基于人工鱼群与Levenberg-Marquardt混合算法的Jiles-Atherton磁滞模型参数提取
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摘要
准确高效地提取J-A磁滞模型参数,是利用该模型模拟磁性元件磁滞特性的首要任务。针对现有J-A模型参数提取方法存在的求解精度低且仿真耗时的问题,提出了一种基于人工鱼群算法与L-M算法混合的J-A模型参数辨识方法。首先,根据人工鱼群算法全局搜索能力强的特点,将其运用于J-A模型参数全局最优解所在区域的定位当中;在满足切换过渡准则后,人工鱼群算法终止迭代并切换至L-M算法;此时,L-M算法利用其局部寻优能力强的优势,将人工鱼群算法提供的最优解作为初始值,快速收敛于全局最优解。仿真及实验结果表明,所提混合算法不仅求解精度较高,同时收敛速度更快。
Accurately and efficiently extraction of Jiles-Atherton(J-A) hysteresis model parameters is the premise to use this model to simulate hysteresis characteristics of magnetic components. To solve the problem of low accuracy and time consuming in parameter extraction of existing J-A models, this paper proposed a new identification method of J-A model parameters on the basis of artificial fish swarm algorithm(AFSA) and Levenberg-Marquardt(L-M) algorithm. Firstly, because of strong global searching ability, the AFSA was applied to the region of the global optimal solution. If the switching transition criterion is satisfied, the iteration of the AFSA terminates, and the hybrid algorithm switches to the L-M algorithm. Meanwhile, with strong local searching ability, the L-M algorithm adopts the optimal solution provided by the AFSA as the initial value and quickly converges to the global optimal solution. The simulation and experiment show that the proposed hybrid algorithm not only has high precision, but also has faster convergence.
Accurately and efficiently extraction of Jiles-Atherton(J-A) hysteresis model parameters is the premise to use this model to simulate hysteresis characteristics of magnetic components. To solve the problem of low accuracy and time consuming in parameter extraction of existing J-A models, this paper proposed a new identification method of J-A model parameters on the basis of artificial fish swarm algorithm(AFSA) and Levenberg-Marquardt(L-M) algorithm. Firstly, because of strong global searching ability, the AFSA was applied to the region of the global optimal solution. If the switching transition criterion is satisfied, the iteration of the AFSA terminates, and the hybrid algorithm switches to the L-M algorithm. Meanwhile, with strong local searching ability, the L-M algorithm adopts the optimal solution provided by the AFSA as the initial value and quickly converges to the global optimal solution. The simulation and experiment show that the proposed hybrid algorithm not only has high precision, but also has faster convergence.
引文
[1] JILES D C, THOELKE J B, DEVINE M K. Numerical determination of hysteresis parameters for the modeling of magnetic properties using the theory of ferromagnetic hysteresis[J]. IEEE Transactions on Magnetics, 1992, 28(1):27-35.
[2] CHWASTEK K, SZCZYGłOWSKI 【math50z】. Modelling dynamic hysteresis loops in steel sheets[J]. Compel International Journal for Computation & Mathematics in Electrical & Electronic Engineering, 2009, 28(3): 603-612.
[3] 王洋, 刘志珍. 基于Jiles-Atherton磁滞理论的直流偏磁下铁心损耗预测[J]. 中国电机工程学报, 2017, 37(1):313-322.WANG Y, LIU Z Z. Prediction of core loss under DC bias based on Jiles-Atherton hysteresis theory[J]. Proceedings of the CSEE, 2017, 37(1):313-322.
[4] LI H, LI Q, XU X B, et al. A modified method for Jiles-Atherton hysteresis model and its application in numerical simulation of devices involving magnetic materials[J]. IEEE Transactions on Magnetics, 2011, 47(5): 1094-1097.
[5] JILES D C,THOELKE J B. Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops[J]. IEEE Transactions on Magnetics, 1989, 25(5): 3928-3930.
[6] 李贞,李庆民,李长云,等. J-A磁化建模理论的质疑与修正方法研究[J]. 中国电机工程学报, 2011, 31(3):124-131.LI Z, LI Q M, LI C Y, et al. Query and correction method of J-A magnetization modeling theory[J]. Proceedings of the CSEE, 2011, 31(3):124-131.
[7] MARION R, SCORRETTI R, SIAUVE N, et al. Identification of Jiles-Atherton model parameters using particle swarm optimization[J]. IEEE Transactions on Magnetics, 2008, 44(6): 894-897.
[8] FULGINEI F R, SALVINI A. Softcomputing for the identification of the Jiles-Atherton model parameters [J]. IEEE Transactions on Magnetics, 2005, 41(3): 1100-1108.
[9] CHWASTEK K, SZCZYGłOWSKI J. Identification of a hysteresis model parameters with genetic algorithms[J]. Mathematics and Computers in Simulation, 2006, 71(3): 206-211.
[10] 耿超,王丰华,苏磊,等. 基于人工鱼群与蛙跳混合算法的变压器Jiles-Atherton模型参数辨识[J]. 中国电机工程学报,2015,35(18):4799-4807.GENG C, WANG F H, LI L, et al. Parameter identification of Jiles-Atherton model for transformer based on artificial fish swarm and shuffled frog leaping algorithm[J]. Proceedings of the CSEE, 2015,35(18):4799-4807.
