Abstract
Electromagnetic optimization procedures require a large number of evaluations in numerical forward models. These computer models simulate complex problems through the use of numerical techniques, e.g. finite elements. Hence, the evaluations need a large computational time. Two-level methods such as space mapping have been developed that include a second model so as to accelerate the inverse procedures. Contrary to existing two-level methods, we propose a scheme that enables acceleration when the second model is based on the initial numerical model with coarse discretizations. This paper validates the proposed refined direct optimization method onto algebraic test functions. Moreover, we applied the methodology onto the geometrical optimization of the magnetic circuit of a switched reluctance motor. The obtained numerical results show the efficiency of the optimization algorithm with respect to the computational time and the accuracy.
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Mirzaeian B, Moallem M, Tahani V, Lucas C (2002) Multiobjective optimization method based on a genetic algorithm for switched reluctance motor design. IEEE Trans Magn 38:4605–4617
Wu W, Dunlop J, Collocott S, Kalan B (2003) Design optimization of a switched reluctance motor by electromagnetic and thermal finite-element analysis. IEEE Trans Magn 39:3334–3336
Vijayakumar K, Karthikeyan R, Paramasivam S, Arumugam R, Srinivas K (2008) Switched reluctance motor modeling, design, simulation, and analysis: a comprehensive review. IEEE Trans Magn 44:4605–4617
Bandler J, Biernacki R, Chen S, Grobelny P, Hemmers H (1994) Space mapping technique for electromagnetic optimization. IEEE Trans Microw Theory Tech 42:2536–2544
Bandler J, Cheng Q, Dakroury S, Mohamed A, Bakr M, Madsen K, Søndergaard J (2004) Space mapping: state of the art. IEEE Trans Microw Theory Tech 52:337–361
Echeverría D, Lahaye D, Encica L, Lomonova E, Hemker P, Vandenput A (2006) Manifold-Mapping optimization applied to linear actuator design. IEEE Trans Magn 42:1183–1186
Crevecoeur G, Sergeant P, Dupré L, Vande Walle R (2008) Two-level response and parameter mapping optimization for magnetic shielding. IEEE Trans Magn 44:301–308
Encica L, Echeverria D, Lomonova E, Vandenput AJA, Hemker P, Lahaye D (2007) Efficient optimal design of electromagnetic actuators using space mapping. Struct Multidisc Optim 33:481–491
Encica L, Paulides J, Lomonova E (2009) Space-mapping optimization in electromechanics: an overview of algorithms and applications. Compel Int J Comp Math Electrical Electron Eng 28:1216–1226
Crevecoeur G, Dupré L, Vande Walle R (2007) Space mapping optimization of the magnetic circuit of electrical machines including local material degradation. IEEE Trans Magn 43:2609–2611
Tran T, Brisset S, Brochet P (2007) Combinatorial and multi-level optimization of a safety isolating transformer. Int J Appl Electromagn Mech 3:201–208
Echeverría D (2007) Multi-level optimization: space mapping and manifold mapping. PhD thesis, Universiteit van Amsterdam.
Alexandrov N, Dennis JE, Lewis RM, Torczon V (1998) A trust region framework for managing the use of approximation models in optimization. Struct Optim 15:16–23
Booker A, Dennis JJ, Frank P, Serafini D, Torczon V, Trosset M (1999) A rigorous framework for optimization of expensive functions by surrogates. Struct Optim 17:1–13
Crevecoeur G, Sergeant P, Dupré L, Vande Walle R (2010) A two-level genetic algorithm for electromagnetic optimization. IEEE Trans Magn 46:2585–2595
Gorissen D, Crombecq K, Couckuyt I, Dhaene T, Demeester P (2010) A surrogate modeling and adaptive sampling toolbox for computer based design. J Mach Learn Res 11:2051–2055
Dyck D, Lowther DA, Malik Z, Spence R, Nelder J (1999) Response surface models of electromagnetic devices and their application to design. IEEE Trans Magn 34:1821–1824
Lebensztajn L, Maretto CAR, Costa L, Coulomb J-L (2004) Kriging: a useful tool for electromagnetic devices optimization. IEEE Trans Magn 40:1196–1199
Mullur A, Messac A (2006) Metamodeling using extended radial basis functions: a comparative approach. Eng Comput 21:203–217
Simpson T, Peplinski J, Koch P, Allen J (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17:129–150
Simpson T, Booker A, Ghosh D, Giunta A, Koch P, Yang R (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidiscip Optim 27:302–313
Lahaye D, Canova A, Gruosso G, Repetto M (2007) Adaptive manifold-mapping using multiquadratic interpolation applied to linear actuator design. Compel Int J Comput Math Elect Electron Eng 26:225–235
Karakasis MK, Giannakoglou KC (2006) On the use of metamodel-assisted, multi-objective evolutionary algorithms. Eng Optim 38:941–957
Couckuyt I, Declercq F, Dhaene T, Rogier H, Knockaert L (2010) Surrogate-based infill optimization applied to electromagnetic problems. Adv Design Optim Microw RF Circuits Syst 20:492–501
Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black-box functions. J Glob Optim 13:445–492
Shan S, Wang G (2010) Survey of modeling and optimization strategies to solve high-dimensional design problems with computationally-expensive black-box functions. Struct Multidiscip Optim 41:219–241
Grosso A, Jamali A, Locatelli M (2009) Finding maximin latin hypercube designs by Iterated Local Search heuristics. Eur J Oper Res 197:541–547
Sacks J, Welch WJ, Mitchell T, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–435
SQPLab available at: http://www-roc.inria.fr/gilbert/modulopt/optimization-routines/sqplab/sqplab.html
Moallem M, Dawson G (1998) An improved magnetic equivalent circuit method for predicting the characteristic of highly saturated electromagnetic devices. IEEE Trans Magn 34:3632–3635
Arkadan AA, Kielagas BW (1994) Switched reluctance motor drive system dynamic performance prediction and experimental verification. IEEE Trans Energy Convers 9:36–44
Miller T (2002) Optimal design of switched reluctance motors. IEEE Trans Ind Electron 49:15–27
Abdallh AA, Dupré L (2010) Local magnetic measurements in magnetic circuits with highly non-uniform electromagnetic fields. Meas Sci Technol 21:045109
Forrester AI, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerospace Sci 45:50–79
Coleman TF, Li Y (1996) An interior, trust region approach for nonlinear minimization subject to bounds. SIAM J Optim 6:418–445
Koziel S, Bandler JW, Madsen K (2008) Quality assessment of coarse models and surrogates for space mapping optimization. Optim Eng 9:375–391
Acknowledgments
This work was supported by the GOA project GOA07/GOA/006 and the IAP project IAP-P6/21. Ivo Couckuyt is funded by the Institute for the Promotion of Innovation through Science and Technology in Flanders (IWT-Vlaanderen). Guillaume Crevecoeur is a postdoctoral researcher of the FWO.
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Crevecoeur, G., Abdallh, A.AE., Couckuyt, I. et al. Two-level refined direct optimization scheme using intermediate surrogate models for electromagnetic optimization of a switched reluctance motor. Engineering with Computers 28, 199–207 (2012). https://doi.org/10.1007/s00366-011-0239-5
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DOI: https://doi.org/10.1007/s00366-011-0239-5