Мониторинг состояния электродвигателей на основе сверточной нейронной сети
Ключевые слова:
асинхронный двигатель, обрыв стержней ротора, анализ сигналов тока, график повторяемости, Грамиановы угловые поля, Марковские переходные поля, сверточная нейронная сеть (CNN)
Аннотация
Асинхронные электродвигатели относятся к категории наиболее критичного электрооборудования в производственных процессах, выход из строя которого приводит к существенным экономическим потерям. В статье рассматривается неисправность стержней короткозамкнутого ротора двигателя, обсуждаются существующие методы ее диагностики по сигналам тока статора и их ограничения. Основной трудностью является отсутствие данных с неисправного двигателя во всех возможных режимах работы для обучения нейросетевой модели. Предложены информативные признаки обрыва стержней ротора и изучен характер их изменения при нестационарном режиме работы двигателя. На основе этого разработан метод аугментации, позволяющий сгенерировать искусственные сигналы тока, имитирующие работу двигателя в нестационарных условиях. Для этого в спектр предобработанных сигналов тока вносятся необходимые искажения, далее применяется обратное преобразование Фурье и по реальным и синтетическим сигналам тока строятся входные изображения для сверточной нейронной сети. Используются три типа изображений временных рядов: график повторяемости, Марковские переходные поля, Грамианово угловое поле. На экспериментальных данных проведены сравнение трех методов получения изображений временных рядов и оценка эффективности метода аугментации. Наилучший прирост точности за счет аугментации демонстрирует модель, обученная на графиках повторяемости.
Литература
1. Сарваров А.С. и др. Анализ состояния электроприводов агрегатов ГОП ОАО «ММК» и пути модернизации. – Вестник МГТУ им. Г. И. Носова, 2011, № 3, с. 5–8.
2. Мусин А.М. Аварийные режимы асинхронных электродвигателей и способы их защиты. М.: Колос, 1979, 112 с.
3. After the Fall: The Costs, Causes & Consequences of Unplanned Downtime [Электрон. ресурс], URL: https://www.techinnews.com/fall-costs-causes-consequences-unplanned-downtime/ (дата обращения 15.05.2025).
4. Крюков О.В. Интеллектуальные датчики прогнозирования технического состояния высоковольтных электродвигателей. – Автоматизация в промышленности, 2013, № 10, с. 38–41.
5. Александров А.И., Кварацхелия Н.Г. Мониторинг и прогноз технического состояния электродвигателей. – Автоматизация в промышленности, 2020, № 10, с. 39–43.
6. Singh G.K., Saleh A. Induction Machine Drive Condition Monitoring and Diagnostic Research – a Survey. – Electric Power Systems Research, 2003, vol. 64, pp. 145–158, DOI: 10.1016/s0378-7796(02)00172-4.
7. Garcia M. et al. Efficiency Assessment of Induction Motors Operating Under Different Faulty Conditions. – IEEE Transactions on Industrial Electronics, 2019, vol. 66 (10), pp. 8072–8081, DOI: 10.1109/TIE.2018.2885719.
8. Вольдек А.И. Электрические машины. Л.: Энергия, 1978, 831 с.
9. Kliman G.B., Stein J. Methods of Motor Current Signature Analysis. – Electric Machines and Power Systems, 1992, vol. 20 (5), pp. 463–474, DOI: 10.1080/07313569208909609.
10. Tang J. et al. Characteristics Analysis and Measurement of Inverter-Fed Induction Motors for Stator and Rotor Fault Detection. – Energies, 2019, vol. 13 (1), DOI: 10.3390/en13010101.
11. Henao H., Razik H., Capolino G.-A. Analytical Approach of the Stator Current Frequency Harmonics Computation for Detection of Induction Machine Rotor Faults. – IEEE Transactions on Industry Applications, 2005, vol. 41 (3), pp. 801–807, DOI: 10.1109/TIA.2005.847320.
12. Panagiotou P.A. et al. A Novel Method for Rotor Fault Diagnostics in Induction Motors Using Harmonic Isolation. – 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), 2023, pp. 265–271, DOI: 10.1109/SDEMPED54949.2023.10271499.
