Techniques for Accelerometer Reading Processing on Railway Transport Using Wavelet Transform

Introduction. Safety issues of railway transport are inevitably connected with the condition of railway tracks and railway wheels. Various defects, such as irregularities of the railway track, may lead to emergencies and incidents. Therefore, it is important to measure and calculate short and impulse irregularities. A joint analysis of vibration acceleration signals is needed in order to study the types and size of railway track irregularities.

Aim. Development of an algorithm for irregularity search based on accelerometer readings with the vertical measurement axis.

Materials and methods. The research encompassed wavelet transformation and wavelet-based signal processing including discrete-time signal processing and continuous wavelet processing. In addition, time-frequency analysis based on Fourier transform and continuous wavelet scalogram was used. These methods provide for time-frequency localization for irregularity detection and measurement.

Results. Algorithms for vibrational signal processing using the continuous and discrete-time wavelet transform are proposed. The results show that the discrete wavelet transform is effective for multiresolution and multiband analysis, and continuous wavelet transform and wavelet scalogram allows extraction of irregularities and determination of their parameters. The relative error for irregularity depth was improved by 18 %, and the absolute error for irregularity length determinations was reduced by 7 times.

Conclusion. Application of the discrete Fourier transform and Fourier spectrogram provides for fine resolution in the frequency domain. However, separation of signal components in the time-frequency domain is impeded. The continuous-time wavelet transform ensures sufficient resolution in the low-frequency domain for component localization and visualization of irregularities.

1. Boronahin А. M., Bokhman E. D, Filatov Yu. V., Larionov D. Yu., Podgornaya L. N., Shalymov R. V. Inertial System for Railway Track Diagnostics. Symp. Inertial Sensors and Systems. Karlsruhe, Germany, 18– 19 Sept. 2012. German Institute of Navigation (DGON), 2012, pp. 17.1–17.20.

2. Boronahin А. M., Larionov D. Yu., Podgornaya L. N., Tkachenko A. N., Shalymov R. V. Inertial Method of Railway Track Diagnostics Incorporating the Condition of Rolling Surfaces of the Railcar's Wheels. 4th Intern. Conf. on Intelligent Transportation Engineering, ICITE 2019. Singapore, 05–07 Sept. 2019. IEEE, 2019, pp. 49–53. doi: 10.1109/ICITE.2019.8880194

3. Bolshakova A. V., Boronakhin A. M., Klionsky D. M., Larionov D. Yu., Tkachenko A. N., Shalymov R. V. Railway Track Diagnostics by Combined Kinematic and Vibroacoustic Analysis. Proc. of the 2022 Intern. Conf. on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS). Saint Petersburg, Russia, 26– 30 Sept. 2022. IEEE, 2022, pp. 188–192. doi: 10.1109/ITQMIS56172.2022.9976711

4. Bolshakova A. V., Boronakhin A. M., Klionsky D. M., Larionov D. Yu., Tkachenko A. N., Shalymov R. V. Peculiarities of Vibration Signal Processing Techniques Application to Inertial Way Diagnostics. Proc. of the 2023 Intern. Conf. on Quality Management, Transport and Information Security, Information Technologies (IT&QM&IS). Petrozavodsk, 25–29 Sept. 2023. IEEE Russia North West Section (in press).

5. Geppener V. V., Klionsky D. M., Oreshko N. I. Classification of Telemetric Signals and Their Spectral Density Estimation with the Help of Wavelets. Pattern Recognition and Image Analysis: Advances in Mathematical Theory and Applications. 2012, vol. 22, no. 4, pp. 576–582. doi:10.1134/S1054661812040098

6. Newland D. E. An Introduction to Random Vibrations, Spectral and Wavelet Analysis, 3rd ed. Harlow, Longman, and New York, John Wiley, 1993, 477 p.

7. Percival D. B., Walden A. T. Wavelet Methods for Time Series Analysis. Cambridge, Cambridge University Press, 2000, 594 p.

8. Newland D. E. Harmonic and Musical Wavelets. Proc. of the Royal Society of London (Mathematical and Physical Sciences). 1994, vol. 444, no. 1922, pp. 605–620. doi: 10.1098/rspa.1994.0042

9. Daubechies I. Ten Lectures Of Wavelets. Philadelphia, Society for Industrial and Applied Mathematics, 1992, 341 p.

10. Mallat S. A Wavelet Tour of Signal Processing. San Diego, Academic Press, 1998, 577 p.

11. Oreshko N. I., Klionskiy D. M., Geppener V. V., Ekalo A. V. Decompositsia na empiricheskije modi v tsifrovoi obrabotke signalov [Empirical Mode Decomposition in Digital Signal Processing]. SPb, Izdvo SPbGETU "LETI", 2013, 164 p. (In Russ.)

12. Klionskiy D. M., Geppener V. V. Technologia Hilberta-Huanga I jee primenenie v tsifrovoi obrabotke signalov [Hilbert-Huang Technology and Its Applications in Digital Signal Processing]. SPb, Izd-vo SPbGETU "LETI", 2019, 150 p. (In Russ.)

13. Chui C. K. An Introduction to Wavelets. Academic Press, 1992, 264 p.

14. Smolentsev N. K. Wawelet analiz v Matlab [Wavelet Analysis in MATLAB]. 3rd ed. Moscow, DMK, 2010, 448 p. (In Russ.)

15. Donoho D. L., Johnstone J. M. Minimax Estimation via Wavelet Shrinkage. Annals of Statistics. 1998, vol. 26, no. 3, pp. 879–921. doi: 10.1214/aos/1024691081