Optimization Design of Parameters for Transverse Flux Induction Heating Device Based on Multi-Island Genetic Algorithm and Response Surface Method
Liu zhiying1,2, Wang Youhua1,2, Liu Chengcheng1,2, Peng Jiangpai1,2, Song Huabin1,2
1. State Key Laboratory of Reliability and Intelligence of Electrical Equipment Hebei University of Technology Tianjin 300130 China; 2. Key Laboratory of Electromagnetic Field and Electrical Apparatus Reliability of Hebei Province Hebei University of Technology Tianjin 300130 China
Abstract：Transverse flux induction heating (TFIH) devices are widely used in the heat treatment process of flat workpieces, such as metal strips. The heating results affect the application performance of metal strips. Ideal average temperature and uniform temperature distribution of the strip at the heater outlet are desired when the heating state of the strip is stable. The standard tempering temperature of 45# steel is 600℃. This paper divides the optimization parameters into structural and power supply parameters to meet heat treatment requirements. Different methods are used to reduce optimization difficulties while maintaining optimization accuracy. The structure of the TFIH device is determined by seven parameters. The air gap between the magnetic pole and the strip should be as small as possible to meet the processing technology. A global sensitivity analysis (GSA) based on the Morris method ranks the sensitivity of the relative non-uniformity to the six coil structural parameters. The top four structural parameters with significant effects are screened out, ensuring optimization accuracy while reducing calculation time. Due to the strong robustness, the radial basis function (RBF) neural network prediction model replaces the finite element calculation model to estimate nonlinear functions. The optimal Latin hypercube design (OLHD) samples 100 times, and the sampling results are used as the training sample points of the prediction model. After testing, the RBF neural network model has high prediction accuracy within the variation range of the input parameters. The multi-island genetic algorithm (MIGA) optimizes the screened structural parameters globally. The results show that the relative non-uniformity is reduced from 2.88% to 2.38% after optimization, effectively improving the temperature distribution uniformity. Based on the optimized structural parameters, the response surface method (RSM) is used to optimize the current and frequency. Consequently, the average temperature is close to the target value, and the relative non-uniformity is maintained at a low level. The relative non-uniformity and the average temperature expressions for power supply parameters are fitted separately using a second-order polynomial. Both models are tested by the variance (ANOVA) analysis. The multi-objective optimization is then performed using the response optimizer in Design-Expert. The results show that after the optimization of structural parameters and power supply parameters, when the strip heating state reaches stability, the relative non-uniformity of the strip surface temperature distribution at the heater outlet is 2.36%, and the average temperature is 600.06°C, which can meet the tempering requirements of 45# steel strip.
刘志赢, 汪友华, 刘成成, 彭江湃, 宋华宾. 基于多岛遗传算法与响应面法的横向磁通感应加热装置参数优化设计[J]. 电工技术学报, 2024, 39(10): 3180-3191.
Liu zhiying, Wang Youhua, Liu Chengcheng, Peng Jiangpai, Song Huabin. Optimization Design of Parameters for Transverse Flux Induction Heating Device Based on Multi-Island Genetic Algorithm and Response Surface Method. Transactions of China Electrotechnical Society, 2024, 39(10): 3180-3191.
