Structural optimization of magnetic flux concentrator based on particle swarm optimization algorithm

doi:10.1088/1674-1056/ae0b38

Abstract This study introduces a structural optimization method for magnetic flux concentrators (MFCs) utilizing the particle swarm optimization (PSO) algorithm, addressing inefficiencies and challenges in achieving optimal structures with traditional methods. By integrating the PSO algorithm with COMSOL Multiphysics simulation software, a co-simulation framework is developed to optimize the parameters of a conical MFC. Compared with traditional methods, this approach enhances optimization results by twofold, achieving a magnetic field amplification factor of up to 200 within the defined parameter range. Additionally, an evaluation criterion for concentrator optimization is proposed, offering novel insights for designing concentrators across various scenarios.

Keywords: magnetic flux concentrator magnetic sensing enhancement particle swarm optimization

Received: 04 July 2025
Revised: 05 September 2025
Accepted manuscript online: 25 September 2025

PACS:	07.55.Ge	(Magnetometers for magnetic field measurements)
	02.60.Pn	(Numerical optimization)
	75.50.-y	(Studies of specific magnetic materials)
	87.55.de	(Optimization)

Fund: The authors are grateful to Professor Du Guanxiang from Nanjing University of Posts and Telecommunications for his constructive suggestions on the simulation and experimental design. His guidance has been instrumental in shaping this research. This work was supported by the Natural Science Foundation of China (Grant No. 62375285) and the Research Project of the National University of Defense Technology (Grant No. 24-ZZCX-XXXX-01-04).

Corresponding Authors: Zhong-Qi Tan
E-mail: zhqitan@sina.com

Cite this article:

Yu-Xiao Wang(王雨潇), Shi-Yu Guan(管世钰), Yi Zhang(张燚), Qi-Yuan Jiang(江奇渊), Bing-Feng Sun(孙兵锋), and Zhong-Qi Tan(谭中奇) Structural optimization of magnetic flux concentrator based on particle swarm optimization algorithm 2026 Chin. Phys. B 35 040701

[1] Schmidt A B, Chekmenev E Y, Maissin H, Groß P R, Petersen S, Nagel L, Schilling F, Schwartz I, Reinheckel T, Hövener J and Knecht S 2024 Anal. Sens. 4 1
[2] Li Y, Cheng H, Alhalili Z, Xu G and Gao G 2021 J. Chin. Chem. Soc. 68 216
[3] Zhen Y Z, Yong B L, Liang C, Qiang Z and Yue S 2024 Minerals 14 837
[4] Mendes B D L, Kontny A, Dudzisz K and Wilke F D H 2024 Meteorit. Planet. Sci. 59 1577
[5] Hao Y P, Wen F F, Feng L, Li H D, Si X L, Jing W and Wei Q 2022 IEEE Trans. Instrum. Meas. 71 0000101
[6] Han Y, Benjamin M and Ferruccio R 2023 Opt. Express 31 27287
[7] Claire A M, Bryan A M, Stephan K, Kenichi O, David D A and Ania C B J 2016 Nano Lett. 16 2450
[8] Song L Y, Ming Y T, Tian Q Y, Xu L, Xian B W and Jin Z 2020 Nano- Micro Lett. 12 181
[9] Lettens J, Avramenko M, Vandevenne I, Chu A, Hengel P, Kern M, Anders J, Moens P, Goovaerts E and Cambré S 2024 J. Magn. Reson. 137 1
[10] Niu L Y, Ren X H, Wang H L, Zhao X Y and You Z 2023 Electron. Des. Eng. 31 99
[11] Liu Y, Kang A G, Li L H and Wu X 2019 Safety in Coal Mines 50 122
[12] Srivatsa C, Chris M, April O, Emma H, Andrew I, Ian C, Scott D and Kai-Mei C F 2020 Phys. Rev. Mater. 4 023402
[13] Gkika V, Kim Y, Matlashov A, Shin Y C, Semertzidis Y, Cantor R, Lohmeyer C, Aggarwal N and Geraci A 2024 J. Low Temp. Phys. 216 386
[14] Yang S R, Wang Q W, Fu J Q and Kong J 2024 Quantum Opt. 30 46
[15] Pan M C, Hu J F, Tian W G, Chen D X and Zhao J Q 2012 Sensors Actuators A 179 92
[16] Almeida J M and Freitas P P 2009 J. Appl. Phys. 105 07E722
[17] Wu D J, Li Z H, Tang J and Liu J 2023 Micronanoelectron. Technol. 60 259
[18] Guo J M, Zhang Z H, Zhang T Y, Zhao X Y, Li C L, Yin L, Song F, Tao L Q, Yan J F, Liang L, Mi W and Han L 2024 IEEE Sens. J. 24 19901
[19] Leroy P, Coillot C, Roux A F and Chanteur G M 2006 IEEE Sens. J. 6 707
[20] Zhang X M, Bi Y, Chen G B, Liu J, Li J, Feng K Q, Lv C and Wang W J 2018 AIP Adv. 8 125222
[21] Rafi A M, Nogina D, Penzar D, et al. 2025 Nat. Biotechnol. 43 1373
[22] Oussous S A, Lail D M, Bouayadi R E and Amine A 2025 IEEE Access 13 64810
[23] Padmavathi B, Dhivya S, Kavitha D, Banu A K and Karthikeyan S M 2024 Int. J. Veh. Struct. Sys. 16 45
[24] Zhou Y X, Nie S H, Sun P F, Su L J and Gao Y 2024 Micro Nanostructures 195 207985
[25] Xue Z, Sun CW, ZhengWH, Lv J C and Liu X G 2025 Bioinformatics 41 btae730
[26] Ye Q L,WangWL andWang Z 2024 J. Zhejiang University (Eng. Sci.) 58 1107
[27] Ding L and Chong J F 2023 J. Anyang Normal University 2 9
[28] Hwang S and Smith R 2012 Korean J. Chem. Eng. 29 25
[29] Netrapalli P 2019 J. Indian Inst. Sci. 99 201
[30] Zhu G L J, Li Y D and Zou C F 1996 J. Magnetic Materials and Devices 2 50
[31] Ji Z Y, Ma Y, Wang Q and Dong C 2022 J. Mat. Eng. 50 69
[32] Shu B 2024 New Technology & New Process 443 107
[33] Leroy P, Coillot C, Roux A and Chanteur G 2009 tm-Tech. Mess. 73 339
[34] Xie Y J 2020 Magnetometry Based on the Ensemble Nitrogen-vacancy Centers in Diamond (Ph.D. Dissertation) (Hefei: University of Science and Technology of China) (in Chinese)
[35] Aharoni A 1998 J. Appl. Phys. 83 3432
[36] Li Z H, Wang T Y, Guo Q, Guo H, Wen H F, Tang J and Liu J 2021 Acta Phys. Sin. 70 147601 (in Chinese)
[37] Wang P F, Yuan Z H, Huang P, Rong X, Wang M Q, Xu X K, Duan C K, Ju C Y, Shi F Z and Du J F 2015 Nat. Commun. 6 6631
[38] Taylor J M, Cappellaro P, Childress L, Jiang L, Budker D, Hemmer P R, Yacoby A, Walsworth R and Lukin M D 2008 Condens. Matter 5 810

