基于随机性与确定性混合优化算法的Jiles-Atherton磁滞模型参数提取
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摘要
基于J-A磁滞模型模拟铁磁材料磁滞特性的关键是模型参数的精确快速辨识。该文针对现有J-A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,提出一种基于随机性优化算法——模拟退火(SA)与确定性优化算法——Levengerg-Marquardt(L-M)混合的J-A模型参数提取方法,该方法综合了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。在迭代优化初期,采用SA算法快速锁定J-A模型参数的优化区域;继而根据引入的普适性混合算法切换过渡准则,将SA算法当前解赋予L-M算法;针对基于传统L-M算法提取J-A模型参数出现的病态矩阵问题,该文将J-A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J-A模型参数快速辨识的归一化L-M算法,该算法在接收到SA算法提供的优化解后,将其作为该算法局部搜索的初始值。仿真及实验结果表明,所提混合算法兼具收敛速度快、提取精度高的优异性能。
The primary task of using J-A hysteresis model to simulate the hysteresis phenomenons of ferromagnetic materials is the model parameters' efficient identification. Owing to the slow convergence rate and low accuracy level of existing parameter extraction methods, a hybrid technique that couples simulated annealing(SA) with Levenberg-Marquardt(L-M) is proposed. This algorithm combines the merits of strong global search ability in SA and fast local convergence speed in L-M. In the initial iteration process, SA is used to quickly lock the optimized region. Then according to the introduced switching criterion, SA stops working, and its current solution is transferred to the L-M.Aiming at the problem of ill-conditioned matrix that appears in the process of parameter extraction when using traditional L-M, the sensitivity function matrix is normalized so as to obtain the normalized L-M,which is suitable for the rapid parameter identification of J-A model parameters. After receiving the solution provided by SA, the normalized L-M takes this values as its initial parameters for local search.The simulation and experimental results show that the proposed hybrid algorithm has the advantages of fast convergence and high accuracy at the same time.
The primary task of using J-A hysteresis model to simulate the hysteresis phenomenons of ferromagnetic materials is the model parameters' efficient identification. Owing to the slow convergence rate and low accuracy level of existing parameter extraction methods, a hybrid technique that couples simulated annealing(SA) with Levenberg-Marquardt(L-M) is proposed. This algorithm combines the merits of strong global search ability in SA and fast local convergence speed in L-M. In the initial iteration process, SA is used to quickly lock the optimized region. Then according to the introduced switching criterion, SA stops working, and its current solution is transferred to the L-M.Aiming at the problem of ill-conditioned matrix that appears in the process of parameter extraction when using traditional L-M, the sensitivity function matrix is normalized so as to obtain the normalized L-M,which is suitable for the rapid parameter identification of J-A model parameters. After receiving the solution provided by SA, the normalized L-M takes this values as its initial parameters for local search.The simulation and experimental results show that the proposed hybrid algorithm has the advantages of fast convergence and high accuracy at the same time.
引文
[1]陈彬,李琳,赵志斌.双向全桥DC-DC变换器中大容量高频变压器绕组与磁心损耗计算[J].电工技术学报,2017,32(22):123-133.Chen Bin,Li Lin,Zhao Zhibin.Calculation of highpower high-frequency transformer's copper loss and magnetic core loss in dual-active-bridge DC-DCconverter[J].Transactions of China Electrotechnical Society,2017,32(22):123-133.
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[6]Li Huiqi,Li Qingfeng,Xu Xiaobang,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.
[7]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.
[8]Vaseghi B,Mathekga D,Rahman S A,et al.Parameter optimization and study of inverse J-A hysteresis model[J].IEEE Transactions on Magnetics,2013,49(5):1637-1640.
[9]Jiles D C,Atherton D L.Theory of ferromagnetic hysteresis[J].Journal of Applied Physics,1984,55(6):2115-2120.
[10]Chwastek K,Szczyg?owski J.Identification of a hysteresis model parameters with genetic algorithms[J].Mathematics and Computers in Simulation,2006,71(3):206-211.
[11]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.
[12]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 Chao,Wang Fenghua,Su Lei,et al.Parameter identification of Jiles-Atherton model for transformer based on hybrid artificial fish swarm and shuffled frog leaping algorithm[J].Proceedings of the CSEE,2015,35(18):4799-4807.
[13]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 Yang,Liu Zhizhen.Determination of Jiles Atherton core hysteresis model parameters based on fuzzy-shuffled frog leaping algorithm[J].Transactions of China Electrotechnical Society,2017,32(4):154-161.
[14]Hernandez E D M,Muranaka C S,Cardoso J R.Identification of the Jiles-Atherton model parameters using random and deterministic searches[J].Physica BCondensed Matter,2000,275(1-3):212-215.
[15]Vasconcelos J A,Saldanha R R,Krahenbuhl L,et al.Genetic algorithm coupled with a deterministic method for optimization in electromagnetics[J].IEEETransactions on Magnetics,1997,33(2):1860-1863.
[16]Nocedal J,Wright S J.Numerical optimization[M].New York:Springer,2006.
[17]Jiles D C.Frequency dependence of hysteresis curves in conducting magnetic materials[J].Journal of Applied Physics,1994,76(10):5849-5855.
