基于模拟退火与Levenberg-Marquardt混合算法的Energetic磁滞模型参数提取
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摘要
利用Energetic磁滞模型进行磁滞特性模拟的首要任务在于模型参数的精确快速辨识。该文针对现有Energetic磁滞模型参数提取方法存在的收敛速度慢、求解精度低的问题,提出一种基于模拟退火(simulated annealing,SA)算法与Levenberg-Marquardt(L-M)混合算法的Energetic模型参数提取方法,其综合SA算法全局搜索能力强,以及L-M算法局部收敛速度快的优点。在混合算法迭代初期,采用SA算法快速锁定全局最优解所在区域;而后,根据引入的普适性混合算法切换过渡准则,将SA算法当前最优解赋予L-M算法;针对基于传统L-M算法提取Energetic模型参数出现的病态矩阵问题,该文将该模型参数的灵敏度函数矩阵进行归一化处理,从而推导出适用于Energetic模型参数快速提取的归一化L-M算法。归一化L-M算法在接收到SA算法提供的最优解后,将其作为初始值,快速收敛于全局最优解。仿真及实验结果表明,该文所提混合算法同时具有收敛速度快、提取精度高的优异性能,可实现Energetic模型参数的准确快速辨识。
The primary task of using the Energetic hysteresis model to simulate the hysteresis characteristics is the accurate and rapid identification of the model parameters. In view of the slow convergence rate and low accuracy of existing parameter extraction methods of Energetic model, a hybrid algorithm of simulated annealing(SA) and LevenbergMarquardt(L-M) was proposed, and it combined the strong global search ability of SA algorithm and the fast local convergence of L-M algorithm. In the initial iteration of hybrid algorithm, SA algorithm was used to quickly lock the global optimal solution region. Then, according to the introduction of universal switched hybrid algorithm transition criterion, SA algorithm's optimal solution was transferred to the L-M algorithm. Aiming at the problem of ill conditioned matrix that appeared in the process of Energetic model parameter extraction based on traditional L-M algorithm, the sensitivity matrix of the function was normalized so as to obtain the normalized L-M algorithm which was suitable for the fast parameter extraction of Energetic model parameters. After receiving the optimal solution provided by SA, the normalized L-M algorithm quickly converged to the global optimal solution. The simulation and experimental results show that the proposed hybrid algorithm has the advantages of fast convergence and high accuracy, and it can be used to accurately and quickly identify the parameters of Energetic model.
The primary task of using the Energetic hysteresis model to simulate the hysteresis characteristics is the accurate and rapid identification of the model parameters. In view of the slow convergence rate and low accuracy of existing parameter extraction methods of Energetic model, a hybrid algorithm of simulated annealing(SA) and LevenbergMarquardt(L-M) was proposed, and it combined the strong global search ability of SA algorithm and the fast local convergence of L-M algorithm. In the initial iteration of hybrid algorithm, SA algorithm was used to quickly lock the global optimal solution region. Then, according to the introduction of universal switched hybrid algorithm transition criterion, SA algorithm's optimal solution was transferred to the L-M algorithm. Aiming at the problem of ill conditioned matrix that appeared in the process of Energetic model parameter extraction based on traditional L-M algorithm, the sensitivity matrix of the function was normalized so as to obtain the normalized L-M algorithm which was suitable for the fast parameter extraction of Energetic model parameters. After receiving the optimal solution provided by SA, the normalized L-M algorithm quickly converged to the global optimal solution. The simulation and experimental results show that the proposed hybrid algorithm has the advantages of fast convergence and high accuracy, and it can be used to accurately and quickly identify the parameters of Energetic model.
引文
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[3]Beatrice C,Dobák S,Ferrara E,et al.Broadband magnetic losses of nanocrystalline ribbons and powder cores[J].Journal of Magnetism and Magnetic Materials,2016,420:317-323.
[4]Fulmek P,Haumer P,Wegleiter H,et al.Energetic model of ferromagnetic hysteresis[J].COMPEL-International Journal of Computations and Mathematics in ElectricalInt J Comput Math Electr Electron Eng,2010,29(6):1504-1513.
