Том 3 № 4 (2025): Промышленная кибернетика
DOI https://doi.org/10.18799/29495407/2025/4/106
Анализ почвенно-температурных серий методами энтропии
Представлены итоги изучения хаотичных характеристик температурных последовательностей почвенных измерений, выполненных с разным временным разрешением на протяжении трёх лет мониторинга. Для детального анализа особенностей временных рядов, оценки степени их хаоса и воспроизведения различных моделей хаотических процессов применялся специализированный инструментарий пакета языка статистики R. Рассчитаны показатели функций взаимной информации, отражающих степень зависимости между элементами ряда, построены диаграммы экспоненты Ляпунова. Проведен контроль наличия нелинейных эффектов с использованием теста нейронных сетей Terasvirta test. Проверка значимости дополнительных компонентов через статистику хи-квадрата и F-статистику подтвердила хаотичный характер изучаемых температурных рядов почвы.
Ключевые слова:
нелинейность, нелинейная динамика, анализ временных рядов, энтропия
Библиографические ссылки:
СПИСОК ЛИТЕРАТУРЫ
1. Xu S., Cheng J., Zhang Q. Reconstructing all-weather land surface temperature using the bayesian maximum entropy method over the Tibetan Plateau and Heihe River Basin // IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing. – 2019. – Vol. 12. – № 9. – P. 3307–3316. DOI: 10.1109/JSTARS.2019.2921924
2. Wu B., Yi J., Yong Q. Research on principle and application of maximum entropy // Chinese Control and Decision Conference (CCDC). – Hefei, China, 2020. – P. 2571–2576. DOI: 10.1109/CCDC49329.2020.9164431.
3. Grivel E., Legrand P., Berthelot B. Multiscale entropy rate: a variant of the multiscale entropy // 32nd European Signal Processing Conference (EUSIPCO). – Lyon, France, 2024. – P. 2572–2576. DOI: 10.23919/EUSIPCO63174.2024.10715011
4. Analysis of characteristics in motor failure of power system based on power spectral entropy / W. Hsu, R. Chen, Z. Yang, C. Huang // 6th International Conference on Energy, Power and Grid (ICEPG). – Guangzhou, China, 2024. – P. 1399–1402. DOI:10.1109/ICEPG63230.2024.10775957
5. Papageorgiou I., Kontoyiannis I. Truly Bayesian entropy estimation // arXiv:2212.06705. https://doi.org/10.48550/arXiv.2212.06705
6. Yang H., Rong P., Sun G. Subject-independent Emotion recognition based on Entropy of EEG Signals // 33rd Chinese Control and Decision Conference (CCDC). – Kunming, China, 2021. – P. 1513–1518. DOI: 10.1109/CCDC52312.2021.9602439
7. Sun M., Hao Q., Yang X. A novel ICEEMDAN-based denoising approach coupled with multi-scale entropy features for ship-radiated noise recognition // 7th International Conference on Information Science, Electrical and Automation Engineering (ISEAE). – Harbin, China, 2025. – P. 970–973. DOI: 10.1109/ISEAE64934.2025.11042007
8. Bearing fault diagnosis based on the refined composite generalized multi-scale bubble entropy / Z. Jinbao, Z. Tiangang, W. Min, C. Shidong // 4th International Conference on Electron Device and Mechanical Engineering (ICEDME). – Guangzhou, China, 2021. – P. 172–175. DOI: 10.1109/ICEDME52809.2021.00044
9. Куркина В.В., Сиринова М.С., Александров Д.А. Обеспечение диагностируемости технологического процесса минимальным числом датчиков на основе энтропийного критерия // Международная научная конференция по проблемам управления в технических системах. – СПб.: Санкт-Петербургский государственный электротехнический университет "ЛЭТИ" им. В.И. Ульянова (Ленина), 2021. – Т. 1. – С. 239–242. EDN IVXXJW
10. Using entropy estimation to detect moving objects / I.U. Kondratieva, H.V. Rudakova, O.V. Polyvoda, Y.O. Lebedenko, V.V. Polyvoda // 2019 IEEE 5th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD). – Kiev, Ukraine, 2019. – P. 270–273. DOI: 10.1109/APUAVD47061.2019.8943839
11. Eponeshnikov A.V., Sulimov A.I. Histogram-based estimation of cir entropy for multipath propagation environments // International Conference on Electrical Engineering and Photonics (EExPolytech). – Saint Petersburg, Russian Federation, 2024. – P. 163–166.
12. The Comprehensive R Archive Network. URL: https://cran.r-project.org/ (access date: 15.08.2025).
13. fNonlinear: Rmetrics – Nonlinear and Chaotic Time Series Modelling. URL: https://cran.r-project.org/web/packages/fNonlinear/index.html (access date: 15.08.2025).
14. tseriesEntropy: Entropy Based Analysis and Tests for Time Series. URL: https://cran.r-project.org/web/packages/tseriesEntropy/index.html (access date: 15.08.2025).