[1]	Quantum control based on three forms of Lyapunov functions Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼). Chin. Phys. B, 2024, 33(4): 040201.
[2]	Identifying influential spreaders in social networks: A two-stage quantum-behaved particle swarm optimization with Lévy flight Pengli Lu(卢鹏丽), Jimao Lan(揽继茂), Jianxin Tang(唐建新), Li Zhang(张莉), Shihui Song(宋仕辉), and Hongyu Zhu(朱虹羽). Chin. Phys. B, 2024, 33(1): 018901.
[3]	Probing the effects of lithium doping on structures, properties, and stabilities of magnesium cluster anions Xiao-Yi Zhang(张小义), Ya-Ru Zhao(赵亚儒), Hong-Xing Li(李红星), Kai-Ge Cheng(成凯格), Zi-Rui Liu(刘子锐), Zhi-Ping Liu(刘芷萍), and Hang He(何航). Chin. Phys. B, 2023, 32(6): 066102.
[4]	Reconstruction and stability of Fe₃O₄(001) surface: An investigation based on particle swarm optimization and machine learning Hongsheng Liu(柳洪盛), Yuanyuan Zhao(赵圆圆), Shi Qiu(邱实), Jijun Zhao(赵纪军), and Junfeng Gao(高峻峰). Chin. Phys. B, 2023, 32(5): 056802.
[5]	Angular insensitive nonreciprocal ultrawide band absorption in plasma-embedded photonic crystals designed with improved particle swarm optimization algorithm Yi-Han Wang(王奕涵) and Hai-Feng Zhang(章海锋). Chin. Phys. B, 2023, 32(4): 044207.
[6]	Inatorial forecasting method considering macro and micro characteristics of chaotic traffic flow Yue Hou(侯越), Di Zhang(张迪), Da Li(李达), and Ping Yang(杨萍). Chin. Phys. B, 2023, 32(10): 100508.
[7]	Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm Yue-Xi Peng(彭越兮), Ke-Hui Sun(孙克辉), Shao-Bo He(贺少波). Chin. Phys. B, 2020, 29(3): 030502.
[8]	Particle swarm optimization and its application to the design of a compact tunable guided-mode resonant filter Dan-Yan Wang(王丹燕), Qing-Kang Wang(王庆康). Chin. Phys. B, 2018, 27(3): 037801.
[9]	Structural optimization of Au-Pd bimetallic nanoparticles with improved particle swarm optimization method Gui-Fang Shao(邵桂芳), Meng Zhu(朱梦), Ya-Li Shangguan(上官亚力), Wen-Ran Li(李文然), Can Zhang(张灿), Wei-Wei Wang(王玮玮), Ling Li(李玲). Chin. Phys. B, 2017, 26(6): 063601.
[10]	Bio-inspired optimization algorithms for optical parameter extraction of dielectric materials: A comparative study Md Ghulam Saber, Kh Arif Shahriar, Ashik Ahmed, Rakibul Hasan Sagor. Chin. Phys. B, 2016, 25(10): 105101.
[11]	Ground-state structure determination and mechanical properties of palladium seminitride Zhang Gang-Tai (张刚台), Bai Ting-Ting (白婷婷), Zhao Ya-Ru (赵亚儒), Lu Cheng (卢成). Chin. Phys. B, 2013, 22(11): 116104.
[12]	Parameters estimation online for Lorenz system by a novel quantum-behaved particle swarm optimization Gao Fei(高飞), Li Zhuo-Qiu(李卓球), and Tong Heng-Qing(童恒庆). Chin. Phys. B, 2008, 17(4): 1196-1201.

