maisМоделирование и анализ информационных системModeling and Analysis of Information Systems1818-10152313-5417Yaroslavl State University10.18255/1818-1015-2025-2-172-205mais-1939Research ArticleComputing Methodologies and ApplicationsОбнаружение прямоугольных импульсных помех на вихретоковых дефектограммах рельсовDetection of square wave impulse interference in eddy current rail defectogramshttps://orcid.org/0000-0002-0610-5466БыстровЛеонид ЮрьевичBystrovLeonid Y.l.bystrov@uniyar.ac.ruhttps://orcid.org/0009-0007-0211-5660ГладковАртемий НиколаевичGladkovArtemy N.a.gladkov@uniyar.ac.ruhttps://orcid.org/0000-0003-0500-306XКузьминЕгор ВладимировичKuzminEgor V.kuzmin@uniyar.ac.ruЯрославский государственный университет им.П.Г. ДемидоваРоссияP.G. Demidov Yaroslavl State UniversityRussian Federation202528062025322172205Copyright © Быстров Л.Ю., Гладков А.Н., Кузьмин Е.В., 20252025Быстров Л.Ю., Гладков А.Н., Кузьмин Е.В.Bystrov L.Y., Gladkov A.N., Kuzmin E.V.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.mais-journal.ru/jour/article/view/1939

Обеспечение безопасности движения на железнодорожном транспорте требует постоянного мониторинга состояния рельсов для своевременного выявления и устранения дефектов. Одним из методов неразрушающего контроля рельсов является вихретоковая дефектоскопия. Данные (дефектограммы), получаемые от вихретоковых дефектоскопов, отличаются значительным объёмом, что делает необходимым разработку эффективных методов их автоматической обработки и анализа. Анализ дефектограмм может быть осложнён присутствием в данных различных помех и шумов. Одними из наиболее опасных помех, существенно искажающих форму полезных сигналов, являются продолжительные импульсные помехи. Они характеризуются выраженной прямоугольной формой. В отличие от мгновенных импульсных помех, продолжительные шумы классическими методами не устраняются. Не существует зарекомендовавших себя эффективных методов не только для подавления прямоугольных помех, но даже для их обнаружения. Данная статья пытается устранить этот недостаток и предлагает действенный метод для обнаружения таких помех на вихретоковых дефектограммах, обладающий хорошей объясняющей способностью. Прямоугольные сигналы исследуются с точки зрения их вероятностного распределения. Введена SW-характеристика, позволяющая оценить правдоподобие данных для распределения биполярных импульсных сигналов. Чем меньше значение SW-характеристики, тем более распределение данных похоже на распределение биполярных импульсных сигналов. Прямоугольные сигналы являются частным случаем биполярных импульсных сигналов. Исследованы свойства SW-характеристики. SW-характеристика вычислена для нормального распределения и распределения гомоскедастичной смеси двух гауссиан. Показано, что значение SW-характеристики нормального распределения примерно разграничивает бимодальную смесь двух гауссиан от унимодального случая. Эти и другие свойства SW-характеристики позволяют использовать её для обнаружения прямоугольных сигналов в данных. Применение критерия на основе SW-характеристики продемонстрировано на реальных примерах вихретоковых дефектограмм, проведено сравнение с критериями на основе EM-алгоритма и многомасштабной дисперсной энтропии. Предложенный в данной статье критерий показал лучшие результаты. Использование SW-характеристики для обнаружения прямоугольного шума доказало свою эффективность на практике при анализе вихретоковых дефектограмм рельсов. Подход может быть адаптирован для работы с другими видами данных.

