Алгоритм обучения системы ультранизкочастотной виброизоляции высокоточных измерительных приборов

Алгоритм обучения системы ультранизкочастотной виброизоляции высокоточных измерительных приборов

Бойко С. В., Прохоров А. Н., Новоселов А. Н., Карпов Е. В.
Сибирский журнал индустриальной математики, 28, 4(104), 40-54 (2025)
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УДК 004.85 
DOI: 10.33048/SIBJIM.2025.28.403

Аннотация:

Предложен алгоритм обучения активных механизмов для систем виброизоляции измерительных приборов, чувствительных к критическим вибрациям почти нулевых частот. Исследуется сравнительная эффективность обучения с помощью модели искусственной нейронной сети, разработка которой основана на алгоритмических методах Левенберга — Марквардта и обратного распространения ошибки. Валидность алгоритма обучения иллюстрируется для параметрической модели позиционного управления прототипом механизма с квазинулевой жёсткостью, c использованием сформированной репрезентативной базы экспериментальных данных. Результаты исследования могут найти применение при разработке и эксплуатации высокоточных и особой точности бортовых и наземных измерительных систем.

Литература:
  1. Lee C. M., Karpov E. V., Goverdovskiy V. N., Larichkin A. Yu., Brovkina Ju. I., Prokhorov A. N. Parametric control of quasi-zero stiffness mechanisms for vibration solation at near-zero frequencies //J. Vibration and Control. 2024. V. 1; DOI: 10.1177/10775463241239381
     
  2. Li D., Liu W. Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches // Internat. J. Mech. System Dynamics. 2023. V. 4. P. 300–330.
     
  3. Kongtawong S., Chubar O., Shaftan T. Simulation of synchrotron radiation from electron beams affected by vibrations and drifts // Phys. Rev. Accelerators and Beams. 2022. V. 25. Article number 024601; DOI:10.1103/PhysRevAccelBeams.25.024601
     
  4. Lee C.-M., Goverdovskiy V. N., Tolochko B. P., Antokhin E. I., Prokhorov A. N., Larichkin A. Yu. A new concept of vibration protection systems with «quasi-zero» stiffness and a new challenge to use such systems // Proceed. 26th International Congress on Sound and Vibration (ICSV26), Montreal, Canada, 2019.
     
  5. Serluca M., Aimard B., Balik G., Caron B., Brunetti L. , Dominjon A., Jeremie A. Vibration analysis and control in particle accelerator // Proceed. FCC-ee MDI workshop CERN, France-Swiss, 2018.
     
  6. Wang M., Xiong J., Fu S. et al. An active vibration isolation and compensation system for improving optical image quality: modeling and experiment // Micromachines. 2023. V. 14. P. 1387; DOI: 10.3390/mi14071387
     
  7. Burdzik R., Khan D. An overview of the current state of knowledge and technology on techniques and procedures for signal processing, analysis, and accurate inference for transportation noise and vibration // Measurement. 2025. V. 252. Article number 117314; DOI: 10.1016/j.measurement.2025.117314
     
  8. Wang F., Zheng S., Huang C. Research and application of vibration isolation platform based on nonlinear vibration isolation system // J. Sensors. 2023. V. 1. P. 1–17; DOI:10.1155/2023/9967142
     
  9. Herzog R. Active versus passive vibration absorbers //J. Dynamic Systems, Measurement and Control. 1994. V. 116. P. 367–371; DOI: 10.1115/1.2899231
     
  10. Sun X., Xu Z. Hybrid optimization approaches for deep learning: Integrating reinforcement learning and evolutionary algorithms // J. Machine Learning Research. 2023. V. 24, N 1. P. 1–25.
     
  11. Qian X., Xiaodan W., Lei L., Yafei S. Dynamic bound adaptive gradient methods with belief in observed gradients // Pattern Recognition. 2025. V. 168. P. 111819; DOI:10.1016/j.patcog.2025.111819
     
  12. Zhang Z.,Yuan G., Qin Z., Luo Q. An improvement by introducing LBFGS idea into the Adam optimizer for machine learning // Expert Syst. Appl. 2026. V. 296. Article number 129002; DOI:10.1016/j.eswa.2025.129002 
     
  13. Alridha H. A., Abd Alsherify F. H., Al-Khafaji Z. A Review of Optimization Techniques: Applications and Comparative Analysis // J. Computer Sci. Math. 2024. V. 5, N 2. P. 122–134; DOI:10.52866/ijcsm.2024.05.02.011 
     
  14. Song M.-H. Trainability and Generalization of Small-Scale Neural Networks. PhD-thesis. University of Illinois, Urabana, USA. 2019.
     
