Robust Optimization of Electromagnetic Design Using Stochastic Collocation Method
Keywords:
Monte Carlo Method, robust, Stochastic Collocation Method, TEAM 22, uncertaintyAbstract
The way to handle the uncertainty of design parameters has attracted wide attention in the optimization of electromagnetic designs. The Monte Carlo Method works well when dealing with uncertainties but it consumes too much time and computational resources. This paper proposes a computationally efficient way to achieve robust optimization based on Stochastic Collocation Method and the TEAM 22 problem is used as a verification example. It is demonstrated that the approach combining Stochastic Collocation Method and a genetic algorithm provides high computational efficiency, without losing accuracy compared with the Monte Carlo Method.
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H. Li, I. Hussain, Y. Wang, and Q. Cao, “Uncertainty analysis of reflection coefficient for a coating with random flaws using adaptive mesh and DGTD method,” Applied Computational Electromagnetics Society Journal, vol. 33, no. 5, 2018.
J. Bai, G. Zhang, L. Wang, and T. Wang, “Uncertainty analysis in EMC simulation based on improved method of moments,” Applied Computational Electromagnetics Society Journal, vol. 31, no. 1, 2016.
L. Codecasa, L. Di Rienzo, K. Weise, and J. Haueisen, “Uncertainty quantification in transcranial magnetic stimulation with correlation between tissue conductivities,” 2017 International Applied Computational Electromagnetics Society Symposium-Italy (ACES), IEEE, 2017.
J.-G. Lee, N.-W. Hwang, H.-R. Ryu, H.-K. Jung, and D.-K. Woo, “Robust optimization approach applied to permanent magnet synchronous motor,” IEEE Transactions on Magnetics, vol. 53, no. 6, pp. 1-4, 2017.
Z. Ren, S. He, D. Zhang, Y. Zhang, and C.-S. Koh, “A possibility-based robust optimal design algorithm in preliminary design stage of electromagnetic devices,” IEEE Transactions on Magnetics, vol. 52, no. 3, pp. 1-4, 2016.
G. Bramerdorfer, “Computationally efficient tolerance analysis of the cogging torque of brushless PMSMs,” IEEE Transactions on Industry Applications, vol. 53, no. 4, pp. 3387-3393, 2017.
G. Bramerdorfer, J. A. Tapia, J. Pyrhonen, and A. Cavagnino, “Modern electrical machine design optimization: Techniques, trends, and best practices,” IEEE Transactions on Industrial Electronics, 2018.
J. Jang, et al., “Space-time kriging surrogate model to consider uncertainty of time interval of torque curve for electric power steering motor,” IEEE Transactions on Magnetics, vol. 54, no. 3, pp. 1-4, 2018.
S. Xiao, Y. Li, M. Rotaru, and J. K. Sykulski, “Considerations of uncertainty in robust optimisation of electromagnetic devices,” International Journal of Applied Electromagnetics and Mechanics, vol. 46, no. 2, pp. 427-436, 2014.
G. Bramerdorfer and A.-C. Zăvoianu, “Surrogatebased multi-objective optimization of electrical machine designs facilitating tolerance analysis,” IEEE Transactions on Magnetics, vol. 53, no. 8, pp. 1-11, 2017.
B. Kang, K. Choi, and D-H. Kim, “An efficient serial-loop strategy for reliability-based robust optimization of electromagnetic design problems,” IEEE Transactions on Magnetics, vol. 54, no. 3, pp. 1-4, 2018.
J. Silly-Carette, D. Lautru, A. Gati, M. Wong, J. Wiart, and V. F. Hanna, “Determination of the uncertainty on the specific absorption rate using the stochastic collocation method and the FDTD,” in 2008 IEEE Antennas and Propagation Society International Symposium, pp. 1-4, 2008.
J. Silly-Carette, D. Lautru, M. Wong, A. Gati, J. Wiart, and V. F. Hanna, “Variability on the propagation of a plane wave using stochastic collocation methods in a bio electromagnetic application,” IEEE Microwave and Wireless Components Letters, vol. 19, no. 4, pp. 185-187, 2009.
Z. Zubac, D. D. Zutter, and D. V. Ginste, “Scattering from two-dimensional objects of varying shape combining the method of moments with the stochastic Galerkin method,” IEEE Transactions on Antennas and Propagation, vol. 62, no. 9, pp. 4852-4856, 2014.
P. Manfredi, D. D. Zutter, and D. V. Ginste, “The relationship between Galerkin and collocation methods in statistical transmission line analysis,” in 2016 IEEE 25th Conference on Electrical Performance of Electronic Packaging And Systems (EPEPS), pp. 35-38, 2016.
D. Poljak, S. Šesnić, M. Cvetković, S. Lallechere, and K. E. K. Drissi, “On some applications of stochastic collocation method in computational electromagnetics: Applications in ground penetrating radar, bioelectromagnetics, grounding systems and buried lines,” in 2016 24th International Conference on Software, Telecommunications and Computer Networks (SoftCOM), pp. 1-5, 2016.
G. L. Soares, R. L. S. Adriano, C. A. Maia, L. Jaulin, and J. A. Vasconcelos, “Robust multiobjective TEAM 22 problem: A case study of uncertainties in design optimization,” IEEE Transactions on Magnetics, vol. 45, no. 3, pp. 1028-1031, 2009.
Z. Ren, C. Park, and C.-S. Koh, “Numerically efficient algorithm for reliability-based robust optimal design of TEAM problem 22,” IEEE Transactions on Magnetics, vol. 50, no. 2, pp. 661- 664, 2014.
A. Pierquin, S. Brisset, T. Henneron, and S. Clénet, “Optimization of the TEAM 22 problem using POD-EIM reduced model,” in 2016 IEEE Conference on Electromagnetic Field Computation (CEFC), pp. 1-1, 2016.
Z. Wang, W. Che, and L. Zhou, “Uncertainty analysis of the rational function model used in the complex permittivity measurement of biological tissues using PMCT probes within a wide microwave frequency band,” Progress In Electromagnetics Research, 90, pp. 137-150, 2009.
U. C. Hasar, et al., “Application of a useful uncertainty analysis as a metric tool for assessing the performance of electromagnetic properties retrieval methods of bianisotropic metamaterials,” Progress In Electromagnetics Research, 128, pp. 365-380, 2012.
B. Jinjun, Z. Gang, and W. Lixin, Uncertainty Analysis in EMC Simulation Based on Stochastic Collocation Method. 2015.
L. Teckentrup, P. Jantsch, C. G. Webster, and M. Gunzburger, “A multilevel stochastic collocation method for partial differential equations with random input data,” SIAM/ASA Journal on Uncertainty Quantification, vol. 3, no. 1, pp. 1046- 1074, 2015.
L. Ma, D. Z. Feng, and J. He, “Reduced-dimension clutter suppression method for airborne multipleinput multiple-output radar based on three iterations,” Radar Sonar & Navigation Iet, vol. 9, no. 3, pp. 249-254, 2015.
