Data – Driven modelling of the interaction force between permanent magnets

Abstract

Understanding the magnetic interaction force between permanent magnets is important for the design and optimization of the system where they are implemented. However, the methods that are utilized in the literature to compute this force are either time-consuming or approximated with a low degree of generalization. This article presents a surrogate model developed based on a data-driven approach using a deep learning method which addresses this problem. Firstly, a charge model is applied to derive a semi-analytical model (SAM) of the interaction forces between permanent magnets. Using this SAM, the features of the deep learning model (DLM) have been selected, and the training, validation and test datasets that are used to train the DLM have been generated. The DLM training process took 2 h and 30 mins to complete. The difference between the SAM and deep learning model is less than 4.2%, and there are 99.2% and 96.05% of the cases over 885 random tested samples where the errors are less than 2% and 1%, respectively; this indicates that the selected deep learning model is feasible and can provide accurate results compared to the original SAM. Moreover, the permutation feature importance (PFI) analysis shows that the most predictive feature is the separation distance between the magnets, and the heights of the magnets have less predictive power than their radii; the generality of the deep learning model is also demonstrated based on the PFI criteria. Furthermore, compared with Finite Element Analysis (FEA) and the SAM, the surrogate model yields a high accuracy of prediction (the minimum, average and maximum differences between the surrogate and FEA models are 0.06%, 0.42% and 1.74%, respectively) while it required a computational time less than 10-4 s, which is multiple orders of magnitude lower than its FEA and SAM counterparts. The developed data-driven surrogate model can facilitate the design, optimization processes of permanent magnet systems and online computation of the magnetic force through a dynamic study. In addition, using the superposition principle, the magnetic forces between cross-shaped permanent magnets can be computed using the surrogate model. The authors have further designed a user-friendly software interface to compute the magnetic force using the recently developed surrogate model; the software is publicly available under the CC BY 4.0 license, and can be found at: https://github.com/vantainguyen/Force-between-magnets-machine-learning.