Comparative analysis of machine learning methods for reconstructing the magnetic characteristic of short samples in a measurement system with a parallel magnetic shunt

The paper addresses the problem of reconstructing the magnetic characteristic of a short sample material from measurements obtained in a magnetic measurement system with a parallel magnetic shunt. Previous studies have shown that introducing a shunt increases measurement sensitivity over a wide range of magnetic permeabilities of the investigated material, which is especially important for short samples and under limitations on the magnetizing current. However, the presence of a parallel branch causes magnetic flux redistribution and complicates the interpretation of measurement data, making direct analytical reconstruction procedures difficult. In this work, machine learning methods are considered for solving the inverse problem of reconstructing the magnetic characteristic from measured dependences. In contrast to earlier research where only neural-network models were analyzed, this paper provides a comparative analysis of five learning algorithms from different model classes. Training and testing are performed under conditions close to real measurements, taking into account possible errors of the measurement channels. It is shown that the best reconstruction quality at the specified noise level is achieved by the Random Forest, which outperforms the alternatives in terms of mean squared error and robustness to disturbances.

1. Surnyaev V.A., Blazhko I.O., Blazhkova E.N., et al. Application of a magnetic shunt to increase the sensitivity of a device for testing samples of magnetostrictive materials. Engineering Journal of Don. 2021;(9). (In Russ.). URL: http://ivdon.ru/en/magazine/archive/n9y2021/7200

2. Surnyaev V.A., Surnyaev D.A. Measuring device of the magnetic characteristics of the magnetostrictive materials. Engineering Journal of Don. 2016;(4). (In Russ.). URL: http://ivdon.ru/en/magazine/archive/n4y2016/3956

3. Hastie T., Tibshirani R., Friedman J. The Elements of Statistical Learning: Data Mining, Inference, and Prediction. New York: Springer; 2009. 745 p. https://doi.org/10.1007/978-0-387-84858-7

4. Pyle D. Data Preparation for Data Mining. San Francisco: Morgan Kaufmann Publishers; 1999. 540 p.

5. Kuhn M., Johnson K. Feature Engineering and Selection: A Practical Approach for Predictive Models. Boca Raton: CRC Press; 2019. 310 p.

6. Bottou L. Large-Scale Machine Learning with Stochastic Gradient Descent. In: Proceedings of COMPSTAT'2010: 19th International Conference on Computational Statistics, 22–27 August 2010, Paris, France. Heidelberg: Physica; 2010. P. 177–186. https://doi.org/10.1007/978-3-7908-2604-3_16

7. Breiman L., Friedman J., Olshen R.A., Stone Ch.J. Classification and Regression Trees. New York: Chapman and Hall/CRC; 1984. 368 p. https://doi.org/10.1201/9781315139470

8. Breiman L. Random Forests. Machine Learning. 2001;45(1):5–32. https://doi.org/10.1023/A:1010933404324

9. Friedman J.H. Greedy Function Approximation: A Gradient Boosting Machine. The Annals of Statistics. 2001;29(5):1189–1232. https://doi.org/10.1214/aos/1013203451

10. Cover T., Hart P. Nearest Neighbor Pattern Classification. IEEE Transactions on Information Theory. 1967;13(1):21–27. https://doi.org/10.1109/TIT.1967.1053964