Digital technology for spectral analysis of oscillation parameters

Performing the Fourier analysis of the harmonic composition of oscillations is an effective approach to the study of vibration processes in machines and mechanisms. This method of express control remains relevant and highly demanded in the acoustic diagnostics of machines due to its relatively high...

Full description

Bibliographic Details
Main Authors: A. V. Gulaj, V. M. Zajcev
Format: Article
Language:English
Published: Belarusian National Technical University 2022-06-01
Series:Sistemnyj Analiz i Prikladnaâ Informatika
Subjects:
Online Access:https://sapi.bntu.by/jour/article/view/545
_version_ 1797873700413898752
author A. V. Gulaj
V. M. Zajcev
author_facet A. V. Gulaj
V. M. Zajcev
author_sort A. V. Gulaj
collection DOAJ
description Performing the Fourier analysis of the harmonic composition of oscillations is an effective approach to the study of vibration processes in machines and mechanisms. This method of express control remains relevant and highly demanded in the acoustic diagnostics of machines due to its relatively high informativeness. The expansion of its analytical capabilities is implemented by introducing additional means for digital processing of vibration signals, including smart systems. The objective of this work consists in creating a digital method for spectral analysis of vibration signals, the implementation of which would be possible with the use of smart devices. This work presents a method of polyharmonic approximation of the parameters of the signals reflecting oscillatory processes in machines based on the additive combinations of sinusoidal functions. The technology of truncation of the time discretised decomposition of the above signals into a Fourier series is implemented using the Rayleigh theorem and the Lyapunov – Parseval equality. The distortion of the frequency spectrum of oscillations is eliminated by suppressing its side lobes using window filters. To compare the efficiency of different windows, the following special parameters are used: width of the main lobe of the frequency spectrum; coefficient of relative expansion of the main lobes; maximum relative level of side lobes; coefficient of relative attenuation of signal energy. In so doing, the windows of Hanning, Nuttall, Hamming, Barlett were considered, and the parameters of a rectangular window were taken as basic values. The limitations of the digit capacity of analogto-digital signal converters depending on the required accuracy of maintaining the energy balance when truncating the discrete Fourier expansions have been determined. An example of implementation of the digital technology of spectral analysis of the parameters of oscillatory processes is given.
first_indexed 2024-04-10T01:19:16Z
format Article
id doaj.art-241362cd4b404c208f88ee880b68c229
institution Directory Open Access Journal
issn 2309-4923
2414-0481
language English
last_indexed 2024-04-10T01:19:16Z
publishDate 2022-06-01
publisher Belarusian National Technical University
record_format Article
series Sistemnyj Analiz i Prikladnaâ Informatika
spelling doaj.art-241362cd4b404c208f88ee880b68c2292023-03-13T09:47:42ZengBelarusian National Technical UniversitySistemnyj Analiz i Prikladnaâ Informatika2309-49232414-04812022-06-01014810.21122/2309-4923-2022-1-4-8407Digital technology for spectral analysis of oscillation parametersA. V. Gulaj0V. M. Zajcev1Белорусский национальный технический университетБелорусский национальный технический университетPerforming the Fourier analysis of the harmonic composition of oscillations is an effective approach to the study of vibration processes in machines and mechanisms. This method of express control remains relevant and highly demanded in the acoustic diagnostics of machines due to its relatively high informativeness. The expansion of its analytical capabilities is implemented by introducing additional means for digital processing of vibration signals, including smart systems. The objective of this work consists in creating a digital method for spectral analysis of vibration signals, the implementation of which would be possible with the use of smart devices. This work presents a method of polyharmonic approximation of the parameters of the signals reflecting oscillatory processes in machines based on the additive combinations of sinusoidal functions. The technology of truncation of the time discretised decomposition of the above signals into a Fourier series is implemented using the Rayleigh theorem and the Lyapunov – Parseval equality. The distortion of the frequency spectrum of oscillations is eliminated by suppressing its side lobes using window filters. To compare the efficiency of different windows, the following special parameters are used: width of the main lobe of the frequency spectrum; coefficient of relative expansion of the main lobes; maximum relative level of side lobes; coefficient of relative attenuation of signal energy. In so doing, the windows of Hanning, Nuttall, Hamming, Barlett were considered, and the parameters of a rectangular window were taken as basic values. The limitations of the digit capacity of analogto-digital signal converters depending on the required accuracy of maintaining the energy balance when truncating the discrete Fourier expansions have been determined. An example of implementation of the digital technology of spectral analysis of the parameters of oscillatory processes is given.https://sapi.bntu.by/jour/article/view/545колебательный процессспектральный анализцифровая технология
spellingShingle A. V. Gulaj
V. M. Zajcev
Digital technology for spectral analysis of oscillation parameters
Sistemnyj Analiz i Prikladnaâ Informatika
колебательный процесс
спектральный анализ
цифровая технология
title Digital technology for spectral analysis of oscillation parameters
title_full Digital technology for spectral analysis of oscillation parameters
title_fullStr Digital technology for spectral analysis of oscillation parameters
title_full_unstemmed Digital technology for spectral analysis of oscillation parameters
title_short Digital technology for spectral analysis of oscillation parameters
title_sort digital technology for spectral analysis of oscillation parameters
topic колебательный процесс
спектральный анализ
цифровая технология
url https://sapi.bntu.by/jour/article/view/545
work_keys_str_mv AT avgulaj digitaltechnologyforspectralanalysisofoscillationparameters
AT vmzajcev digitaltechnologyforspectralanalysisofoscillationparameters