[1]	WANG JIAN (王坚), WU XING-FANG (吴杏芳), FANG ZHENG-ZHI (方正知). DIFFUSIVE AGGREGATION ON ION IMPLANTED THIN FILMS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 81 -85 .
[2]	TANG WEN-GUO (唐文国), GONG TAO (龚涛), LI ZI-YUAN (李自元), LIU XIANG-NA (刘湘娜), HE YU-LIANG (何宇亮). PHOTOLUMINESCENCE PROPERTIES OF NANO-SIZE CRYSTALLINE SILICON FILMS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(10): 776 -781 .
[3]	CHEN ZONG-YUN (陈宗蕴), LI ZAI-GUANG (李再光), HUANG NIAN-NING (黄念宁). GENERAL SOLITON SOLUTIONS OF THE NLS⁺ EQUATION UNDER NON-VANISHING BOUNDARY CONDITION[J]. Acta Physica Sinica (Overseas Edition), 1994, 3(1): 1 -17 .
[4]	FAN XU-DONG (范旭东), GU BEN-YUAN (顾本源), YANG GUO-ZHEN (杨国桢), LIN ZONG-HAN (林宗涵). QUANTUM PERCOLATION AND BALLISTIC CONDUCTANCE IN A SYSTEM OF DOUBLE-COUPLED CHAINS[J]. Acta Physica Sinica (Overseas Edition), 1994, 3(10): 769 -779 .
[5]	Zhang Ning (张宁), Zhang Sheng (张胜), Xu Yin-lin (徐寅林), Ding Wei-ping (丁维平), Zhong Wei (钟伟), Du You-wei (都有为). GRAIN SIZE DEPENDENT MAGNETISM IN GRANULAR MANGANESE PEROVSKITE La_0.82Sr_0.18MnO₃[J]. Acta Physica Sinica (Overseas Edition), 1998, 7(10): 757 -763 .
[6]	Wang Yuan-fei (王远飞), Han Bao-shan (韩宝善). ANNIHILATION OF VERTICAL-BLOCH-LINE CHAINS IN THE WALLS OF THE SECOND KIND OF DUMBBELL DOMAINS SUBJECTED TO JOINT STATIC BIAS FIELD AND IN-PLANE FIELD[J]. Acta Physica Sinica (Overseas Edition), 1999, 8(7): 539 -544 .
[7]	Tang Zhi-ming (唐智明). A POSSIBLE EXPERIMENTAL TEST ON THE GRAVITATION THEORY OF COMPLEX FIELD[J]. Chinese Physics, 2000, 9(12): 881 -884 .
[8]	Li Xiang (李翔), Guo Guang-can (郭光灿). QUANTUM GAP SOLITON IN PARAMETRIC PROCESS[J]. Chinese Physics, 2000, 9(2): 131 -137 .
[9]	Feng Shi-de (冯士德), Mao Jiang-yu (毛江玉), Zhang Qiong (张琼). LATTICE BOLTZMANN EQUATION MODEL IN THE CORIOLIS FIELD[J]. Chinese Physics, 2001, 10(12): 1103 -1105 .
[10]	Liu Yu-Yan (刘煜炎), Huang Guang-Ming (黄光明), Duan Chuan-Xi (段传喜), Shi Li-Hua (石丽华), Cai Xin (蔡欣). Analysis of far-infrared laser magnetic resonance spectra of CH₂Br at 447.3 and 671.1μm[J]. Chinese Physics, 2002, 11(11): 1170 -1174 .

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Structural optimization of magnetic flux concentrator based on particle swarm optimization algorithm

Cite this article:

Online attention