Traffic safety in rail transport requires continuous monitoring of the rail condition for timely detection and elimination of defects. One of the methods of non-destructive testing of rails is eddy current flaw detection. The data obtained from eddy current flaw detectors (defectograms) are characterized by a significant volume, which makes it necessary to develop effective methods for their automatic processing and analysis. The analysis of defectograms is complicated by various interferences and noises present in the data. One of the most dangerous interferences that significantly distort the shape of useful signals is prolonged impulse interference. They are characterized by a pronounced square wave shape. Unlike instant impulse interference, prolonged noise cannot be eliminated by classical methods. There are no proven effective methods not only for suppressing square wave interference, but even for detecting it. This article attempts to eliminate this drawback and proposes an effective method for detecting square wave impulse interference on eddy current defectograms, which has good explanatory power. Square signals are explored from the point of view of their probability distribution. SW-characteristic was introduced, which allows to estimate the likelihood of data to the distribution of bipolar impulse signals. The smaller the value of SW-characteristic, the more similar the data distribution is to the distribution of bipolar impulse signals (upon condition that the data are normal). Square wave signals are particular example of bipolar impulse signals. The properties of SW-characteristic were examined. SW-characteristic were calculated for the normal distribution and the distribution of a homoscedastic mixture of two Gaussians. It was shown that the value of SW-characteristic for the normal distribution approximately separates the bimodal mixture of two Gaussians from the unimodal case. These and other properties of SW-characteristic allow using it to detect square wave signals in data by comparing with a threshold, which should satisfy a number of conditions. The application of the criterion based on SW-characteristic was demonstrated on the examples of eddy current defectograms; a comparison was made with criteria based on the EM-algorithm and multiscale disperse entropy. The criterion proposed in the article showed the best results. The use of SW-characteristic for detecting square wave noise has proven its effectiveness in the analysis of eddy current defectograms and can be adapted in the future to work with other types of data.

импульсный шумпрямоугольные помехиsw-характеристикавихретоковая дефектоскопиясмесь двух гауссианimpulse noisesquare wave interferencesw-characteristiceddy current testingmixture of two gaussiansЯрГУ (проект VIP-016).Yaroslavl State University (project VIP-016).ReferencesK. V. Vlasov and A. L. Bobrov, “Influence of Object Physical Properties Instability on Edge Current Method Sensitivity,” Vestnik IzhGTU imeni M. T. Kalashnikova, vol. 27, no. 1, pp. 55–62, 2024, doi: 10.22213/2413-1172-2024-1-55-62.K. V. Vlasov and A. L. Bobrov, “Influence of Object Physical Properties Instability on Edge Current Method Sensitivity,” Vestnik IzhGTU imeni M. T. Kalashnikova, vol. 27, no. 1, pp. 55–62, 2024, doi: 10.22213/2413-1172-2024-1-55-62.E. V. Kuzmin, O. E. Gorbunov, P. O. Plotnikov, and V. A. Tyukin, “Finding the Level of Useful Signals on Interpretation of Magnetic and Eddy-Current Defectograms,” Automatic Control and Computer Sciences, vol. 