15. nlts: Nonlinear Time Series Analysis. URL: https://cran.r-project.org/web/packages/nlts/index.html (access date: 15.08.2025).
16. nonlinearTseries: Nonlinear Time Series Analysis. URL: https://cran.r-project.org/web/packages/nonlinearTseries/index.html (access date: 15.08.2025).
17. Всероссийский научно-исследовательский институт гидрометеорологической информации – Мировой центр данных. URL: http://meteo.ru/data/ (дата обращения: 15.08.2025).
REFERENCES
1. Xu S., Cheng J., Zhang Q. Reconstructing all-weather land surface temperature using the bayesian maximum entropy method over the Tibetan Plateau and Heihe River Basin. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, vol. 12, no. 9, pp. 3307–3316. DOI: 10.1109/JSTARS.2019.2921924
2. Wu B., Yi J., Yong Q. Research on principle and application of maximum entropy. Chinese Control and Decision Conference (CCDC). Hefei, China, 2020. pp. 2571–2576. DOI: 10.1109/CCDC49329.2020.9164431
3. Grivel E., Legrand P., Berthelot B. Multiscale entropy rate: a variant of the multiscale entropy. 32nd European Signal Processing Conference (EUSIPCO). Lyon, France, 2024. pp. 2572–2576. DOI: 10.23919/EUSIPCO63174.2024.10715011
4. Hsu W., Chen R., Yang Z., Huang C. Analysis of characteristics in motor failure of power system based on power spectral entropy. 6th International Conference on Energy, Power and Grid (ICEPG). Guangzhou, China, 2024. pp. 1399–1402. DOI: 10.1109/ICEPG63230.2024.10775957
5. Papageorgiou I., Kontoyiannis I. Truly Bayesian entropy estimation. arXiv:2212.06705. https://doi.org/10.48550/arXiv.2212.06705
6. Yang H., Rong P., Sun G. Subject-independent Emotion recognition based on Entropy of EEG Signals. 33rd Chinese Control and Decision Conference (CCDC). Kunming, China, 2021. pp. 1513–1518. DOI: 10.1109/CCDC52312.2021.9602439
7. Sun M., Hao Q., Yang X. A Novel ICEEMDAN-based denoising approach coupled with multi-scale entropy features for ship-radiated noise recognition. 7th International Conference on Information Science, Electrical and Automation Engineering (ISEAE). Harbin, China, 2025. pp. 970–973. DOI: 10.1109/ISEAE64934.2025.11042007
8. Jinbao Z., Tiangang Z., Min W., Shidong C. Bearing fault diagnosis based on the refined composite generalized multi-scale bubble entropy. 4th International Conference on Electron Device and Mechanical Engineering (ICEDME). Guangzhou, China, 2021. pp. 172–175. DOI: 10.1109/ICEDME52809.2021.00044
9. Kurkina V.V., Sirinova M.S., Aleksandrov D.A. Ensuring diagnosability of the technological process with a minimum number of sensors based on the entropy criterion. International Scientific Conference on Control Problems in Technical Systems. St Petersburg, Saint Petersburg Electrotechnical University "LETI" named after V.I. Ulyanov (Lenin) Publ., 2021. Vol. 1,
pp. 239–242. (In Russ.) EDN: IVXXJW
10. Kondratieva I.U., Rudakova H.V., Polyvoda O.V., Lebedenko Y.O., Polyvoda V.V. Using entropy estimation to detect moving objects. 2019 IEEE 5th International Conference Actual Problems of Unmanned Aerial Vehicles Developments (APUAVD). Kiev, Ukraine, 2019. pp. 270–273. DOI: 10.1109/APUAVD47061.2019.8943839
11. Eponeshnikov A.V., Sulimov A.I. Histogram-based estimation of cir entropy for multipath propagation environments. International Conference on Electrical Engineering and Photonics (EExPolytech). Saint Petersburg, Russian Federation, 2024. pp. 163–166.
12. The Comprehensive R Archive Network. Available at: https://cran.r-project.org/ (accessed: 15 August 2025).
13. fNonlinear: Rmetrics – Nonlinear and Chaotic Time Series Modelling. Available at: https://cran.r-project.org/web/packages/fNonlinear/index.html (accessed: 15 August 2025).
14. tseriesEntropy: Entropy Based Analysis and Tests for Time Series. Available at: https://cran.r-project.org/web/packages/tseriesEntropy/index.html (accessed: 15 August 2025).
15. nlts: Nonlinear Time Series Analysis. Available at: https://cran.r-project.org/web/packages/nlts/index.html (accessed: 15 August 2025).
16. nonlinearTseries: Nonlinear Time Series Analysis. Available at: https://cran.r-project.org/web/packages/nonlinearTseries/ index.html (accessed: 15 August 2025).
17. All-Russian Research Institute of Hydrometeorological Information – World Data Center. (In Russ.) Available at: http://meteo.ru/data/ (accessed: 15 August 2025).
