Digital Analysis of the Vibration Signals Amplitude Spectrum Based on Fourier Processing of the Binary-Sign Analog-Stochastic Quantization Result

The article is devoted to the problem of developing a digital algorithm for operational harmonic analysis of complex vibration signals. The basis for solving this problem was the generalized equation of statistical measurements, which defines the measurement procedure as the sequential execution of interrelated measurement and computational transformations. During the development of the algorithm, special attention is paid to analog-to-digital conversion because it directly affects the computational efficiency of digital procedures for obtaining the final result. As such a conversion, the use of binarysign analog-stochastic quantization is justified, which allows performing two-level quantization without systematic error regardless of the statistical properties of the analyzed signals. The discrete-event model of the binary-sign analog-stochastic quantization result allowed for the analytical calculation of integration operations in the transition to estimating the amplitude spectrum in digital form. As a result, the developed algorithm of harmonic analysis does not require performing digital multiplication operations typical for classical algorithms, which are based on the calculation of the direct discrete Fourier transform. The execution of the algorithm is reduced to the implementation of the addition and subtraction arithmetic operations of the cosine-function values in the time moments determined by the result of the binary-sign analogue-stochastic quantization. The exclusion of digital multiplication operations provided an increase in the computational efficiency of amplitude spectrum estimation. Laboratory studies of the developed algorithm were carried out using simulation modeling. The simulation results showed that the algorithm allows calculating estimates of the amplitude spectrum of complex signals with high accuracy and frequency resolution in the presence of additive noise. In real conditions, the testing of the developed algorithm was carried out during bench studies of the operational status of the MAZ-206067 bus, designed for the transportation of passengers on urban and suburban routes of average workload. Analysis of the results of experimental studies confirmed the possibility of using the algorithm as part of the diagnosability provision for operational monitoring of vibration signals in a complex noise environment.

1. Klyuev V. V., Sosnin F. R., Kovalev A. V., Filinov V. N. et al. Nondestructive testing and diagnostics: Handbook, Under ed. V. V. Klyuyev, Moscow, Mashinostroenie, 2003, 656 p. (in Russian).

2. Kolobov A. B. Vibration diagnostics: theory and practice, Moscow, INFRA-Engineering, 2019, 252 p. (in Russian).

3. Benaroya H., Nagurka M., Han S. Mechanical vibration: Analysis, uncertainties, and control, CRC Press, Taylor & Francis Group, 2017, 579 p.

4. Adams M. L. Rotating machinery vibration: from analysis to troubleshooting, CRC Press, Taylor & Francis Group, 2010, 476 p.

5. Brandt A. Noise and vibration analysis: Signal analysis and experimental procedures, Chichester: Wiley, 2011, 464 p.

6. . Taylor J. I. The vibration analysis handbook: A practical guide for solving rotating machinery problems, VCI, 2003, 375 p.

7. State Standard 20911—89. Technical diagnostics. Terms and definitions, Moscow, Standartinform Publ., 2009, 11 p. (In Russian).

8. State Standard 24346—80. Vibration. Terms and definitions, Moscow, Standartinform Publ., 2010, 26 p. (In Russian).

9. State Standard R ISO 13373-2—2009. Condition monitoring and diagnostics of machines. Vibration condition monitoring. Part 2: Processing, analysis and presentation of vibration data, Moscow, Standartinform Publ., 2010, 32 p. (in Russian).

10. Lyons R. G. Understanding digital signal processing, Third Edition, Prentice Hall PTG, 2011, 944 p.

11. Proakis J. G., Manolakis D. G. Digital signal processing. Principles, algorithms and applications, Pearson Prentice Hall, 2007, 1084 p.

12. Manolakis D. G., Ingle V. K. Applied digital signal processing: Theory and practice, Cambridge University Press, 2011, 991 p.

13. Blahut R. E. Fast algorithms for signal processing, Cambridge University Press, 2010, 453 p.

14. Bi G., Zeng Y. Transforms and fast algorithms for signal analysis and representations, Springer-Science + Business Media, LLC, 2004, 422 p.

15. Britanak V., Yip P. C., Rao K. R. Discrete cosine and sine transforms: General properties, fast algorithms and integer approximations, Academic Press, Elsevier, 2006, 368 p.