52, pp. 658–666, 2018, doi: 10.3103/S0146411618070179.E. V. Kuzmin, O. E. Gorbunov, P. O. Plotnikov, and V. A. Tyukin, “Finding the Level of Useful Signals on Interpretation of Magnetic and Eddy-Current Defectograms,” Automatic Control and Computer Sciences, vol. 52, pp. 658–666, 2018, doi: 10.3103/S0146411618070179.E. V. Kuzmin and others, “Application of Convolutional Neural Networks for Recognizing Long Structural Elements of Rails in Eddy Current Defectograms,” Automatic Control and Computer Sciences, vol. 55, pp. 712–722, 2021, doi: 10.3103/S0146411621070099.E. V. Kuzmin and others, “Application of Convolutional Neural Networks for Recognizing Long Structural Elements of Rails in Eddy Current Defectograms,” Automatic Control and Computer Sciences, vol. 55, pp. 712–722, 2021, doi: 10.3103/S0146411621070099.E. V. Kuzmin and others, “Assessing Flaw Severity on Interpretation of Eddy-Current Defectograms,” Automatic Control and Computer Sciences, vol. 56, pp. 723–734, 2023, doi: 10.3103/S0146411622070124.E. V. Kuzmin and others, “Assessing Flaw Severity on Interpretation of Eddy-Current Defectograms,” Automatic Control and Computer Sciences, vol. 56, pp. 723–734, 2023, doi: 10.3103/S0146411622070124.L. Y. Bystrov, A. N. Gladkov, and E. V. Kuzmin, “Suppression of additive periodic low-frequency interference on eddy current defectograms,” Modeling and Analysis of Information Systems, vol. 31, no. 2, pp. 164–181, 2024, doi: 10.18255/1818-1015-2024-2-164-181.L. Y. Bystrov, A. N. Gladkov, and E. V. Kuzmin, “Suppression of additive periodic low-frequency interference on eddy current defectograms,” Modeling and Analysis of Information Systems, vol. 31, no. 2, pp. 164–181, 2024, doi: 10.18255/1818-1015-2024-2-164-181.P. A. Lyakhov and A. R. Orazaev, “New method for detecting and removing random-valued impulse noise from images,” Computer Optics, vol. 47, pp. 262–271, 2023, doi: 10.18287/2412-6179-CO-1145.P. A. Lyakhov and A. R. Orazaev, “New method for detecting and removing random-valued impulse noise from images,” Computer Optics, vol. 47, pp. 262–271, 2023, doi: 10.18287/2412-6179-CO-1145.R. Kunsoth and M. Biswas, “Modified decision based median filter for impulse noise removal,” in Proceedings of the International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), 2016, pp. 1316–1319, doi: 10.1109/WiSPNET.2016.7566350.R. Kunsoth and M. Biswas, “Modified decision based median filter for impulse noise removal,” in Proceedings of the International Conference on Wireless Communications, Signal Processing and Networking (WiSPNET), 2016, pp. 1316–1319, doi: 10.1109/WiSPNET.2016.7566350.G. Manmadha Rao and others, “Reduction of Impulsive Noise from Speech and Audio Signals by using Sd-Rom Algorithm,” International Journal of Recent Technology and Engineering, vol. 10, no. 1, pp. 265–268, 2021, doi: 10.35940/ijrte.A5943.0510121.G. Manmadha Rao and others, “Reduction of Impulsive Noise from Speech and Audio Signals by using Sd-Rom Algorithm,” International Journal of Recent Technology and Engineering, vol. 10, no. 1, pp. 265–268, 2021, doi: 10.35940/ijrte.A5943.0510121.S. Pham and A. Dinh, “Adaptive-Cognitive Kalman Filter and Neural Network for an Upgraded Nondispersive Thermopile Device to Detect and Analyze Fusarium Spores,” Sensors, vol. 19, no. 22, p. 4900, 2021, doi: 10.3390/s19224900.S. Pham and A. Dinh, “Adaptive-Cognitive Kalman Filter and Neural Network for an Upgraded Nondispersive Thermopile Device to Detect and Analyze Fusarium Spores,” Sensors, vol. 19, no. 