techniques (1999)
10.2514/2.1391 / AIAA J. / A Survey of Shape Parameterization Techniques for High-Fidelity Multidisciplinary Shape Optimization (2001)
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 (10.2514/6.2004-4482)
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.
{'year': '1979', 'key': '2019100615160377700_B8', 'article-title': 'Approximation Concepts for Numerical Airfoil Optimization'} / Approximation Concepts for Numerical Airfoil Optimization (1979)
Kulfan, B. M., 2007, “A Universal Parametric Geometry Representation Method–“CST”,” 45th AIAA Aerospace Science Meeting and Exhibit, AIAA–2007-0062. (10.2514/6.2007-62)
10.1007/3-540-28349-8_2 / Grouping Multidimensional Data / A Survey of Clustering Data Mining Techniques (2006)
10.2514/1.C000264 / J. Aircr. / Data Mining of Parato-Optimal Transonic Airfoil Shapes Using Proper Orthogonal Decomposition (2010)
10.1115/1.1830047 / ASME J. Mech. Des. / Multidimensional Clustering Interpretation and Its Application to Optimization of Coolant Passages of a Turbine Blade (2005)
10.1090/qam/910462 / Q. Appl. Math. / Turbulence and Dynamics of Coherent Structures Part 1: Coherent Structures (1987)
10.1007/978-3-642-84010-4_1 / Lect. Notes Eng. / XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils (1989)
{'volume-title': 'Theory of Wing Sections Including a Summary of Airfoil Data', 'year': '1959', 'key': '2019100615160377700_B15'} / Theory of Wing Sections Including a Summary of Airfoil Data (1959)
10.1115/1.555419 / ASME J. Turbomach. / A Detailed Analysis of Film Cooling Physics: Part IV–Compound-Angle Injection With Shaped Holes (2000)
10.1115/1.1860562 / ASME J. Heat Transfer / A Review of Shaped Hole Turbine Film Cooling Technology (2005)
{'year': '2008', 'key': '2019100615160377700_B18', 'article-title': 'A Numerical Study of Anti-Vortex Film Cooling Designs at High Blowing Ratio'} / A Numerical Study of Anti-Vortex Film Cooling Designs at High Blowing Ratio (2008)
10.1016/j.ijheatmasstransfer.2010.03.032 / J. Heat Mass Transfer / Shape Optimization of Fan-Shaped Hole to Enhance Film-Cooling Effectiveness (2010)
{'key': '2019100615160377700_B20', 'first-page': '2237', 'article-title': 'Film Cooling Effectiveness: Comparison of Adiabatic and Conjugate Heat Transfer CFD Models', 'volume': '48', 'year': '2009', 'journal-title': 'J. Transfer Sci.'} / J. Transfer Sci. / Film Cooling Effectiveness: Comparison of Adiabatic and Conjugate Heat Transfer CFD Models (2009)
10.1115/1.2437781 / ASME J. Turbomach. / Film Effectiveness Performance of an Arrowhead-Shaped Film Cooling Hole Geometry (2007)
Naik, S., and Vogel, G., 2008, “Gas Turbine Airfoil With Leading Edge Cooling,” U.S. Patent No. 7,997,866.
{'issue': '7', 'key': '2019100615160377700_B23', 'first-page': '808', 'article-title': 'An Introduction to the Proper Orthogonal Decomposition', 'volume': '78', 'year': '2000', 'journal-title': 'Curr. Sci.'} / Curr. Sci. / An Introduction to the Proper Orthogonal Decomposition (2000)

Dates

Type	When
Created	11 years ago (Aug. 12, 2014, 8:34 a.m.)
Deposited	5 years, 10 months ago (Oct. 6, 2019, 11:16 a.m.)
Indexed	3 weeks, 3 days ago (July 30, 2025, 10:09 a.m.)
Issued	10 years, 10 months ago (Oct. 20, 2014)
Published	10 years, 10 months ago (Oct. 20, 2014)
Published Online	10 years, 10 months ago (Oct. 20, 2014)
Published Print	10 years, 8 months ago (Dec. 1, 2014)

Funders 0

None

BibTeX

@article{Yonekura_2014, title={A Shape Parameterization Method Using Principal Component Analysis in Applications to Parametric Shape Optimization}, volume={136}, ISSN={1528-9001}, url={http://dx.doi.org/10.1115/1.4028273}, DOI={10.1115/1.4028273}, number={12}, journal={Journal of Mechanical Design}, publisher={ASME International}, author={Yonekura, Kazuo and Watanabe, Osamu}, year={2014}, month=oct }

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