13. Sobczyk T.J., Maciolek W. Diagnostics of Rotor-Cage Faults Supported by Effects Due to Higher Mmf Harmonics. – 2003 IEEE Bologna Power Tech Conference Proceedings, 2003, vol. 2, pp. 288–292, DOI: 10.1109/PTC.2003.1304324.
14. Lee S.B. et al. Condition Monitoring of Industrial Electric Machines: State of the Art and Future Challenges. – IEEE Industrial Electronics Magazine, 2020, vol. 14, No. 4, pp. 158–167, DOI: 10.1109/MIE.2020.3016138.
15. Sinitsin V. et al. Intelligent Bearing Fault Diagnosis Method Combining Mixed Input and Hybrid CNN-MLP Model. – Mechanical Systems and Signal Processing, 2022, vol. 180, DOI: 10.1016/j.ymssp.2022.109454.
16. Wang Z., Oates T. Imaging Time-Series to Improve Classification and Imputation [Электрон. ресурс], URL: https://arxiv.org/abs/1506.00327 (дата обращения 10.05.2025).
17. Yang C. et al. Rolling Bearing Fault Diagnosis Method Based on GAF-MTF and Deep Residual Network. – 2024 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), 2024, pp. 106–111, DOI: 10.1109/SDPC62810.2024.10707712.
18. Mukhopadhyay S., Kar I., Ralte Z. Robust Fault Diagnostics of Industrial Motors: The Signal-to-Image Approaches for Sensor Data Using Multi-Task Transformers with Diverse Attention Mechanism. – 2024 IEEE 3rd International Conference on Control, Instrumentation, Energy & Communication (CIEC), 2024, pp. 129–134, DOI: 10.1109/CIEC59440.2024.10468531.
19. Eckmann J.-P., Kamphorst S.O., Ruelle D. Recurrence Plots of Dynamical Systems. – Europhysics Letters, 1987, vol. 4, pp. 973–977, DOI: 10.1209/0295-5075/4/9/004.
20. Tarek A., Sameh M. Improved Deep-Learning Rotor Fault Diagnosis Based on Multi Vibration Sensors and Recurrence Plots. – Journal of Vibration and Control, 2025, vol. 31, No. 9–10, pp. 1874–1883, DOI: 10.1177/10775463241250367.
21. Jung W. et al. Fault Diagnosis of Inter-turn Short Circuit in Permanent Magnet Synchronous Motors with Current Signal Imaging and Semi-Supervised Learning. – IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society, 2022, DOI: 10.1109/IECON49645.2022.9968718.
22. Zhao P. et al. Gearbox Fault Diagnosis Method Based on Improved Semi-Supervised MTDL and GAF. – Measurement and Control, 2024, vol. 57, No. 8, pp. 1181–1193, DOI: 10.1177/00202940241230488.
23. Park C.H. et al. A Health Image for Deep Learning-Based Fault Diagnosis of a Permanent Magnet Synchronous Motor Under Variable Operating Conditions: Instantaneous Current Residual Map. – Reliability Engineering and System Safety, 2022, vol. 226, DOI: 10.1016/j.ress.2022.108715.
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Исследование выполнено при финансовой поддержке Министерства науки и высшего образования Российской Федерации (государственное задание на выполнение фундаментальных научных исследований №FENU-2023-0010 (2023010ГЗ)).
#
1. Sarvarov A.S. et al. Vestnik MGTU im. G. I. Nosova – in Russ. (Vestnik of Nosov Magnitogorsk State Technical University), 2011, No. 3, pp. 5–8.
2. Musin A.M. Avariynye rezhimy asinhronnyh elektrodvigateley i sposoby ih zashchity (Emergency Modes of Asynchronous Electric Motors and Methods of Their Protection). M.: Kolos, 1979, 112 p.
3. After the Fall: The Costs, Causes & Consequences of Unplanned Downtime [Electron. resource], URL: https://www.techinnews.com/fall-costs-causes-consequences-unplanned-downtime/ (Access on 15.05.2025).
4. Kryukov O.V. Avtomatizatsiya v promyshlennosti – in Russ. (Automation in Industry), 2013, No. 10, pp. 38–41.
5. Aleksandrov A.I., Kvaratsheliya N.G. Avtomatizatsiya v pro-myshlennosti – in Russ. (Automation in Industry), 2020, No. 10, pp. 39–43.
