Probabilistic models and statistical methods for the analysis of vibrational signals in the problems of diagnostics of machines and structures

Mykhailyshyn, V. Yu.; Yavors’kyi, I. M.; Vasylyna, Yu. T.; Drabych, O. P.; Isaev, I. Yu.

doi:10.1007/bf02537594

Cited by 13 publications

(11 citation statements)

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“…The Fourier coefficients of the covariance function and spectral density are the total characteristics of the amplitude and the phase modulation of the BPCRP carrier harmonics. The zero th spectral component, as can be seen from (10), is a sum of the power of the spectral densities of the modulating processes ξ pq (t) shifted by Λ pq . The spectral component f kl (ω) (9) is a sum of the shifted cross-spectral densities for modulating processes, the numbers of which differ by numbers k and l, respectively.…”

Section: It Follows From (8) That Cross-correlations Of Modulating Processesmentioning

confidence: 99%

“…It was mentioned above that the BPCRP spectral composition is defined by the zero th spectral component (10). Assume that Λ 10 ≥ sΛ 01 , where s is some natural number.…”

Section: Gear Fault Detection As Pcrp Estimation Issuementioning

confidence: 99%

“…The methodology for the vibration signal processing, developed in our investigations [10,17,28], has some specific content. It involves the sequential employment of the methods for the covariance and spectral analysis of the stationary random processes, the methods of searching for hidden periodicities of the first and the second order [29][30][31][32], their separation and individual analysis, empirical harmonic analysis on the basis of Fourier series and Fourier transformations, and the methods of PCRP covariance and spectral analysis [4,8,9,[34][35][36].…”

Section: Gear Fault Detection As Pcrp Estimation Issuementioning

confidence: 99%

“…The latter are caused by deterministic oscillations. In order to estimate the period of these oscillations, the coherent, the component, and the least squares methods can be applied [9,10,17,[29][30][31][32]. The values of the estimated period, apart from rare cases, are not multiples of the sampling interval and, therefore, the interpolation of the raw experimental data is required if the coherent technique is used.…”

Section: The Detection and The Analysis Of The Hidden Periodicities Of The First Ordermentioning

confidence: 99%

“…These processes are also called periodically or almost periodically correlated random processes [5][6][7][8][9]. Therefore, it is advisable to choose these parameters for the construction of the indicators for fault detection [10][11][12][13][14][15][16][17]. Gear pair vibration is excited by two main factors, namely, the periodic variation of teeth stiffness, due to the meshing phase, and manufacturing errors.…”

Section: Introductionmentioning

confidence: 99%

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Methods of Hidden Periodicity Discovering for Gearbox Fault Detection

Javorskyj

Matsko

Yuzefovych

et al. 2021

Sensors

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It is shown that the models of gear pair vibration, proposed in literature, are particular cases of the bi-periodically correlated random processes (BPCRPs), which describe its stochastic recurrence with two periods. The possibility of vibration and analysis within the framework of BPCRP approximation, in the form of periodically correlated random processes (PCRPs), is grounded and the implementation of vibration processing procedures using PCRP techniques, which are worked out by the authors, is given. Searching for hidden periodicities of the first and the second orders was considered as the main issue of this approach. The estimation of the non-stationary period (basic frequency) allowed us to carry out a detailed analysis of the deterministic part, the covariance structure of the stochastic part, and to form, using their parameters, the sensitive indicators for fault detection. The results of the processing of the wind turbine gearbox vibration signals are presented. The amplitude spectra of the deterministic oscillations and the time changes of the stochastic part power for different fault stages are analyzed. The most efficient indicators, which are formed using the amplitude spectra for practical applications, are proposed. The presented approach was compared with known in literature cyclostationary analysis and envelope techniques, and its advantages are shown.

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Section: It Follows From (8) That Cross-correlations Of Modulating Processesmentioning

confidence: 99%

“…It was mentioned above that the BPCRP spectral composition is defined by the zero th spectral component (10). Assume that Λ 10 ≥ sΛ 01 , where s is some natural number.…”

Section: Gear Fault Detection As Pcrp Estimation Issuementioning

confidence: 99%