  15. Li S. , Zhang N., Tao Z. A kind of vibratory isolation algorithms based on neural network // Proceed. Internat. Conf. «Geo-Informatics in Resource Management and Sustainable Ecosystem». 2016. P. 128– 136; DOI: 10.1007/978 − 3 − 662 − 49155 − 312
     
  16. Ghahremani A., Hamid Khaloozadeh H., Ghahremani P. Adaptive sliding neural network-based vibration control of a nonlinear quarter car active suspension system with unknown dynamics // Vibroengineering Procedia. 2018. V. 17, N 10. P. 67–72; DOI: 0.21595/vp.2018.19871
     
  17. Han S.-Y., Dong J.-F., Zhou J. , Chen Y.-H. Adaptive fuzzy PID control strategy for vehicle active suspension based on road evaluation // Electronics. 2022. V. 921. Article number 11060921.
     
  18. Yang K. , Tong W., Zhou X. Active vibration isolation of a monostable nonlinear electromagnetic actuator using machine learning adaptive feedforward control // Chaos, Solitons and Fractals. 2025. V. 192. P. 116035.
     
  19. Lee C.-M., Goverdovskiy V. N. Vibration Protection Systems. Negative and Quasi-Zero Stiffness. Cambridge University Press, 2021. DOI:10.1016/j.chaos.2025.116035.
     
  20. Zhang L. J., Das T., Yu X. Y. Neural network-based control and active vibration mitigation in a fullyflexible arm space robot under elastic base influence: A luenberger observer approach // Internat. J. Comput. Intelligence Systems. 2023. V. 2, N 2. P. 197–208; https://doi.org/10.56578/jisc020402.
     
  21. Xia Y., Ghasempoor Ah. Active Vibration Suppression Using Neural Networks. The World Congress on Engrg. V. II. London, U.K., 2009.
     
  22. Kaygorodtseva A. A., Shutov A. V. Inspection of ratcheting models for pathological error sensitivity and overparametrization // Meccanica. 2022. V. 57, N 8. P. 1975–2000; DOI: 10.1007/s11012-022-01533-5
     
  23. Rumelhart D. E., Hinton G. E., Williams R. J. Learning representations by back-propagating errors // Nature. 1986. V. 323. P. 533–536.
     
  24. Kirsan A. S., Takano K., Mansurina S. T. Z. EksPy: A new Python framework for developing graphical user interface based PyQt5 // Internat. J. Electrical and Comput. Engrg. 2024. V. 14, N 1. P. 520–531; DOI:10.11591/ijece.v14i1.pp520-531
     
  25.  Saabith S., Vinothraj T., Fareez M. A review on python libraries and ides for data science // Internat. J. Research Engrg. Sci. 2021. V. 9, N 11. P. 36–53.
     
  26. He R., Li B., Li F., Qingqing S. A Review of Feature Engineering Methods in Regression Problems // Academic J. Natural Sci. 2024. V. 9, N 11. P. 32–40; DOI: 10.5281/zenodo.13905622
     
  27. Говердовский В. Н., Ли Ч.-М., Прохоров А. Н., Ларичкин А. Ю., Полубояров В. А. Способ виброизоляции и механизм для реализации способа. РФ патент № 2753061, 2021.

Исследование выполнено при финансовой поддержке Российского научного фонда (проект № 23-19-00258). Других источников финансирования проведения или руководства данным конкретным исследованием не было.