6. Singh G.K., Saleh A. Induction Machine Drive Condition Monitoring and Diagnostic Research – a Survey. – Electric Power Systems Research, 2003, vol. 64, pp. 145–158, DOI: 10.1016/s0378-7796(02)00172-4.
7. Garcia M. et al. Efficiency Assessment of Induction Motors Operating Under Different Faulty Conditions. – IEEE Transactions on Industrial Electronics, 2019, vol. 66 (10), pp. 8072–8081, DOI: 10.1109/TIE.2018.2885719.
8. Vol’dek A.I. Elektricheskie mashiny (Electric Machines). L.: Energiya, 1978, 831 p.
9. Kliman G.B., Stein J. Methods of Motor Current Signature Analysis. – Electric Machines and Power Systems, 1992, vol. 20 (5), pp. 463–474, DOI: 10.1080/07313569208909609.
10. Tang J. et al. Characteristics Analysis and Measurement of Inverter-Fed Induction Motors for Stator and Rotor Fault Detection. – Energies, 2019, vol. 13 (1), DOI: 10.3390/en13010101.
11. Henao H., Razik H., Capolino G.-A. Analytical Approach of the Stator Current Frequency Harmonics Computation for Detec-tion of Induction Machine Rotor Faults. – IEEE Transactions on Industry Applications, 2005, vol. 41 (3), pp. 801–807, DOI: 10.1109/TIA.2005.847320.
12. Panagiotou P.A. et al. A Novel Method for Rotor Fault Diagnostics in Induction Motors Using Harmonic Isolation. – 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), 2023, pp. 265–271, DOI: 10.1109/SDEMPED54949.2023.10271499.
13. Sobczyk T.J., Maciolek W. Diagnostics of Rotor-Cage Faults Supported by Effects Due to Higher Mmf Harmonics. – 2003 IEEE Bologna Power Tech Conference Proceedings, 2003, vol. 2, pp. 288–292, DOI: 10.1109/PTC.2003.1304324.
14. Lee S.B. et al. Condition Monitoring of Industrial Electric Machines: State of the Art and Future Challenges. – IEEE Industrial Electronics Magazine, 2020, vol. 14, No. 4, pp. 158–167, DOI: 10.1109/MIE.2020.3016138.
15. Sinitsin V. et al. Intelligent Bearing Fault Diagnosis Method Combining Mixed Input and Hybrid CNN-MLP Model. – Mechanical Systems and Signal Processing, 2022, vol. 180, DOI: 10.1016/j.ymssp.2022.109454.
16. Wang Z., Oates T. Imaging Time-Series to Improve Classification and Imputation [Electron. resource], URL: https://arxiv.org/abs/1506.00327 (Access on 10.05.2025).
17. Yang C. et al. Rolling Bearing Fault Diagnosis Method Based on GAF-MTF and Deep Residual Network. – 2024 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), 2024, pp. 106–111, DOI: 10.1109/SDPC62810.2024.10707712.
18. Mukhopadhyay S., Kar I., Ralte Z. Robust Fault Diagnostics of Industrial Motors: The Signal-to-Image Approaches for Sensor Data Using Multi-Task Transformers with Diverse Attention Mechanism. – 2024 IEEE 3rd International Conference on Control, Instrumentation, Energy & Communication (CIEC), 2024, pp. 129–134, DOI: 10.1109/CIEC59440.2024.10468531.
19. Eckmann J.-P., Kamphorst S.O., Ruelle D. Recurrence Plots of Dynamical Systems. – Europhysics Letters, 1987, vol. 4, pp. 973–977, DOI: 10.1209/0295-5075/4/9/004.
20. Tarek A., Sameh M. Improved Deep-Learning Rotor Fault Diagnosis Based on Multi Vibration Sensors and Recurrence Plots. – Journal of Vibration and Control, 2025, vol. 31, No. 9–10, pp. 1874–1883, DOI: 10.1177/10775463241250367.
21. Jung W. et al. Fault Diagnosis of Inter-turn Short Circuit in Permanent Magnet Synchronous Motors with Current Signal Imaging and Semi-Supervised Learning. – IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society, 2022, DOI: 10.1109/IECON49645.2022.9968718.