[18]Chwastek K.Modelling of dynamic hysteresis loops using the Jiles-Atherton approach[J].Mathematical&Computer Modelling of Dynamical Systems,2009,15(1):95-105.
[19]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.
[20]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].IEEE Transactions on Magnetics,1992,28(2):1541-1544.
[21]Vasin V V,Perestoronina G Y.The LevenbergMarquardt 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.
[22]Fan Jinyan,Pan Jianyu.A note on the LevenbergMarquardt parameter[J].Applied Mathematics and Computation,2009,207(2):351-359.
[23]Marquardt D W.An algorithm for least-squares estimation of nonlinear parameters[J].Journal of the Society for Industrial and Applied Mathematics,1963,11(2):431-441.
[24]严正,范翔,赵文恺,等.自适应LevenbergMarquardt方法提高潮流计算收敛性[J].中国电机工程学报,2015,4(20):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,2015,4(20):1909-1918.
[25]Trigeassou J C,Poinot T,Moreau S.A methodology for estimation of physical parameters[J].Systems Analysis Modelling Simulation,2003,43(7):925-943.
[2]陈彬,李琳,赵志斌.典型非正弦电压波激励下高频磁心损耗[J].电工技术学报,2018,33(8):1696-1704.Chen Bin,Li Lin,Zhao Zhibin.Magnetic core losses under high-frequency typical non-sinusoidal voltage magnetization[J].Transactions of China Electrotechnical Society,2018,33(8):1696-1704.
[3]De La Barrière O,Ragusa C,Appino C,et al.Prediction of energy losses in soft magnetic materials under arbitrary induction waveforms and DC bias[J].IEEE Transactions on Industrial Electronics,2017,64(3):2522-2529.
[4]Beatrice C,Appino C,De La Barrière O,et al.Broadband magnetic losses in Fe-Si and Fe-Co laminations[J].IEEE Transactions on Magnetics,2014,50(4):1-4.
[5]Hamada S,Louai F Z,Nait-Said N,et al.Dynamic hysteresis modeling including skin effect using diffusion equation model[J].Journal of Magnetism&Magnetic Materials,2016,410:137-143.
[6]Li Huiqi,Li Qingfeng,Xu Xiaobang,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.
[7]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.
[8]Vaseghi B,Mathekga D,Rahman S A,et al.Parameter optimization and study of inverse J-A hysteresis model[J].IEEE Transactions on Magnetics,2013,49(5):1637-1640.
[9]Jiles D C,Atherton D L.Theory of ferromagnetic hysteresis[J].Journal of Applied Physics,1984,55(6):2115-2120.
[10]Chwastek K,Szczyg?owski J.Identification of a hysteresis model parameters with genetic algorithms[J].Mathematics and Computers in Simulation,2006,71(3):206-211.
[11]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.
[12]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 Chao,Wang Fenghua,Su Lei,et al.Parameter identification of Jiles-Atherton model for transformer based on hybrid artificial fish swarm and shuffled frog leaping algorithm[J].Proceedings of the CSEE,2015,35(18):4799-4807.
[13]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 Yang,Liu Zhizhen.Determination of Jiles Atherton core hysteresis model parameters based on fuzzy-shuffled frog leaping algorithm[J].Transactions of China Electrotechnical Society,2017,32(4):154-161.
[14]Hernandez E D M,Muranaka C S,Cardoso J R.Identification of the Jiles-Atherton model parameters using random and deterministic searches[J].Physica BCondensed Matter,2000,275(1-3):212-215.
[15]Vasconcelos J A,Saldanha R R,Krahenbuhl L,et al.Genetic algorithm coupled with a deterministic method for optimization in electromagnetics[J].IEEETransactions on Magnetics,1997,33(2):1860-1863.
[16]Nocedal J,Wright S J.Numerical optimization[M].New York:Springer,2006.
[17]Jiles D C.Frequency dependence of hysteresis curves in conducting magnetic materials[J].Journal of Applied Physics,1994,76(10):5849-5855.
[18]Chwastek K.Modelling of dynamic hysteresis loops using the Jiles-Atherton approach[J].Mathematical&Computer Modelling of Dynamical Systems,2009,15(1):95-105.
[19]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.
[20]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].IEEE Transactions on Magnetics,1992,28(2):1541-1544.
[21]Vasin V V,Perestoronina G Y.The LevenbergMarquardt 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.
[22]Fan Jinyan,Pan Jianyu.A note on the LevenbergMarquardt parameter[J].Applied Mathematics and Computation,2009,207(2):351-359.
[23]Marquardt D W.An algorithm for least-squares estimation of nonlinear parameters[J].Journal of the Society for Industrial and Applied Mathematics,1963,11(2):431-441.
[24]严正,范翔,赵文恺,等.自适应LevenbergMarquardt方法提高潮流计算收敛性[J].中国电机工程学报,2015,4(20):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,2015,4(20):1909-1918.
[25]Trigeassou J C,Poinot T,Moreau S.A methodology for estimation of physical parameters[J].Systems Analysis Modelling Simulation,2003,43(7):925-943.
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