22, p. 4900, 2021, doi: 10.3390/s19224900.Y. Huo, K. Yang, Y. Qi, and T. Xu, “Robust Maximum Correlation Entropy Kalman Filtering Algorithm Based on S-functions under Impulse Noise,” Signal, Image and Video Processing, vol. 18, pp. 1–15, 2024, doi: 10.1007/s11760-024-03135-y.Y. Huo, K. Yang, Y. Qi, and T. Xu, “Robust Maximum Correlation Entropy Kalman Filtering Algorithm Based on S-functions under Impulse Noise,” Signal, Image and Video Processing, vol. 18, pp. 1–15, 2024, doi: 10.1007/s11760-024-03135-y.Y. Cheng, C. Li, S. Chen, and Z. Zhou, “An Enhanced Impulse Noise Control Algorithm Using a Novel Nonlinear Function,” Circuits, Systems, and Signal Processing, vol. 42, pp. 1–20, 2023, doi: 10.1007/s00034-023-02421-3.Y. Cheng, C. Li, S. Chen, and Z. Zhou, “An Enhanced Impulse Noise Control Algorithm Using a Novel Nonlinear Function,” Circuits, Systems, and Signal Processing, vol. 42, pp. 1–20, 2023, doi: 10.1007/s00034-023-02421-3.C. Xing, Y. Ran, G. Tan, Q. Meng, and M. Lu, “Impulse Noise Mitigation and Channel Estimation Method in OFDM Systems Based on TMSBL,” IEEE Access, vol. 12, pp. 123376–123387, 2024, doi: 10.1109/ACCESS.2024.3454316.C. Xing, Y. Ran, G. Tan, Q. Meng, and M. Lu, “Impulse Noise Mitigation and Channel Estimation Method in OFDM Systems Based on TMSBL,” IEEE Access, vol. 12, pp. 123376–123387, 2024, doi: 10.1109/ACCESS.2024.3454316.J. Behboodian, “On the Modes of a Mixture of Two Normal Distributions,” Technometrics, vol. 12, no. 1, pp. 131–139, 1970, doi: 10.1080/00401706.1970.10488640.J. Behboodian, “On the Modes of a Mixture of Two Normal Distributions,” Technometrics, vol. 12, no. 1, pp. 131–139, 1970, doi: 10.1080/00401706.1970.10488640.M. 'A. Carreira-Perpi n'an and C. K. I. Williams, “On the Number of Modes of a Gaussian Mixture,” Scale Space Methods in Computer Vision, pp. 625–640, 2003, doi: 10.1007/3-540-44935-3_44.M. 'A. Carreira-Perpi n'an and C. K. I. Williams, “On the Number of Modes of a Gaussian Mixture,” Scale Space Methods in Computer Vision, pp. 625–640, 2003, doi: 10.1007/3-540-44935-3_44.Y. A. Dubnov и A. V. Bulychev, «Bayesian Identification of a Gaussian Mixture Model», Journal of Information Technologies and Computing Systems, вып. 1, сс. 101–111, 2017.Y. A. Dubnov и A. V. Bulychev, «Bayesian Identification of a Gaussian Mixture Model», Journal of Information Technologies and Computing Systems, вып. 1, сс. 101–111, 2017.S. Jammalamadaka and Q. Jin, “A Bayesian Test for the Number of Modes in a Gaussian Mixture,” Asian Journal of Earth Sciences, vol. 1, pp. 9–22, 2021.S. Jammalamadaka and Q. Jin, “A Bayesian Test for the Number of Modes in a Gaussian Mixture,” Asian Journal of Earth Sciences, vol. 1, pp. 9–22, 2021.L. Dan, W. Xue, W. Guiqin, and Q. Zhihong, “A Methodological Approach for Detecting Burst Noise in the Time Domain,” World Academy of Science, Engineering and Technology, vol. 58, pp. 974–978, Oct. 2009.L. Dan, W. Xue, W. Guiqin, and Q. Zhihong, “A Methodological Approach for Detecting Burst Noise in the Time Domain,” World Academy of Science, Engineering and Technology, vol. 58, pp. 974–978, Oct. 2009.X. Chen, Y. Han, and J. Wu, “Burst Noise Measuring on the Basis of Wavelet and Fourier Transform,” in Proceedings of the International Conference on Measuring Technology and Mechatronics Automation, 2010, pp. 769–771, doi: 10.1109/ICMTMA.2010.366.X. Chen, Y. Han, and J. Wu, “Burst Noise Measuring on the Basis of Wavelet and Fourier Transform,” in Proceedings of the International Conference on Measuring Technology