22. Zhao P. et al. Gearbox Fault Diagnosis Method Based on Improved Semi-Supervised MTDL and GAF. – Measurement and Control, 2024, vol. 57, No. 8, pp. 1181–1193, DOI: 10.1177/00202940241230488.
23. Park C.H. et al. A Health Image for Deep Learning-Based Fault Diagnosis of a Permanent Magnet Synchronous Motor Under Variable Operating Conditions: Instantaneous Current Residual Map. – Reliability Engineering and System Safety, 2022, vol. 226, DOI: 10.1016/j.ress.2022.108715
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The research was financially supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment for fundamental scientific research No. FENU-2023-0010 (2023010GZ))
2. Мусин А.М. Аварийные режимы асинхронных электродвигателей и способы их защиты. М.: Колос, 1979, 112 с.
3. After the Fall: The Costs, Causes & Consequences of Unplanned Downtime [Электрон. ресурс], URL: https://www.techinnews.com/fall-costs-causes-consequences-unplanned-downtime/ (дата обращения 15.05.2025).
4. Крюков О.В. Интеллектуальные датчики прогнозирования технического состояния высоковольтных электродвигателей. – Автоматизация в промышленности, 2013, № 10, с. 38–41.
5. Александров А.И., Кварацхелия Н.Г. Мониторинг и прогноз технического состояния электродвигателей. – Автоматизация в промышленности, 2020, № 10, с. 39–43.
6. Singh G.K., Saleh A. Induction Machine Drive Condition Monitoring and Diagnostic Research – a Survey. – Electric Power Systems Research, 2003, vol. 64, pp. 145–158, DOI: 10.1016/s0378-7796(02)00172-4.
7. Garcia M. et al. Efficiency Assessment of Induction Motors Operating Under Different Faulty Conditions. – IEEE Transactions on Industrial Electronics, 2019, vol. 66 (10), pp. 8072–8081, DOI: 10.1109/TIE.2018.2885719.
8. Вольдек А.И. Электрические машины. Л.: Энергия, 1978, 831 с.
9. Kliman G.B., Stein J. Methods of Motor Current Signature Analysis. – Electric Machines and Power Systems, 1992, vol. 20 (5), pp. 463–474, DOI: 10.1080/07313569208909609.
10. Tang J. et al. Characteristics Analysis and Measurement of Inverter-Fed Induction Motors for Stator and Rotor Fault Detection. – Energies, 2019, vol. 13 (1), DOI: 10.3390/en13010101.
11. Henao H., Razik H., Capolino G.-A. Analytical Approach of the Stator Current Frequency Harmonics Computation for Detection of Induction Machine Rotor Faults. – IEEE Transactions on Industry Applications, 2005, vol. 41 (3), pp. 801–807, DOI: 10.1109/TIA.2005.847320.
12. Panagiotou P.A. et al. A Novel Method for Rotor Fault Diagnostics in Induction Motors Using Harmonic Isolation. – 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), 2023, pp. 265–271, DOI: 10.1109/SDEMPED54949.2023.10271499.
13. Sobczyk T.J., Maciolek W. Diagnostics of Rotor-Cage Faults Supported by Effects Due to Higher Mmf Harmonics. – 2003 IEEE Bologna Power Tech Conference Proceedings, 2003, vol. 2, pp. 288–292, DOI: 10.1109/PTC.2003.1304324.
14. Lee S.B. et al. Condition Monitoring of Industrial Electric Machines: State of the Art and Future Challenges. – IEEE Industrial Electronics Magazine, 2020, vol. 14, No. 4, pp. 158–167, DOI: 10.1109/MIE.2020.3016138.
15. Sinitsin V. et al. Intelligent Bearing Fault Diagnosis Method Combining Mixed Input and Hybrid CNN-MLP Model. – Mechanical Systems and Signal Processing, 2022, vol. 180, DOI: 10.1016/j.ymssp.2022.109454.
16. Wang Z., Oates T. Imaging Time-Series to Improve Classification and Imputation [Электрон. ресурс], URL: https://arxiv.org/abs/1506.00327 (дата обращения 10.05.2025).
