350 rub
Journal Neurocomputers №2 for 2025 г.
Article in number:
Setting up the parameters of dynamic models of the organizational and technological process of railway transport technical vehicles re-pair using Neural ODE
Type of article: scientific article
DOI: https://doi.org/10.18127/j19998554-202502-05
UDC: 519.6, 519.711.3, 004.89
Authors:

O.V. Druzhinina1, I.V. Makarenkova2, V.V. Maksimova3
1–3 FRС «Computer Science and Control» of RAS (Moscow, Russia)

1 ovdruzh@mail.ru, 2 imakarenkova@ipiran.ru, 3 vmaksimova@mail.ru

Abstract:

The problems related to parametric identification of dynamic models of transport infrastructure’s technical objects are of great current interest. The solution to these problems is aimed at ensuring the safety and stability of traffic, expanding the functionality of monitoring and diagnostic systems. Currently, data mining and neural network modeling methods are widely used to study the properties of dynamic models described by various types of multidimensional nonlinear differential equations, along with classical methods of control theory. The objectives of the article are to analyze trajectory dynamics and to adjust the parameters of a mathematical model of the organizational and technological process of repairing railway transport technical vehicles using artificial intelligence tools. The article proposes a scheme for setting the parameters of an analytical dynamic model that describes the organizational and technological process of repairing railway transport technical vehicles trough neural differential equations (Neural ODE). We propose to use sets of time series with data on the observed characteristics of repaired equipment as input parameters for Neural ODE. The article shows that the implementation of machine learning cycles leads to the production of refined parametric sets while the empirical data used in the learning process are considered. A series of computer experiments has been conducted, the interpretation has been given, and the results of parametric setting performed using deep learning based on Neural ODE have been described. A deep learning framework with appropriate classes and libraries has been used to programmatically implement the parameter tuning algorithm. The results can be used in solving optimal control problems related to setting the parameters of technical facilities, parametric identification and numerical modeling problems. The approach to studying models of the organizational and technological process of repairing technical means of transport can be used to create digital twins in the transport industry, to optimize the number of vehicles and improve the transportation process, and to predict the modes of operation of transport infrastructure components.

Pages: 43-53
For citation

Druzhinina O.V., Makarenkova I.V., Maksimova V.V. Setting up the parameters of dynamic models of the organizational and technological process of railway transport technical vehicles repair using Neural ODE. Neurocomputers. 2025. V. 27. № 2. P. 43–53. DOI: https://doi.org/10.18127/j19998554-202502-05 (in Russian)

