volume | PIER Journals

Abstract

Computation of the magnetic field generated by permanent magnets is essential in the design and optimization of a wide range of applications. However, the existing methods to calculate the magnetic field can be time-consuming or ungeneralised. In this research, a deep learning-based fast-computed and generalised model of three-dimensional (3D) magnetic field is studied. The volumetric deep neural network model (V-Net) which consists of a contracting part to learn the geometrical context and an expanding part to enable the concise localization was applied. We synthetically generated the ground truth datasets from permanent magnets of different 3D shapes to train the V-Net. The accuracy and efficiency of this deep learning model are validated. Predicting on 50 random samples, the V-Net took 4.6 s with a GPU T4 and 23.2 s with the CPU whereas the others took a few hundreds to thousands of seconds. Therefore, the deep learning model can be potentially utilised to replace the other methods in the computation and study of the magnetic field for the design and optimization of magnetic devices (the codes used in this research are published openly in https://github.com/vantainguyen/3D_V-Net_MagneticField).

1. Arias, P., L. Adn-Arcay, B. Puerta-Catoira, A. Madrid, and J. Cudeiro, "Transcranial static magnetic field stimulation of M1 reduces corticospinal excitability without distorting sensorimotor integration in humans," Brain Stimulation: Basic, Translational, and Clinical Research in Neuromodulation, Vol. 10, No. 2, 340-342, 2017.

2. Huettel, S. A., A. W. Song, and G. McCarthy, Functional Magnetic Resonance Imaging, Vol. 1, Sinauer Associates Sunderland, 2004.

3. Atallah, K., S. Calverley, and D. Howe, "Design, analysis and realisation of a high-performance magnetic gear," IEE Proceedings-Electric Power Applications, Vol. 151, No. 2, 135-143, 2004.
doi:10.1049/ip-epa:20040224

4. Molokanov, O., P. Dergachev, S. Osipkin, E. Kuznetsova, and P. Kurbatov, "A novel double-rotor planetary magnetic gear," IEEE Transactions on Magnetics, Vol. 54, No. 11, 1-5, 2018.
doi:10.1109/TMAG.2018.2837679

5. Wu, W., H. Lovatt, and J. Dunlop, "Analysis and design optimisation of magnetic couplings using 3D nite element modelling," IEEE Transactions on Magnetics, Vol. 33, No. 5, 4083-4094, 1997.
doi:10.1109/20.619670

6. Hu, J., J. Zou, F. Xu, Y. Li, and Yanchao Fu, "An improved PMSM rotor position sensor based on linear Hall sensors," IEEE Transactions on Magnetics, Vol. 48, No. 11, 3591-3594, 2012.
doi:10.1109/TMAG.2012.2202279

7. Li, K., Y. Xu, Z, Zhao, and M. Q.-H. Meng, "External and internal sensor fusion based localization strategy for 6-dof pose estimation of a magnetic capsule robot," IEEE Robotics and Automation Letters, Vol. 7, No. 3, 6878-6885, 2022.
doi:10.1109/LRA.2022.3178473

8. O'Connell, J. L., W. S. Robertson, and B. S. Cazzolato, "Optimization of the magnetic field produced by frustum permanent magnets for single magnet and planar halbach array congurations," IEEE Transactions on Magnetics, Vol. 57, No. 8, 1-9, 2021.
doi:10.1109/TMAG.2021.3085108

9. Furlani, E. P., Permanent Magnet and Electromechanical Devices: Materials, Analysis, and Applications, Academic Press, 2001.