17. Yang C. et al. Rolling Bearing Fault Diagnosis Method Based on GAF-MTF and Deep Residual Network. – 2024 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), 2024, pp. 106–111, DOI: 10.1109/SDPC62810.2024.10707712.
18. Mukhopadhyay S., Kar I., Ralte Z. Robust Fault Diagnostics of Industrial Motors: The Signal-to-Image Approaches for Sensor Data Using Multi-Task Transformers with Diverse Attention Mechanism. – 2024 IEEE 3rd International Conference on Control, Instrumentation, Energy & Communication (CIEC), 2024, pp. 129–134, DOI: 10.1109/CIEC59440.2024.10468531.
19. Eckmann J.-P., Kamphorst S.O., Ruelle D. Recurrence Plots of Dynamical Systems. – Europhysics Letters, 1987, vol. 4, pp. 973–977, DOI: 10.1209/0295-5075/4/9/004.
20. Tarek A., Sameh M. Improved Deep-Learning Rotor Fault Diagnosis Based on Multi Vibration Sensors and Recurrence Plots. – Journal of Vibration and Control, 2025, vol. 31, No. 9–10, pp. 1874–1883, DOI: 10.1177/10775463241250367.
21. Jung W. et al. Fault Diagnosis of Inter-turn Short Circuit in Permanent Magnet Synchronous Motors with Current Signal Imaging and Semi-Supervised Learning. – IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society, 2022, DOI: 10.1109/IECON49645.2022.9968718.
22. Zhao P. et al. Gearbox Fault Diagnosis Method Based on Improved Semi-Supervised MTDL and GAF. – Measurement and Control, 2024, vol. 57, No. 8, pp. 1181–1193, DOI: 10.1177/00202940241230488.
23. Park C.H. et al. A Health Image for Deep Learning-Based Fault Diagnosis of a Permanent Magnet Synchronous Motor Under Variable Operating Conditions: Instantaneous Current Residual Map. – Reliability Engineering and System Safety, 2022, vol. 226, DOI: 10.1016/j.ress.2022.108715.
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Исследование выполнено при финансовой поддержке Министерства науки и высшего образования Российской Федерации (государственное задание на выполнение фундаментальных научных исследований №FENU-2023-0010 (2023010ГЗ)).
#
1. Sarvarov A.S. et al. Vestnik MGTU im. G. I. Nosova – in Russ. (Vestnik of Nosov Magnitogorsk State Technical University), 2011, No. 3, pp. 5–8.
2. Musin A.M. Avariynye rezhimy asinhronnyh elektrodvigateley i sposoby ih zashchity (Emergency Modes of Asynchronous Electric Motors and Methods of Their Protection). M.: Kolos, 1979, 112 p.
3. After the Fall: The Costs, Causes & Consequences of Unplanned Downtime [Electron. resource], URL: https://www.techinnews.com/fall-costs-causes-consequences-unplanned-downtime/ (Access on 15.05.2025).
4. Kryukov O.V. Avtomatizatsiya v promyshlennosti – in Russ. (Automation in Industry), 2013, No. 10, pp. 38–41.
5. Aleksandrov A.I., Kvaratsheliya N.G. Avtomatizatsiya v pro-myshlennosti – in Russ. (Automation in Industry), 2020, No. 10, pp. 39–43.
6. Singh G.K., Saleh A. Induction Machine Drive Condition Monitoring and Diagnostic Research – a Survey. – Electric Power Systems Research, 2003, vol. 64, pp. 145–158, DOI: 10.1016/s0378-7796(02)00172-4.
7. Garcia M. et al. Efficiency Assessment of Induction Motors Operating Under Different Faulty Conditions. – IEEE Transactions on Industrial Electronics, 2019, vol. 66 (10), pp. 8072–8081, DOI: 10.1109/TIE.2018.2885719.
8. Vol’dek A.I. Elektricheskie mashiny (Electric Machines). L.: Energiya, 1978, 831 p.
9. Kliman G.B., Stein J. Methods of Motor Current Signature Analysis. – Electric Machines and Power Systems, 1992, vol. 20 (5), pp. 463–474, DOI: 10.1080/07313569208909609.