С. В. Бойко
  1. Институт гидродинамики им. М. А. Лаврентьева СО РАН, 
    просп. Лаврентьева, 15, Новосибирск 630090, Россия
  2. Московский политехнический университет, 
    Большая Семёновская, 38, Москва 107023, Россия

E-mail: boykosv.hydro@gmail.com 

А. Н. Прохоров
  1. Московский политехнический университет, 
    Большая Семёновская, 38, Москва 107023, Россия

E-mail: prohorovan05@yandex.ru 

А. Н. Новоселов
  1. Институт гидродинамики им. М. А. Лаврентьева СО РАН, 
    просп. Лаврентьева, 15, Новосибирск 630090, Россия
  2. Московский политехнический университет, 
    Большая Семёновская, 38, Москва 107023, Россия

E-mail: Aleksey.Novoselov@gmail.com 

Е. В. Карпов
  1. Институт гидродинамики им. М. А. Лаврентьева СО РАН, 
    просп. Лаврентьева, 15, Новосибирск 630090, Россия
  2. Московский политехнический университет, 
    Большая Семёновская, 38, Москва 107023, Россия

E-mail: evkarpov@mail.ru 

Статья поступила 07.08.2024 г.
После доработки — 14.11.2025 г.
Принята к публикации 03.12.2025 г.

Abstract:

This paper presents an algorithm for learning the active mechanisms for vibration isolation systems of measuring instruments sensitive to critical vibrations at near-zero frequencies. The comparative effectiveness is studied for the learning using a model of artificial neural network under development based on the algorithmic methods of Levenberg-Marquardt and error back propagation. The validity of the learning algorithm is illustrated for a parametric model of positional control by using a prototype mechanism with quasi-zero stiffness, for which a representative database of experimental data has been formed. The results of the study can be used for developing and operating the high-precision and ultra-high-precision on-board and ground-based measuring systems.

References:
  1. Lee C. M., Karpov E. V., Goverdovskiy V. N., Larichkin A. Yu., Brovkina Ju. I., Prokhorov A. N. Parametric control of quasi-zero stiffness mechanisms for vibration solation at near-zero frequencies. J. Vibration and Control, 2024, Vol. 1; DOI: 10.1177/10775463241239381
     
  2. Li D., Liu W. Vibration control for the solar panels of spacecraft: Innovation methods and potential approaches. Internat. J. Mech. System Dynamics, 2023, Vol. 4, pp. 300–330.
     
  3. Kongtawong S., Chubar O., Shaftan T. Simulation of synchrotron radiation from electron beams affected by vibrations and drifts. Phys. Rev. Accelerators and Beams, 2022, Vol. 25, Article number 024601; DOI:10.1103/PhysRevAccelBeams.25.024601
     
  4. Lee C.-M., Goverdovskiy V. N., Tolochko B. P., Antokhin E. I., Prokhorov A. N., Larichkin A. Yu. A new concept of vibration protection systems with «quasi-zero» stiffness and a new challenge to use such systems. Proceed. 26th International Congress on Sound and Vibration (ICSV26), Montreal, Canada, 2019.
     
  5. Serluca M., Aimard B., Balik G., Caron B., Brunetti L. , Dominjon A., Jeremie A. Vibration analysis and control in particle accelerator. Proceed. FCC-ee MDI workshop CERN, France-Swiss, 2018.
  6.  
  7. Wang M., Xiong J., Fu S. et al. An active vibration isolation and compensation system for improving optical image quality: modeling and experiment. Micromachines, 2023, Vol. 14, pp. 1387; DOI: 10.3390/mi14071387
     
  8. Burdzik R., Khan D. An overview of the current state of knowledge and technology on techniques and procedures for signal processing, analysis, and accurate inference for transportation noise and vibration. Measurement, 2025, Vol. 252, Article number 117314; DOI: 10.1016/j.measurement.2025.117314
     
  9. Wang F., Zheng S., Huang C. Research and application of vibration isolation platform based on nonlinear vibration isolation system. J. Sensors, 2023, Vol. 1, pp. 1–17; DOI:10.1155/2023/9967142
     
  10. Herzog R. Active versus passive vibration absorbers. J. Dynamic Systems, Measurement and Control, 1994, Vol. 116, pp. 367–371; DOI: 10.1115/1.2899231
     
  11. Sun X., Xu Z. Hybrid optimization approaches for deep learning: Integrating reinforcement learning and evolutionary algorithms. J. Machine Learning Research, 2023, Vol. 24, No. 1, pp. 1–25.
     