[11] VASIN VV, PERESTORONINA GY. 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(1): 174-182.
[12] BAGHEL A P S, RAM B S, CHWASTEK K, et al. Hysteresis modelling of GO laminations for arbitrary in-plane directions taking into account the dynamics of orthogonal domain walls[J]. Journal of Magnetism & Magnetic Materials, 2016, 418:14-20.
[13] JILES D C, ATHERTON D L. Theory of ferromagnetic hysteresis[J]. Journal of Magnetism and Magnetic Materials, 1986, 61(1): 48-60.
[14] GUAN X, YIN Y X. An improved artificial fish swarm algorithm and its application[J]. Advanced Materials Research, 2012, 433-440:4434-4438.
[15] 王洋,刘志珍. 基于蛙跳模糊算法的Jiles-Atherton铁心磁滞模型参数确定[J]. 电工技术学报,2017,32(4):154-161.WANG Y, LIU Z Z. Parameter determination of Jiles-Atherton core hysteresis model based on frog leaping fuzzy algorithm[J]. Transactions of China Electrotechnical Society, 2017,32(4):154-161.
[16] FAN J Y,PAN J Y.A note on the Levenberg- Marquardt parameter[J]. Applied Mathematics and Computation, 2009, 207(2): 351-359.
[2] CHWASTEK K, SZCZYGłOWSKI 【math50z】. Modelling dynamic hysteresis loops in steel sheets[J]. Compel International Journal for Computation & Mathematics in Electrical & Electronic Engineering, 2009, 28(3): 603-612.
[3] 王洋, 刘志珍. 基于Jiles-Atherton磁滞理论的直流偏磁下铁心损耗预测[J]. 中国电机工程学报, 2017, 37(1):313-322.WANG Y, LIU Z Z. Prediction of core loss under DC bias based on Jiles-Atherton hysteresis theory[J]. Proceedings of the CSEE, 2017, 37(1):313-322.
[4] LI H, LI Q, XU X B, et al. A modified method for Jiles-Atherton hysteresis model and its application in numerical simulation of devices involving magnetic materials[J]. IEEE Transactions on Magnetics, 2011, 47(5): 1094-1097.
[5] JILES D C,THOELKE J B. Theory of ferromagnetic hysteresis: determination of model parameters from experimental hysteresis loops[J]. IEEE Transactions on Magnetics, 1989, 25(5): 3928-3930.
[6] 李贞,李庆民,李长云,等. J-A磁化建模理论的质疑与修正方法研究[J]. 中国电机工程学报, 2011, 31(3):124-131.LI Z, LI Q M, LI C Y, et al. Query and correction method of J-A magnetization modeling theory[J]. Proceedings of the CSEE, 2011, 31(3):124-131.
[7] MARION R, SCORRETTI R, SIAUVE N, et al. Identification of Jiles-Atherton model parameters using particle swarm optimization[J]. IEEE Transactions on Magnetics, 2008, 44(6): 894-897.
[8] FULGINEI F R, SALVINI A. Softcomputing for the identification of the Jiles-Atherton model parameters [J]. IEEE Transactions on Magnetics, 2005, 41(3): 1100-1108.
[9] CHWASTEK K, SZCZYGłOWSKI J. Identification of a hysteresis model parameters with genetic algorithms[J]. Mathematics and Computers in Simulation, 2006, 71(3): 206-211.
[10] 耿超,王丰华,苏磊,等. 基于人工鱼群与蛙跳混合算法的变压器Jiles-Atherton模型参数辨识[J]. 中国电机工程学报,2015,35(18):4799-4807.GENG C, WANG F H, LI L, et al. Parameter identification of Jiles-Atherton model for transformer based on artificial fish swarm and shuffled frog leaping algorithm[J]. Proceedings of the CSEE, 2015,35(18):4799-4807.
[11] VASIN VV, PERESTORONINA GY. 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(1): 174-182.
[12] BAGHEL A P S, RAM B S, CHWASTEK K, et al. Hysteresis modelling of GO laminations for arbitrary in-plane directions taking into account the dynamics of orthogonal domain walls[J]. Journal of Magnetism & Magnetic Materials, 2016, 418:14-20.
[13] JILES D C, ATHERTON D L. Theory of ferromagnetic hysteresis[J]. Journal of Magnetism and Magnetic Materials, 1986, 61(1): 48-60.
[14] GUAN X, YIN Y X. An improved artificial fish swarm algorithm and its application[J]. Advanced Materials Research, 2012, 433-440:4434-4438.
[15] 王洋,刘志珍. 基于蛙跳模糊算法的Jiles-Atherton铁心磁滞模型参数确定[J]. 电工技术学报,2017,32(4):154-161.WANG Y, LIU Z Z. Parameter determination of Jiles-Atherton core hysteresis model based on frog leaping fuzzy algorithm[J]. Transactions of China Electrotechnical Society, 2017,32(4):154-161.
[16] FAN J Y,PAN J Y.A note on the Levenberg- Marquardt parameter[J]. Applied Mathematics and Computation, 2009, 207(2): 351-359.