16. Chu E. Discrete and continuous Fourier transforms: Analysis, applications and fast algorithms, CRC Press, Taylor & Francis Group, 2008, 423 p.

17. Madisetti V. K. (ed.) The digital signal processing handbook. Digital signal processing fundamentals, CRC Press, Taylor & Francis Group, 2009, 904 p.

18. Solonina A. I., Ulyakhovich D. A., Yakovlev L. A. Algorithms and processors digital signal processing, St. Petersburg, BHV-Petersburg, 2002, 464 p. (in Russian).

19. Suzev V. V. Theory fundamentals of digital signal processing, Moscow, RTSoft, 2014, 752 p. (in Russian).

20. Ulyanov M. V. Resource-efficient computer algorithms. Development and analysis, Moscow, Fizmatlit, 2008, 304 p. (in Russian).

21. Tsvetkov E. I. Theory fundamentals of the statistical measurements, Leningrad, Energoatomizdat: Leningrad Branch, 1986, 256 p. (in Russian).

22. Yakimov V. N. Izvestiya samarskogo nauchnogo tsentra RAN, vol. 18, 2016, no. 4(7), pp. 1346—1353 (in Russian).

23. Yakimov V. N., Batyschev V. I., Mashkov A. V. Mekhatronika, Avtomatizatsiya, Upravlenie, vol.18, 2017, no. 9, pp. 604—611 (in Russian).

24. Max J. Methodes et techniques de traitement du signal et applications aux mesures physiques. Tome 1: Principes generaux et methodes classiques, Paris, Masson, 1996, XXVII. 355 p.

25. Mirsky G. Ya. Characteristics of stochastic interrelation and their measurements, Moscow, Energoizdat, 1982, 320 p. 611 (in Russian).

26. Yakimov V. N. Measurement techniques, Springer US, New York, vol. 49, 2006, no. 4, pp. 341—347.

27. Yakimov V. N., Mashkov A. V., Gorbachev O. V. Tsifrovaya Obrabotka Signalov, 2016, no. 2, pp. 31—34 (in Russian).

28. Yakimov V. N., Mashkov A. V. Nauchnoe priborostroenie, vol. 27, 2017, no. 2, pp. 83—90 (in Russian).

29. Yakimov V. N., Gorbachev O. V. Instruments and experimental techniques, Springer US, New York, vol. 56, 2013, no. 5, pp. 540—545 (in Russian).

30. Yakimov V. N., Mashkov A. V. Datchiki i Sistemy (Sensors and Systems), 2018, no. 6, pp. 25—30 (in Russian).

31. Yakimov V. N., Mashkov A. V. Kontrol’. Diagnostika, 2018, no. 8, pp. 40—45 (in Russian).

32. Wainer G. A., Mosterman P. J. Discrete-Event Modeling and Simulation: Theory and Applications, CRC Press, Taylor & Francis Group, 2011, 493 p.

33. Vasilchuk A. V., Kulikovskiy K. L., Lange P. K. Information and measuring systems bench testing products of the automotive industry, Moscow, Mashinostroyeniye-1, 2005, 504 p. (in Russian).

34. State Standard ISO 5348—2002. Mechanical vibration and shock. Mechanical mounting of accelerometers, Moscow, Stan dartinform Publ., 2007, 16 p. (in Russian).

35. State Standard 31191.1—2004 (ISO 2631-1:1997). Vibration and shock. Measurement and evaluation of human exposure to whole-body vibration. Part 1. General requirements, Moscow, Standartinform Publ., 2010. 25 p. (in Russian).

36. State Standard 55855—2013. Motor vehicles. Methods of measurement and evaluation of general vibrations, Moscow, Standartinform Publ., 2014, 21 p. (in Russian).

37. State Standard ISO 10326-1—2002. Vibration. Laboratory method for evaluating vehicle seat vibration. Part 1. Basic requirements, Moscow, Standartinform Publ., 2017, 12 p. (in Russian).

38. State Standard ISO 8002—99. Mechanical vibration. Land vehicles. Method for reporting measured data, Minsk, Interstate council for standardization, metrology and certification Publ., 2000, 16 p. (in Russian).