  12. Qian X., Xiaodan W., Lei L., Yafei S. Dynamic bound adaptive gradient methods with belief in observed gradients. Pattern Recognition, 2025, Vol. 168, pp. 111819; DOI:10.1016/j.patcog.2025.111819
     
  13. Zhang Z.,Yuan G., Qin Z., Luo Q. An improvement by introducing LBFGS idea into the Adam optimizer for machine learning. Expert Syst. Appl., 2026, Vol. 296, Article number 129002; DOI:10.1016/j.eswa.2025.129002 
     
  14. Alridha H. A., Abd Alsherify F. H., Al-Khafaji Z. A Review of Optimization Techniques: Applications and Comparative Analysis. Iraqi J. Computer Sci. Math., 2024, Vol. 5, No. 2, pp. 122–134; DOI:10.52866/ijcsm.2024.05.02.011
     
  15. Song M.-H. Trainability and Generalization of Small-Scale Neural Networks, PhD-thesis. University of Illinois, Urabana, USA. 2019.
     
  16. Li S. , Zhang N., Tao Z. A kind of vibratory isolation algorithms based on neural network. Proceed. Internat. Conf. «Geo-Informatics in Resource Management and Sustainable Ecosystem», 2016, pp. 128– 136; DOI: 10.1007/978 − 3 − 662 − 49155 − 3_12
     
  17. Ghahremani A., Hamid Khaloozadeh H., Ghahremani P. Adaptive sliding neural network-based vibration control of a nonlinear quarter car active suspension system with unknown dynamics. Vibroengineering Procedia, 2018, Vol. 17, No. 10, pp. 67–72; DOI: 0.21595/vp.2018.19871
     
  18. Han S.-Y., Dong J.-F., Zhou J. , Chen Y.-H. Adaptive fuzzy PID control strategy for vehicle active suspension based on road evaluation. Electronics, 2022, Vol. 921, Article number 11060921.
     
  19. Yang K. , Tong W., Zhou X. Active vibration isolation of a monostable nonlinear electromagnetic actuator using machine learning adaptive feedforward control. Chaos, Solitons and Fractals, 2025, Vol. 192, pp. 116035.
     
  20. Lee C.-M., Goverdovskiy V. N. Vibration Protection Systems. Negative and Quasi-Zero Stiffness. Cambridge University Press, 2021. DOI:10.1016/j.chaos.2025.116035.
     
  21. Zhang L. J., Das T., Yu X. Y. Neural network-based control and active vibration mitigation in a fully-flexible arm space robot under elastic base influence: A luenberger observer approach. Internat. J. Comput. Intelligence Systems, 2023, Vol. 2, No. 2, pp. 197–208; https://doi.org/10.56578/jisc020402
     
  22. Xia Y., Ghasempoor Ah. Active Vibration Suppression Using Neural Networks. The World Congress on Engrg., V. II. London, U.K., 2009.
     
  23. Kaygorodtseva A. A., Shutov A. V. Inspection of ratcheting models for pathological error sensitivity and overparametrization. Meccanica, 2022, Vol. 57, No. 8, pp. 1975–2000; DOI: 10.1007/s11012-022-01533-5
     
  24. Rumelhart D. E., Hinton G. E., Williams R. J. Learning representations by back-propagating errors. Nature, 1986, Vol. 323, pp. 533–536.
     
  25. Kirsan A. S., Takano K., Mansurina S. T. Z. EksPy: A new Python framework for developing graphical user interface based PyQt5. Internat. J. Electrical and Comput. Engrg., 2024, Vol. 14, No. 1, pp. 520–531; DOI:10.11591/ijece.v14i1.pp520-531
     
  26. Saabith S., Vinothraj T., Fareez M. A review on python libraries and ides for data science. Internat. J. Research Engrg. Sci., 2021, Vol. 9, No. 11, pp. 36–53.
     
  27. He R., Li B., Li F., Qingqing S. A Review of Feature Engineering Methods in Regression Problems. Academic J. Natural Sci., 2024, Vol. 9, No. 11, pp. 32–40; DOI: 10.5281/zenodo.13905622
     
  28. Goverdovskii V. N., Li Ch.-M., Prokhorov A. N., Larichkin A. Yu., Poluboyarov V. A. Sposob vibroizolyatsii i mekhanizm dlya realizatsii sposoba [A vibration isolation method and a mechanism for implementing the method]. Patent № 2753061, Russia, 2021.