Journal of Electrical Engineering and Technology

The Korean Institute of Electrical Engineers (대한전기학회)
권호 표지
DOI QR코드

DOI QR Code

A New Sensitivity-Based Reliability Calculation Algorithm in the Optimal Design of Electromagnetic Devices

  • Ren, Ziyan (College of Electrical and Computer Engineering, Chungbuk National University) ;
  • Zhang, Dianhai (College of Electrical and Computer Engineering, Chungbuk National University) ;
  • Koh, Chang Seop (College of Electrical and Computer Engineering, Chungbuk National University)
  • Received : 2011.06.07
  • Accepted : 2012.11.12
  • Published : 2013.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

A new reliability calculation method is proposed based on design sensitivity analysis by the finite element method for nonlinear performance constraints in the optimal design of electromagnetic devices. In the proposed method, the reliability of a given design is calculated by using the Monte Carlo simulation (MCS) method after approximating a constraint function to a linear one in the confidence interval with the help of its sensitivity information. The validity and numerical efficiency of the proposed sensitivity-assisted MCS method are investigated by comparing its numerical results with those obtained by using the conventional MCS method and the first-order reliability method for analytic functions and the TEAM Workshop Problem 22.

Keywords

References

  1. Z. Y. Ren, M. T. Pham, M. H. Song, D. H. Kim, and C. S. Koh, "A robust global optimization algorithm of electromagnetic devices utilizing gradient index and multi-objective optimization method," IEEE Trans. Magn., Vol. 47, No. 5, pp. 1254-1257, May. 2011. https://doi.org/10.1109/TMAG.2010.2080664
  2. X. Jiang, H. J. Li, and H. P. Long, "Reliability-based robust optimization design for cantilever structure," in Proceedings of 2nd IEEE ICISE Conference, Hangzhou, China, pp. 1402-1404, Dec., 2010.
  3. B. D. Youn, and K. K. Choi, "Selecting probabilistic approaches for reliability-based design optimization," AIAA Journal, Vol. 42, No. 1, pp. 124-131, Jan., 2004. https://doi.org/10.2514/1.9036
  4. K. Deb, S. Gupta, D. Daum, J. Branke, A. K. Mall, and D. Padmanabhan, "Reliability-based optimization using evolutionary algorithms," IEEE Trans. Evol. Comput., Vol. 13, No. 5, pp. 1054-1073, Oct., 2009. https://doi.org/10.1109/TEVC.2009.2014361
  5. Z. P. Mourelatos and J. H. Liang, "A methodology for trading-off performance and robustness under uncertainty," ASME J. Mech., Vol. 128, pp. 856-863, 2006. https://doi.org/10.1115/1.2202883
  6. V. Cavaliere, M. Cioffi, A. Formisano, and R. Martone, "Robust design of high field magnets through Monte Carlo analysis," COMPEL, Vol. 22, No. 3, pp. 589- 602, 2003. https://doi.org/10.1108/03321640310475056
  7. I. Lee, K. K. Choi, and L. Zhao, "Sampling-based RBDO using the stochastic sensitivity analysis and dynamic Kriging method," Struct Multidisc Optim, Vol. 44, pp. 299-317, 2011. https://doi.org/10.1007/s00158-011-0659-2
  8. Y. K. Lee, and D. S. Hwang, "A study on the techniques of estimating the probability of failure," J. Chungcheong Mathematical Society, Vol. 21, No. 4, pp. 573-583, Dec., 2008.
  9. N. D. Lagaros, V. Plevris, and M. Papadrakakis, "Multiobjective design optimization using cascade evolutionary computations," Comput. Methods Appl. Mechanics Eng., Vol. 194, No. 30-33, pp. 3496-3515, 2005. https://doi.org/10.1016/j.cma.2004.12.029
  10. M. Rosenblatt, "Remarks on a multivariate transformation," The Annals of Mathematical Statistics, Vol. 23, No. 3, pp. 470-472, Sep., 1952. https://doi.org/10.1214/aoms/1177729394
  11. Y. G. Zhao, M. ASCE, and Z. H. Lu, "Fourth-moment standardization for structural reliability assessment," J. Struct. Eng., pp. 916-924, July, 2007.
  12. A. M. Hasofer, and N. C. Lind, "Exact and invariant second-moment code format," ASCE J. Eng. Mechanics Division, Vol. 100, pp. 111-121, 1974.
  13. K. Bae, S. Wang, K. K. Choi, "Reliability-based topology optimization," In: AIAA 2002-5542, 9th AIAA/ISSMO Symposium on multidisciplinary Analysis and Optimization, USA, 4-6, Sept., 2002.
  14. J. S. Ryu, Y. Y. Yao, C. S. Koh, S. Yoon, and D. S. Kim, "Optimal shape design of 3-D nonlinear electromagnetic devices using parameterized design sensitivity analysis," IEEE Trans. Magn., Vol. 41, No. 5, pp. 1792-1795, May, 2005. https://doi.org/10.1109/TMAG.2005.845982
  15. P. G. Alotto, U. Baumgartner, F. Freschi, M. Jaindl, A. Kostinger, Ch. Magele, and W. Repetto, "SMES optimization Benchmark: TEAM workshop problem 22". Available: http://www.igte.tugraz.at/team 22.
  16. R. H. C. Takahashi, J. A. Vasconcelos, J. A. Ramirez, and L. Krahenbuhl, "A multiobjective methodology for evaluating genetic operators," IEEE Trans. Magn., Vol. 39, No. 3, pp. 1321-1324, May, 2003. https://doi.org/10.1109/TMAG.2003.810371
  17. G. Steiner, A. Weber, and C. Magele, "Managing uncertainties in electromagnetic design problems with robust optimization," IEEE Trans. Magn., Vol. 40, No. 2, pp. 1094-1099, Mar., 2004. https://doi.org/10.1109/TMAG.2004.824556
  18. P. Alotto, U. Baumgartner, F. Freschi, M. Jaindl, A. Kostinger, Ch. Magele, W. Renhart, and M. Reoetto, "SMES optimization benchmark extended: introducing pareto optimal solutions into TEAM22," IEEE Trans. Magn., Vol. 44, No. 6, pp. 1066-1069, Jun., 2008. https://doi.org/10.1109/TMAG.2007.916091

Cited by

  1. Numerically Efficient Algorithm for Reliability-Based Robust Optimal Design of TEAM Problem 22 vol.50, pp.2, 2014, https://doi.org/10.1109/TMAG.2013.2285929
  2. Optimal Design of Inverse Electromagnetic Problems with Uncertain Design Parameters Assisted by Reliability and Design Sensitivity Analysis vol.19, pp.3, 2014, https://doi.org/10.4283/JMAG.2014.19.3.266
  3. Investigation of reliability analysis algorithms for effective reliability-based optimal design of electromagnetic devices vol.10, pp.1, 2016, https://doi.org/10.1049/iet-smt.2014.0368
  4. A New Reliability Analysis Method Combining Adaptive Kriging With Weight Index Monte Carlo Simulation vol.54, pp.3, 2018, https://doi.org/10.1109/TMAG.2017.2763198
  5. A Novel 3-D Analytical Modeling Method of Trapezoidal Shape Permanent Magnet Halbach Array for Multi-objective Optimization vol.14, pp.2, 2019, https://doi.org/10.1007/s42835-019-00109-w