[1] 黄亚飞, 蒋兴良, 任晓东, 等. 采用涡流自热环防止输电线路冰雪灾害的方法研究[J]. 电工技术学报, 2021, 36(10): 2169-2177. Huang Yafei, Jiang Xingliang, Ren Xiaodong, et al.Study on preventing icing disasters of transmission lines by use of eddy self-heating ring[J]. Transactions of China Electrotechnical Society, 2021, 36(10): 2169-2177. [2] 段志荣, 解社娟, 李丽娟, 等. 基于磁力传动式阵列涡流探头的管道缺陷检测[J]. 电工技术学报, 2020, 35(22): 4627-4635. Duan Zhirong, Xie Shejuan, Li Lijuan, et al.Detection of defects in pipeline structures based on magnetic transmission eddy current array probe[J]. Transactions of China Electrotechnical Society, 2020, 35(22): 4627-4635. [3] 涂彦昕, 梅红伟, 刘立帅, 等. 基于动态扫描涡流热成像技术的碳钢结构损伤检测[J]. 电工技术学报, 2023, 38(11): 2999-3008. Tu Yanxin, Mei Hongwei, Liu Lishuai, et al.Structural damage evaluation of carbon steel based on dynamic scanning eddy current infrared thermo- graphy[J]. Transactions of China Electrotechnical Society, 2023, 38(11): 2999-3008. [4] Xu H, Kamada H, Isobe T, et al.Feasibility study on a real-scale high-frequency electromagnets for mag- netic hyperthermia base on a magnetic scaling law[J]. IEEE Transactions on Applied Superconductivity, 2022, 32(6): 1-5. [5] Bao Li, Wang Bo, You Xiaoping, et al.Numerical and experimental research on localized induction heating process for hot stamping steel sheets[J]. International Journal of Heat and Mass Transfer, 2020, 151: 119422. [6] 冷朝霞, 刘庆丰. 基于多电平逆变器的感应加热双频率输出设计[J]. 电工技术学报, 2016, 31(24): 195-204. Leng Zhaoxia, Liu Qingfeng.Design of dual frequency output of induction heating based on multilevel inverter[J]. Transactions of China Elec- trotechnical Society, 2016, 31(24): 195-204. [7] Plumed E, Lope I, Acero J.Modeling and design of cookware for induction heating technology with balanced electromagnetic and thermal characteri- stics[J]. IEEE Access, 2022, 10: 83793-83801. [8] Peng Wen, Chen Xiaorui, Zhang Li, et al.Finite element analysis of temperature uniformity in transverse induction heating process in ESP rolling[J]. The International Journal of Advanced Manufacturing Technology, 2021, 115(11-12): 3423-3439. [9] Wang Youhua, Li Bin, Yin Liuxia, et al.Velocity- controlled particle swarm optimization (PSO) and its application to the optimization of transverse flux induction heating apparatus[J]. Energies, 2019, 12(3): 487. [10] 汪友华, 吴建成, 李宾, 等. 新型带材横向磁通感应加热器设计与相关激励参数优选[J]. 电工技术学报, 2020, 35(4): 745-757. Wang Youhua, Wu Jiancheng, Li Bin, et al.Design and optimization of relative excitation parameters for a new strip transverse flux induction heating apparatus[J]. Transactions of China Electrotechnical Society, 2020, 35(4): 745-757. [11] Song Huabin, Wang Youhua, Peng Jiangpai, et al.Study on the uniformity of temperature distribution of transverse flux induction heating based on a new magnetic pole[J]. Energies, 2022, 15(19): 7450. [12] 许家忠, 赵辉, 付天宇, 等. 感应加热CFRP温度控制算法[J]. 东北大学学报(自然科学版), 2022, 43(1): 17-23, 39. Xu Jiazhong, Zhao Hui, Fu Tianyu, et al.Temperature control algorithm of induction heating CFRP[J]. Journal of Northeastern University (Natural Science), 2022, 43(1): 17-23, 39. [13] Chang C J, Chiang T H, Tai C C.A modified self-tuning fuzzy logic temperature controller for metal induction heating[J]. The Review of Scientific Instruments, 2020, 91(6): 064905. [14] Wang Junhua, Wang Youhua, Ho S L, et al.Design and FEM analysis of a new distributed vernier traveling wave induction heater for heating moving thin strips[J]. IEEE Transactions on Magnetics, 2011, 47(10): 2612-2615. [15] Morandi A, Fabbri M.In-depth induction heating of large steel slabs by means of a DC saturating field produced by superconducting coils[J]. IEEE Transa- ctions on Applied Superconductivity, 2016, 26(4): 1-7. [16] 汪友华, 吴建成, 刘成成, 等. 横向磁通连续感应加热过程中带材涡流场和温度场的仿真分析[J]. 金属热处理, 2019, 44(1): 229-234. Wang Youhua, Wu Jiancheng, Liu Chengcheng, et al.Simulation and analysis of eddy current field and temperature field of strips during transverse flux continuous induction heating[J]. Heat Treatment of Metals, 2019, 44(1): 229-234. [17] 王晗, 侯恺, 刘晓楠, 等. 基于全局灵敏度分析的电气互联系统韧性提升方法[J]. 电力系统自动化, 2023, 47(3): 59-67. Wang Han, Hou Kai, Liu Xiaonan, et al.Resilience enhancement method for electricity-gas intercon- nection system based on global sensitivity analysis[J]. Automation of Electric Power Systems, 2023, 47(3): 59-67. [18] 何琨, 严正, 徐潇源, 等. 