10. Tang J. et al. Characteristics Analysis and Measurement of Inverter-Fed Induction Motors for Stator and Rotor Fault Detection. – Energies, 2019, vol. 13 (1), DOI: 10.3390/en13010101.
11. Henao H., Razik H., Capolino G.-A. Analytical Approach of the Stator Current Frequency Harmonics Computation for Detec-tion of Induction Machine Rotor Faults. – IEEE Transactions on Industry Applications, 2005, vol. 41 (3), pp. 801–807, DOI: 10.1109/TIA.2005.847320.
12. Panagiotou P.A. et al. A Novel Method for Rotor Fault Diagnostics in Induction Motors Using Harmonic Isolation. – 2023 IEEE 14th International Symposium on Diagnostics for Electrical Machines, Power Electronics and Drives (SDEMPED), 2023, pp. 265–271, DOI: 10.1109/SDEMPED54949.2023.10271499.
13. Sobczyk T.J., Maciolek W. Diagnostics of Rotor-Cage Faults Supported by Effects Due to Higher Mmf Harmonics. – 2003 IEEE Bologna Power Tech Conference Proceedings, 2003, vol. 2, pp. 288–292, DOI: 10.1109/PTC.2003.1304324.
14. Lee S.B. et al. Condition Monitoring of Industrial Electric Machines: State of the Art and Future Challenges. – IEEE Industrial Electronics Magazine, 2020, vol. 14, No. 4, pp. 158–167, DOI: 10.1109/MIE.2020.3016138.
15. Sinitsin V. et al. Intelligent Bearing Fault Diagnosis Method Combining Mixed Input and Hybrid CNN-MLP Model. – Mechanical Systems and Signal Processing, 2022, vol. 180, DOI: 10.1016/j.ymssp.2022.109454.
16. Wang Z., Oates T. Imaging Time-Series to Improve Classification and Imputation [Electron. resource], URL: https://arxiv.org/abs/1506.00327 (Access on 10.05.2025).
17. Yang C. et al. Rolling Bearing Fault Diagnosis Method Based on GAF-MTF and Deep Residual Network. – 2024 IEEE International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), 2024, pp. 106–111, DOI: 10.1109/SDPC62810.2024.10707712.
18. Mukhopadhyay S., Kar I., Ralte Z. Robust Fault Diagnostics of Industrial Motors: The Signal-to-Image Approaches for Sensor Data Using Multi-Task Transformers with Diverse Attention Mechanism. – 2024 IEEE 3rd International Conference on Control, Instrumentation, Energy & Communication (CIEC), 2024, pp. 129–134, DOI: 10.1109/CIEC59440.2024.10468531.
19. Eckmann J.-P., Kamphorst S.O., Ruelle D. Recurrence Plots of Dynamical Systems. – Europhysics Letters, 1987, vol. 4, pp. 973–977, DOI: 10.1209/0295-5075/4/9/004.
20. Tarek A., Sameh M. Improved Deep-Learning Rotor Fault Diagnosis Based on Multi Vibration Sensors and Recurrence Plots. – Journal of Vibration and Control, 2025, vol. 31, No. 9–10, pp. 1874–1883, DOI: 10.1177/10775463241250367.
21. Jung W. et al. Fault Diagnosis of Inter-turn Short Circuit in Permanent Magnet Synchronous Motors with Current Signal Imaging and Semi-Supervised Learning. – IECON 2022 – 48th Annual Conference of the IEEE Industrial Electronics Society, 2022, DOI: 10.1109/IECON49645.2022.9968718.
22. Zhao P. et al. Gearbox Fault Diagnosis Method Based on Improved Semi-Supervised MTDL and GAF. – Measurement and Control, 2024, vol. 57, No. 8, pp. 1181–1193, DOI: 10.1177/00202940241230488.
23. Park C.H. et al. A Health Image for Deep Learning-Based Fault Diagnosis of a Permanent Magnet Synchronous Motor Under Variable Operating Conditions: Instantaneous Current Residual Map. – Reliability Engineering and System Safety, 2022, vol. 226, DOI: 10.1016/j.ress.2022.108715
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The research was financially supported by the Ministry of Science and Higher Education of the Russian Federation (state assignment for fundamental scientific research No. FENU-2023-0010 (2023010GZ))
