REVIEW OF ALTERNATIVE APPROACHES TO SIMULATION OF THE ELECTROMAGNETIC SITUATION AT A HIGH-VOLTAGE ELECTRIC SUBSTATION

Authors

Asan uulu A.
Bakasova A. B. Machinery researching and Automatics Institute of Kyrgyz Republic National Academy of Science

Keywords:

electromagnetic field, electromagnetic compatibility, electromagnetic environment, boundary value problems, boundary conditions, artificial intelligence, neural network

Abstract

In the field of electromagnetism, boundary value problems are problems for which the electromagnetic field in a given region of space is determined from knowledge of the field over the boundary of the region. To solve boundary problems, traditional numerical methods are usually used, such as the finite difference method (FDM) in the time domain and the finite element method (FEM). However, these methods involve discretizing the domain to reduce it to a higher order system of linear algebraic equations and finding a solution for them. As you know, these methods are not local, i.e. they do not give the value of the solution directly at an arbitrary point where the field is to be defined, but its value must be extracted from the full solution of the field, and therefore cannot be processed in parallel. In this regard, the article considers the use of neural networks for boundary value problems with the Dirichlet boundary condition and with mixed boundary conditions.

References

I. E. Lagaris, A. Likas and D. I. Fotiadis, ”Artificial neural networks for solving ordinary and partial differential equations,” in IEEE Transactions on Neural Networks, vol. 9, no. 5, pp. 987-1000, Sep 1998. doi: 10.1109/72.712178

К. С. Макфолл и Дж. Р. Махан, «Метод искусственной нейронной сети для решения краевых задач с точным удовлетворением произвольных граничных условий», в IEEE Transactions on Neural Networks, vol. 20, нет. 8, стр. 1221-1233, август 2009 г. doi: 10.1109/TNN.2009.2020735

M. M. Chiaramonte, M. Kiener. Solving differential equations using neural networks. http://cs229.stanford.edu/proj2013/ ChiaramonteKiener-SolvingDifferentialEquationsUsingNeuralNetworks. pdf.

СР. Харрингтон, Роджер. (1961). Гармоническое электромагнитное поле во времени. 10.1109/9780470546710.

Бакасова, А. Б. Применение нейронных сетей в задачах электромагнитных помех / А. Б. Бакасова, А. Асан Уулу // Проблемы автоматики и управления. – 2022. – № 1(43). – С. 95-103. – EDN DJPYDH.

Верзунов, С. Н. Система искусственного интеллекта для онлайн мониторинга подземных силовых кабельных линий на основе технологий глубокого обучения / С. Н. Верзунов // Проблемы автоматики и управления. – 2021. – № 3(42). – С. 83-94. – EDN DVCIKE.

Р. Йентис и М. Э. Заглул, «Реализация СБИС локально связанной нейронной сети для решения уравнений в частных производных», в IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 43, нет. 8, стр. 687-690, август 1996 г. doi: 10.1109/81.526685

J. Han. Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differ¬ential equations ftp://ftp.math.ucla.edu/pub/camreport/cam17-41.pdf

К. Макфолл, Метод искусственной нейронной сети для решения краевых задач, Германия, Saarbrcken: VDM Verlag, 2006. https://smartech.gatech.edu/bitstream/handle/1853/10506/mcfalLkevin_C200605_phd.pdf (Дата обращения 25.04.2022)

Библиотеки, используемые в этом проекте: Tensor Flow: https://www.tensorflow.org/; NumPy: http://www.numpy.org/; Matplotlib: https://matplotlib.org/; (Дата обращения 01.04.2022)

SH Kolluru, Preliminary Investigations of a Stochastic Method to solve Electrostatic and Electrodynamic Problems. Masters The¬sis, UNIVERSITY OF MASSACHUSETTS AMHERST, August 2008, http://scholarworks.umass.edu/cgi/viewcontent.cgi?article=1261& context=theses