基于Sobol’法的孤岛微电网潮流全局灵敏度分析[J]. 电力系统自动化, 2018, 42(14): 99-106. He Kun, Yan Zheng, Xu Xiaoyuan, et al.Sobol’ method based global sensitivity analysis of power flow in islanded microgrid[J].Automation of Electric Power Systems, 2018, 42(14): 99-106. [19] Morris M D.Factorial sampling plans for preliminary computational experiments[J]. Technometrics, 1991, 33(2): 161-174. [20] Campolongo F, Cariboni J, Saltelli A.An effective screening design for sensitivity analysis of large models[J]. Environmental Modelling & Software, 2007, 22(10): 1509-1518. [21] 戴睿, 张岳, 王惠军, 等. 基于多物理场近似模型的高速永磁电机多目标优化设计[J]. 电工技术学报, 2022, 37(21): 5414-5423. Dai Rui, Zhang Yue, Wang Huijun, et al.Multi- objective optimization design of high-speed per- manent magnet machine based on multi-physics approximate model[J]. Transactions of China Electrotechnical Society, 2022, 37(21): 5414-5423. [22] McKay M D, Beckman R J, Conover W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technimetrics, 1979, 21(2): 239-245. [23] Park J S.Optimal Latin-hypercube designs for computer experiments[J]. Journal of Statistical Planning and Inference, 1994, 39(1): 95-111. [24] 吴月宝, 赵晋斌, 张少腾, 等. 基于径向基神经网络的多负载无线电能传输系统自适应阻抗匹配方法[J]. 电工技术学报, 2021, 36(19): 3969-3977. Wu Yuebao, Zhao Jinbin, Zhang Shaoteng, et al.An adaptive impedance matching method based on radial basis function neural network in multi-load wireless power transfer systems[J]. Transactions of China Electrotechnical Society, 2021, 36(19): 3969-3977. [25] 陈宗遥, 卜旭辉, 郭金丽. 基于神经网络的数据驱动互联电力系统负荷频率控[J]. 电工技术学报, 2022, 37(21): 5451-5461. Chen Zongyao, Bu Xuhui, Guo Jinli.Neural network based data-driven load frequency control for inter- connected power systems[J]. Transactions of China Electrotechnical Society, 2022, 37(21): 5451-5461. [26] 王超, 李文栋, 陈泰然, 等. 550kV GIS盆式绝缘子小型化设计(一)——几何形状优化[J]. 电工技术学报, 2022, 37(7): 1847-1855. Wang Chao, Li Wendong, Chen Tairan, et al.Compact design of 550kV basin-type spacer in gas insulated switchgear (part I)—structure optimi- zation[J]. Transactions of China Electrotechnical Society, 2022, 37(7): 1847-1855. [27] Zhang Wenwen, Qi Hong, Yu Zhiqiang, et al.Optimization configuration of selective solar absorber using multi-island genetic algorithm[J]. Solar Energy, 2021, 224: 947-955. [28] 罗玉涛, 卢若皓. 基于结构参数分级优化的电机电磁噪声抑制[J]. 电工技术学报, 2021, 36(14): 2957-2970. Luo Yutao, Lu Ruohao.Hierarchical optimization of structural parameters for motor electromagnetic noise suppression[J]. Transactions of China Electrotech- nical Society, 2021, 36(14): 2957-2970. [29] 张嘉伟, 曾正, 孙鹏, 等. 基于响应面的车用功率模块Pin-Fin优化设计[J]. 电工技术学报, 2022, 37(22): 5836-5850. Zhang Jiawei, Zeng Zheng, Sun Peng, et al.Optimized Pin-Fin design of power module for electric vehicle application by response surface[J]. Transactions of China Electrotechnical Society, 2022, 37(22): 5836-5850. [30] 吉敬华, 沈人洁, 徐亮, 等. 考虑运行工况的模块化双永磁游标电机多工作点优化设计[J]. 电工技术学报, 2022, 37(22): 5649-5659. Ji Jinghua, Shen Renjie, Xu Liang, et al.Multi- working point optimization of modular double permanent-magnet vernier motor considering oper- ation condition[J]. Transactions of China Electro- technical Society, 2022, 37(22): 5649-5659. [31] Paese E, Geier M, Homrich R P, et al.Assessment of process parameters in the optimization of the metal sheet electromagnetic forming process[J]. IEEE Transactions on Applied Superconductivity, 2022, 32(6): 1-6. [32] 唐昭晖, 许志红. 基于响应面法的交流接触器弹簧系统优化设计方法[J]. 电工技术学报, 2022, 37(2): 515-527. Tang Zhaohui, Xu Zhihong.Optimal design method for AC contactor spring system based on response surface method[J]. Transactions of China Electro- technical Society, 2022, 37(2): 515-527. [33] Zhang Bangfu, Cheng Ming, Cao Ruiwu, et al.Analysis of linear flux-switching permanent magnet motor using response surface methodology[J]. IEEE Transactions on Magnetics, 2014, 50(11): 1-4.
2024, Vol. 39 