[5]Ibrahim M,Pillay P.A hybrid model for improved hysteresis loss prediction in electrical machine[J].IEEETransactions on Industry Applications,2014,50(4):2503-2511.
[6]Ibrahim M,Pillay P.Core loss prediction in electrical machine laminations considering skin effect and minor hysteresis loops[J].IEEE Transactions on Industry Applications,2013,49(5):2061-2068.
[7]Zhang Yu,Pillay P,Ibrahim M,et al.Magnetic characteristics and core losses in machine laminations:high-frequency loss prediction from low-frequency measurements[J].IEEE Transactions on Industry Applications,2012,48(2):623-629.
[8]Hauser H.Energetic model of ferromagnetic hysteresis[J].Journal of Applied Physics,1994,75(5):2584-2597.
[9]Hauser H.Energetic model of ferromagnetic hysteresis 2:magnetization calculations of(110)[001]FeSi sheets by statistic domain behavior[J].Journal of Applied Physics,1995,77(6):2625-2633.
[10]Hauser H.Energetic model of ferromagnetic hysteresis:isotropic magnetization[J].Journal of Applied Physics,2004,96(5):2753-2767.
[11]Zhang Yu,Cheng M C,Pillay P.A novel hysteresis core loss model for magnetic laminations[J].IEEETransactions on Energy Conversion,2011,26(4):993-999.
[12]Hamimid M,Mimoune S M,Feliachi M.Dynamic formulation for energetic model compared with hybrid magnetic formulation of ferromagnetic hysteresis[J].International Journal of Numerical Modelling:Electronic Networks,Devices and Fields,2017,30(6):1-5.
[13]Drago G,Manella A,Nervi M,et al.A combined strategy for optimization in non linear magnetic problems using simulated annealing and search techniques[J].IEEETransactions on Magnetics,1992,28(2):1541-1544.
[14]Nocedal J,Wright S J.Numerical optimization[M].New York:Springer,2006.
[15]Li Cunbin,Ding Jia,Pan Zhangyi.Transmission model of risk elements neural network in entropy system based on simulated annealing[J].Journal of Industrial and Production Engineering,2017,34(5):375-381.
[16]袁澎,艾芊,赵媛媛.基于改进的遗传-模拟退火算法和误差度分析原理的PMU多目标优化配置[J].中国电机工程学报,2014,34(13):2178-2187.Yuan Peng,Ai Qian,Zhao Yuanyuan.Research on multi-objective optimal PMU placement based on error analysis theory and improved GASA[J].Proceedings of the CSEE,2014,34(13):2178-2187(in Chinese).
[17]Vasconcelos J A,Saldanha R R,Krahenbuhl L,et al.Genetic algorithm coupled with a deterministic method for optimization in electromagnetics[J].IEEE Transactions on Magnetics,1997,33(2):1860-1863.
[18]Vasin V V,Perestoronina G Y.The Levenberg-Marquardt method and its modified versions for solving nonlinear equations with application to the inverse gravimetry problem[J].Proceedings of the Steklov Institute of Mathematics,2013,280(S1):174-182.
[19]Fan Jinyan,Pan Jianyu.A note on the LevenbergMarquardt parameter[J].Applied Mathematics and Computation,2009,207(2):351-359.
[20]Wikipedia.Levenberg-Marquardt algorithm[EB/OL].https://en.wikipedia.org/wiki/LevenbergMarquardt_algorithm.
[21]严正,范翔,赵文恺,等.自适应Levenberg-Marquardt方法提高潮流计算收敛性[J].中国电机工程学报,2015,35(8):1909-1918.Yan Zheng,Fan Xiang,Zhao Wenkai,et al.Improving the convergence of power flow calculation by a selfadaptive Levenberg-Marquardt method[J].Proceedings of the CSEE,2015,35(8):1909-1918(in Chinese).
[22]Trigeassou J C,Poinot T,Moreau S.A methodology for estimation of physical parameters[J].Systems Analysis Modelling Simulation,2003,43(7):925-943.