References
  1. Prokhorov A., Lysachev M. Tsifrovoj dvojnik. Analiz, trendy, mirovoj opyt. Pod red. A. Borovkova. M.: OOO «Al'yans-Print». 2020. (in Russian)
  2. Kontseptsiya realizatsii kompleksnogo nauchno-tekhnicheskogo proekta «Tsifrovaya zheleznaya doroga». M.: OAO RZhD. 2017. (in Russian)
  3. Chechenova L.M., Uskov V.S. Tsifrovoe modelirovanie ob''ektov transportnoj infrastruktury (na primere postroeniya modeli «umnoj» tsifrovoj infrastruktury Rossijskikh zheleznykh dorog). Transportnoe delo Rossii. 2022. № 6. S. 28–30. (in Russian)
  4. Belousov V.V., Druzhinina O.V., Korepanov E.R., Makarenkova I.V., Maksimova V.V. Podkhod k otsenke tekhnicheskogo sostoyaniya elementov i uzlov transportnykh sistem s primeneniem metodov nejrosetevogo modelirovaniya i tekhnologii tsifrovykh dvojnikov. Nejrokomp'yutery: razrabotka, primenenie. 2021. T. 23. № 5. S. 5–20. (in Russian)
  5. Kulikov M.Yu., Kuzyutin A.S., Dybo M.I. Razrabotka matematicheskoj modeli tekhnologicheskoj sistemy vagonoremontnogo predpriyatiya. Transportnoe mashinostroenie. 2018. № 6 (67). S. 38–45. (in Russian)
  6. Turanov Kh.T., Chuev N.P., Portnova O.Yu. Chislennoe modelirovanie dvizheniya gruzovykh vagonov na pod''ezdnykh putyakh promyshlennykh predpriyatij v Maple. Nauchnyj informatsionnyj sbornik «Transport: nauka, tekhnika, upravlenie». 2013. № 12. S. 7–14. (in Russian)
  7. Turanov Kh.T., Chuev N.P., Portnova O.Yu. Matematicheskoe modelirovanie dvizheniya gruzovykh vagonov na pod''ezdnykh putyakh predpriyatiya. Nauka i tekhnika transporta. 2013. № 1. S. 26–42. (in Russian)
  8. Chuev N.P., Skripaj A.S. Analiticheskie issledovaniya dinamiki chislennosti podvizhnogo sostava. Vestnik Ural'skogo gosudarstvennogo universiteta putej soobshcheniya. 2014. № 1 (21). S. 4–13. (in Russian)
  9. Chuev N.P., Gorokhova K.O. O nekotorykh differentsial'nykh modelyakh iznosa i remonta tekhnicheskikh sredstv zheleznodorozhnogo transporta. Vestnik Ural'skogo gosudarstvennogo universiteta putej soobshcheniya. 2015. № 3 (27). S. 4–13. (in Russian)
  10. Turanov Kh.T., Ilesaliev D.I. Issledovanie matematicheskoj modeli obespecheniya vagonami zernoelevatorov. Nauchnyj informatsionnyj sbornik «Transport: nauka, tekhnika, upravlenie». 2020. № 5. S. 37–40. (in Russian)
  11. Druzhinina O.V., Makarenkova I.V., Maksimova V.V. Postroenie i komp'yuternoe issledovanie matematicheskikh modelej remonta i ekspluatatsii tekhnicheskikh sredstv zheleznodorozhnogo transporta. Nelinejnyj mir. 2023. T. 21. № 1. S. 5–12. DOI: 10.18127/j20700970-202301-01. (in Russian)
  12. Druzhinina O.V., Makarenkova I.V., Maksimova V.V. Issledovanie nestatsionarnykh dinamicheskikh modelej organizatsionno-tekhno­logicheskogo protsessa remonta tekhnicheskikh sredstv zheleznodorozhnogo transporta. Nelinejnyj mir. 2024. T. 22. № 2. S. 5–17. DOI: 10.18127/j20700970-202402-01. (in Russian)
  13. Dejch A.M. Metody identifikatsii dinamicheskikh ob''ektov. M.: Energiya. 1979. (in Russian)
  14. Bojkov I.V. Analiticheskie i chislennye metody identifikatsii dinamicheskikh sistem. Penza: Izd-vo Penzenskogo gos. un-ta. 2016. (in Russian)
  15. Chen R.T.Q., Rubanova Yu., Bettencourt J., Duvenaud D. Neural ordinary differential equations. Advances in Neural Information Processing Systems. 2018. V. 31. P. 6571–6583.
  16. Chen R.T.Q., Amos B., Nickel M. Learning neural event functions for ordinary differential equations. arXiv preprint arXiv:2011.03902v4 [Elektronnyj resurs]. URL: https://arxiv.org/pdf/2011.03902 (data obrashcheniya: 27.12.2024).
  17. Borovkov A.I., Zhitkov Yu.B., Vorob'ev A.S. Razrabotka podkhodov k raschetu prochnosti i resursa elementov konstruktsii podvizhnogo sostava s primeneniem tekhnologii tsifrovogo dvojnika i tsifrovoj platformy CML-Bench. Sb. materialov pervoj Mezhdunar. nauch.-tekhnich. konf. «Zheleznodorozhnyj podvizhnoj sostav: problemy, resheniya, perspektivy» (Tashkent, 20–23 aprelya 2022 g.). Tashkent: Tashkentskij gosudarstvennyj transportnyj universitet. 2022. S. 34–38. (in Russian)
  18. Rao D.J. Digital twin for the railway network. Making trains «Look» for track defects. GE Transportation – Digital Solutions. 2018 [Elektronnyj resurs]. URL: https://www.slideshare.net/DattarajRao/digital-twin-for-the-railwaynetwork (data obrashcheniya: 27.12.2024). (in Russian)
  19. Druzhinina O.V., Korepanov E.R., Petrov A.A., Makarenkova I.V., Maksimova V.V. Postroenie modeli generatsii dannykh dlya resheniya zadach klassifikatsii v diagnostike neispravnostej transportnykh sistem. Nelinejnyj mir. 2023. T. 21. № 3. S. 16–26. DOI: 10.18127/ j20700970-202303-02. (in Russian)
  20. Moskvichev O.V., Moskvicheva E.E., Khishova A.A. Obzornyj analiz realizatsii otechestvennykh tsifrovykh tekhnologij v rabote gruzovykh zheleznodorozhnykh stantsij. Vestnik Rostovskogo gosudarstvennogo universiteta putej soobshcheniya. 2024. № 2 (94). S. 156–164. (in Russian)
  21. Semenov A., Fradkov A. Parameters identification of the multispecies Lotka–Volterra model using discrete algorithm. 7th Scientific School Dynamics of Complex Networks and their Applications DCNA. Kaliningrad, Russian Federation. 2023. P. 237–240. DOI: https://doi.org/ 10.1109/DCNA59899.2023.10290695.
  22. Semenov A., Fradkov A. Identification of parameters of conservative multispecies Lotka–Volterra system based on sampled data. Mathematics. 2024. V. 12. № 2. P. 248.
  23. Shakurov I.R., Asadullin R.M. Identifikatsiya parametrov sistem nelinejnykh differentsial'nykh uravnenij na primere modeli Lotki–Vol'terra. Biofizika. 2014. T. 59. № 2. S. 414–415. (in Russian)
  24. Kondrashkov A.V., Pichugin Yu.A. Identifikatsiya i statisticheskaya proverka ustojchivosti modeli Vol'terry. Nauchno-tekhnicheskie vedomosti SPbGPU. 2014. № 1 (189). S. 124–135. (in Russian)
  25. Margasov A.O. O nejronnykh obyknovennykh differentsial'nykh uravneniyakh i ikh veroyatnostnom rasshirenii. Izvestiya Komi NTs UrO RAN. Seriya «Fiziko-matematicheskie nauki». 2021. № 6 (52). S. 14–19. (in Russian)
  26. Bárcena-Petisco J.A. Optimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problems. HAL archive: hal-03299270v4 [Elektronnyj resurs]. URL: https://hal.science/hal-03299270v4 (data obrashcheniya: 27.12.2024).
  27. PyTorch implementation of differentiable ODE solvers [Elektronnyj resurs]. URL: https://github.com/rtqichen/torchdiffeq (data obra­shcheniya: 25.12.2024).
  28. Hannay K. Differential equations as a Pytorch neural network layer. April 8, 2023. [Elektronnyj resurs]. URL: https://khannay.com/ posts/pytorch-ode/ode.html (data obrashcheniya: 25.12.2024).
Date of receipt: 31.01.2025
Approved after review: 18.02.2025
Accepted for publication: 14.03.2025