10. Caciagli, A., R. J. Baars, A. P. Philipse, and B. W. M. Kuipers, "Exact expression for the magnetic field of a finite cylinder with arbitrary uniform magnetization," Journal of Magnetism and Magnetic Materials, Vol. 456, 423-432, 2018.
doi:10.1016/j.jmmm.2018.02.003

11. O'Connell, J. L., W. S. Robertson, and B. S. Cazzolato, "Simplied equations for the magnetic field due to an arbitrarily-shaped polyhedral permanent magnet," Journal of Magnetism and Magnetic Materials, Vol. 510, 166894, 2020.
doi:10.1016/j.jmmm.2020.166894

12. Nguyen, V. T. and T.-F. Lu, "Modelling of magnetic field distributions of elliptical cylinder permanent magnets with diametrical magnetization," Journal of Magnetism and Magnetic Materials, Vol. 491, 165569, 2019.
doi:10.1016/j.jmmm.2019.165569

13. Hart, S., K. Hart, and J. P. Selvaggi, "Analytical expressions for the magnetic field from axially magnetized and conically shaped permanent magnets," IEEE Transactions on Magnetics, Vol. 56, No. 7, 1-9, 2020.
doi:10.1109/TMAG.2020.2992191

14. Nguyen, V. T., "Magnetic field distribution of a conical permanent magnet with an application in magnetic resonance imaging," Journal of Magnetism and Magnetic Materials, Vol. 498, No. 5, 166136, 2020.
doi:10.1016/j.jmmm.2019.166136

15. Nguyen, V., S. Bollmann, M. Bermingham, and M. S. Dargusch, "Efficient modelling of permanent magnet field distribution for deep learning applications," Journal of Magnetism and Magnetic Materials, Vol. 559, 169521, 2022.
doi:10.1016/j.jmmm.2022.169521

16. Mateev, V. and I. Marinova, "Machine learning in magnetic field calculations," 2019 19th International Symposium on Electromagnetic Fields in Mechatronics, Electrical and Electronic Engineering (ISEF), 1-2, IEEE, 2019.

17. Milletari, F., N. Navab, and S.-A. Ahmadi, "V-net: Fully convolutional neural networks for volumetric medical image segmentation," 2016 Fourth International Conference on 3D Vision (3DV), 565-571, IEEE, 2016.
doi:10.1109/3DV.2016.79

18. Kelleher, J. D., Deep Learning, MIT Press, 2019.
doi:10.7551/mitpress/11171.001.0001

19. Pan, R., T. Yang, J. Cao, K. Lu, and Z. Zhang, "Missing data imputation by K nearest neighbours based on grey relational structure and mutual information," Applied Intelligence, Vol. 43, No. 3, 614-632, 2015.
doi:10.1007/s10489-015-0666-x

20. Shanker, M., M. Y. Hu, and M. S. Hung, "Effect of data standardization on neural network training," Omega, Vol. 24, No. 4, 385-397, 1996.
doi:10.1016/0305-0483(96)00010-2

21., https://www.tensor ow.org/tutorials/load data/tfrecord, (latest access on Sep. 23, 2022).

22., https://www.tensor ow.org/api docs/python/tf/keras/optimizers/Adam, (latest access Apr. 23, 2023).

23. Ronneberger, O., P. Fischer, and T. Brox, "U-net: Convolutional networks for biomedical image segmentation," International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer, 2015.

24. Weiss, K., T. M. Khoshgoftaar, and D. Wang, "A survey of transfer learning," Journal of Big Data, Vol. 3, No. 1, 1-40, 2016.
doi:10.1186/s40537-016-0043-6

25., EMS 2020 User Guide, https://www.emworks.com/portal/download, (latest access on Sep. 30, 2022).

26. Chandra, S. S., M. B. Lorenzana, X. Liu, S. Liu, S. Bollmann, and S. Crozier, "Deep learning in magnetic resonance image reconstruction," Journal of Medical Imaging and Radiation Oncology, Vol. 65, No. 5, 564-577, 2021.
doi:10.1111/1754-9485.13276

27. Karniadakis, G. E., I. G. Kevrekidis, L. Lu, P. Perdikaris, S.Wang, and L. Yang, "Physics-informed machine learning," Nature Reviews Physics, Vol. 3, No. 6, 422-440, 2021.
doi:10.1038/s42254-021-00314-5

Dr. Van Tai Nguyen

Dr. Steffen Bollmann

Dr. Michael Bermingham

Dr. Ha Xuan Nguyen

Dr. Matthew S. Dargusch