An Adaptive Optimization Algorithm Based on Kriging Interpolation with Spherical Model and its Application to Optimal Design of Switched Reluctance Motor

  • Xia, Bin ;
  • Ren, Ziyan ;
  • Zhang, Yanli ;
  • Koh, Chang-Seop
  • Received : 2012.08.02
  • Accepted : 2014.02.14
  • Published : 2014.09.01


In this paper, an adaptive optimization strategy utilizing Kriging model and genetic algorithm is proposed for the optimal design of electromagnetic devices. The ordinary Kriging assisted by the spherical covariance model is used to construct surrogate models. In order to improve the computational efficiency, the adaptive uniform sampling strategy is applied to generate sampling points in design space. Through several iterations and gradual refinement process, the global optimal point can be found by genetic algorithm. The proposed algorithm is validated by application to the optimal design of a switched reluctance motor, where the stator pole face and shape of pole shoe attached to the lateral face of the rotor pole are optimized to reduce the torque ripple.


Ordinary Kriging;Spherical covariance model;Surrogate model;Switched reluctance motor;Torque ripple


  1. J. J. M. Rijpkema, and L. F. P. Etman. "Using of design sensitivity information in response surface and Kriging metamodels," Optimization and Engineering, vol. 2, pp. 469-484, 2001.
  2. A. I. J. Forrester, and A. J. Keane, "Recent advances in surrogate-based optimization," Progress in Aerospace Sciences, vol. 45, no. 1, pp. 50-79, Jan. 2009.
  3. Y. L. Zhang, H. S. Yoon, P. S. Shin, and C. S. Koh, "A robust and computationally efficient optimal design algorithm of electromagnetic devices using adaptive response surface method," Journal of Electrical Engineering & Technology, vol. 3, no. 2, pp. 143-295, Jun., 2008.
  4. H. P. Liu, "Taylor Kriging for simulation metamodeling," Auburn, Auburn University, Dissertation, pp. 99-124, 2009.
  5. L. Wang, and D. A. Lowther, "Selection of approximation models for electromagnetic device optimization," IEEE Trans. Magn., vol. 42, no. 4, pp. 1227- 1230, Apr. 2006.
  6. D. K. Woo, I. W. Kim, and H. K. Jung, "Optimal rotor structure design of interior permanent magnet synchronous machine based on efficient genetic algorithm using Kriging model," Journal of Electrical Engineering & Technology, vol. 7, no. 4, pp. 530-537, 2012.
  7. Z. H. Wei, Z. F. Liu, and Q. Chen, "GA-based Kriging for isoline drawing," 2nd Conference on Environmental Science and Information Application Technology, 2010.
  8. Y. L. Zhang, and B. Xia, "Optimum design of switched reluctance motor to minimize torque ripple using ordinary Kriging model and genetic algorithm," International Conference on Electrical Machines and Systems (ICEMS2011), 2011.
  9. I. Husain, "Minimization of torque ripple in SRM drives," IEEE Trans. Ind. Electron., vol. 49, no. 1, pp. 28-39, 2002.
  10. Y. Ohdachi, Y. Kawase, Y. Miura, and Y. Hayashi, "Optimum design of switched reluctance motors using dynamic finite element analysis," IEEE Trans. Magn., vol. 41, no. 2, pp. 2033-2036, Mar, 1997.
  11. Y. K. Choi, H. S. Yoon, and C. S. Koh, "Pole shape optimization of a switched reluctance motor for torque ripple reduction," IEEE Trans. Magn., vol. 43, no. 4, pp. 1797-1800, 2007.

Cited by

  1. A New Surrogate-assisted Robust Multi-objective Optimization Algorithm for an Electrical Machine Design pp.2093-7423, 2019,
  2. A Novel 3-D Analytical Modeling Method of Trapezoidal Shape Permanent Magnet Halbach Array for Multi-objective Optimization vol.14, pp.2, 2019,


Supported by : NRF of Korea