3D Shape Optimization of Nonlinear Electromagnetic Device Using Parameterized Sensitivity Analysis

매개화된 민감도 해석에 의한 비선형 전자소자의 3차원 형상최적화

  • ;
  • Yingying Yao (College of EE, Zhejiang University, CHIN) ;
  • 류재섭 (충북대 대학원 전기공학과) ;
  • ;
  • 고창섭 (충북대 전기전자컴퓨터 공학부)
  • Published : 2004.08.01


In this paper, a 3D shape optimization algorithm which guarantees a smooth optimal shape is presented using parameterized sensitivity analysis. The design surface is parameterized using Bezier spline and B-spline, and the control points of the spline are taken as the design variables. The parameterized sensitivity for the control points are found from that for nodal points. The design sensitivity and adjoint variable formulae are also derived for the 3D non-linear problems. Through an application to the shape optimization of 3D electromagnet to get a uniform magnetic field, the effectiveness of the proposed algorithm is shown.


  1. J. A. Ramirez, E. M. Freeman, C. Cat-uthai, D. A. Lowther, 'Sensitivity Analysis for the Automatic Shape Design of Electromagnetic Devices in 3D Using FEM,' IEEE Trans. on Magn., vol. 33, pp. 1856-1859, 1997 https://doi.org/10.1109/20.582644
  2. 류재섭, 고창섭, 윤소남, '매개화된 민감도 해석에 의한 3차원 비선형 모델의 형상 최적화', 대한전기학회 하계학술대회논문집 B권, pp. 915-917, 2003
  3. I. H. Park, B. T. Lee, S. Y. Hahn, 'Design sensitivity analysis for nonlinear magnetostatic problems using finite element method', IEEE Trans. on Magn., Vol.28, No.2, pp. 1533-1536, 1992 https://doi.org/10.1109/20.123989
  4. Y. Yingying, C. S. Koh, and X. Dexin, '3D shape optimization of electromagnetic devices including eddy currents by using design sensitivity analysis,' IEEE CEFC 2002, Perugia, Italy, pp. 292, June 16-19, 2002
  5. K. Weeber and S. R. H. Hoole, 'Geometric Parameterization and Constrained Optimization Techniques in the Design of Salient Pole Synchronous Machines,' IEEE Trans. on Magn., vol. 28, pp. 1948-1960, 1992 https://doi.org/10.1109/20.144753
  6. S. Subramaniarn, A. A. Arkadan, and S. R. H. Hoole, 'Optimization of a Magnetic Pole Face Using Linear Constraints to Avoid Jagged Contours,' IEEE Trans. on Magn., vol. 30, pp. 3455-3458, 1994 https://doi.org/10.1109/20.312682
  7. 이향범, 박일한, 한송엽, '설계변수 매개화를 이용한 전기기기 최적설계,' 대한전기학회 논문지, Vol, 50B, No. 11, pp. 546-555, 2001
  8. H. B. Lee, I. H. Park, and S. Y. Hahn, 'Optimum shape design of electro-magnetic devices by Bezier spline parameterization of sensitivity,' IEEE CEFC 2002, Perugia, Italy, pp. 21, June 16-19, 2002
  9. K. Weeber and S. R. H. Hoole, 'A Structural Mapping Technique for Geometric Parameterization in the Optimization of Magnetic Devices', International Journal for Numerical Methods in Engineering, vol.33, pp. 2145-2179, 1992 https://doi.org/10.1002/nme.1620331010
  10. Yingying Yao, 고창섭, Dexin Xie, '전자소자의 형상최적화를 위한 3차원 요소의 재생성법', 대한전기학회 하계학술대회논문집 B권, pp. 841-843, 2002
  11. O. C. Zienkiewicz, The Finite Element Method, McGraw-Hill, 1977
  12. 강병길, 류재섭, 고창섭, 'FEM을 이용한 3-D 비선형 정자계 모델의 해석.' 대한전기학회 추계학술대회 논문집 B권, pp. 324-326, 2000
  13. D. F. Rogers and J. A. Adams, Mathematical Elements for Computer Graphics, McGraw-Hill, 1990
  14. David F. Rogers, An Intorduction to NURBS: With Historical Persopective, Morgan Kaufmann Publishers, 2001