and Mechatronics Automation, 2010, pp. 769–771, doi: 10.1109/ICMTMA.2010.366.R. Zhou, J. Han, Z. Guo, and T. Li, “De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition,” Remote Sensing, vol. 13, no. 23, pp. 1–19, 2021, doi: 10.3390/rs13234932.R. Zhou, J. Han, Z. Guo, and T. Li, “De-Noising of Magnetotelluric Signals by Discrete Wavelet Transform and SVD Decomposition,” Remote Sensing, vol. 13, no. 23, pp. 1–19, 2021, doi: 10.3390/rs13234932.X. Zhang and others, “Separation of magnetotelluric signals based on refined composite multiscale dispersion entropy and orthogonal matching pursuit,” Earth, Planets and Space, vol. 73, pp. 1–18, 2021, doi: 10.1186/s40623-021-01399-z.X. Zhang and others, “Separation of magnetotelluric signals based on refined composite multiscale dispersion entropy and orthogonal matching pursuit,” Earth, Planets and Space, vol. 73, pp. 1–18, 2021, doi: 10.1186/s40623-021-01399-z.L. Zhang and others, “Identification and Suppression of Magnetotelluric Noise via a Deep Residual Network,” Minerals, vol. 12, p. 766, 2022, doi: 10.3390/min12060766.L. Zhang and others, “Identification and Suppression of Magnetotelluric Noise via a Deep Residual Network,” Minerals, vol. 12, p. 766, 2022, doi: 10.3390/min12060766.G. Zuo and others, “Magnetotelluric Noise Attenuation Using a Deep Residual Shrinkage Network,” Minerals, vol. 12, no. 9, p. 1086, 2022, doi: 10.3390/min12091086.G. Zuo and others, “Magnetotelluric Noise Attenuation Using a Deep Residual Shrinkage Network,” Minerals, vol. 12, no. 9, p. 1086, 2022, doi: 10.3390/min12091086.G. Li and others, “Low-Frequency Magnetotelluric Data Denoising Using Improved Denoising Convolutional Neural Network and Gated Recurrent Unit,” IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1–16, 2024, doi: 10.1109/TGRS.2024.3374950.G. Li and others, “Low-Frequency Magnetotelluric Data Denoising Using Improved Denoising Convolutional Neural Network and Gated Recurrent Unit,” IEEE Transactions on Geoscience and Remote Sensing, vol. 62, pp. 1–16, 2024, doi: 10.1109/TGRS.2024.3374950.W. Feller, An Introduction to Probability Theory and Its Applications, 3rd ed., vol. 1. John Wiley & Sons, 1970, p. 509.W. Feller, An Introduction to Probability Theory and Its Applications, 3rd ed., vol. 1. John Wiley & Sons, 1970, p. 509.V. Boss, Lekcii po matematike: Veroyatnost', informaciya, statistika, vol. 4. KomKniga, 2005.V. Boss, Lekcii po matematike: Veroyatnost', informaciya, statistika, vol. 4. KomKniga, 2005.A. N. Shiryaev, Veroyatnost', 3rd ed., vol. 1. MCNMO, 2004, p. 520.A. N. Shiryaev, Veroyatnost', 3rd ed., vol. 1. MCNMO, 2004, p. 520.A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data Via the EM Algorithm,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 39, no. 1, pp. 1–22, 1977, doi: 10.1111/j.2517-6161.1977.tb01600.x.A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum Likelihood from Incomplete Data Via the EM Algorithm,” Journal of the Royal Statistical Society: Series B (Methodological), vol. 39, no. 1, pp. 1–22, 1977, doi: 10.1111/j.2517-6161.1977.tb01600.x.K. P. Burham and D. R. Anderson, Model Selection and Multimodel Inference, 2nd ed. Springer New York, 2002.K. P. Burham and D. R. Anderson, Model Selection and Multimodel Inference, 2nd ed. Springer New York, 2002.L. D. Kudryavcev, Kurs matematicheskogo analiza, vol. 1. Vysshaya shkola, 1981.L. D. Kudryavcev, Kurs matematicheskogo analiza, vol. 1. Vysshaya shkola, 1981.

The authors declare that there are no conflicts of interest present.