Publications

Analysis of rotary mechanism fault features on the base of the spectral structure for vibration stochastic recurrence

The result of the application of the spectral methods for searching and analysis of the hidden periodicities in the properties of the vibration signals of the rotary machinery which allow to discover the spectral band of the vibration periodical non-stationarity, to determine the spectrum forms, to evaluate the power of their time variation. The typical peculiarities of the defects are established on this basis, the new diagnostic indicators are formed for their detection and typification.

Periodically Non-Stationary Analytic Signals and their Properties

Hilbert transform of periodically non-stationary random signal (PNRS) is analyzed. The relations for covariance and spectral components of PNRS and its Hilbert transform are obtained. The analytic signal and envelope properties for multi-and monocomponent signal are analyzed.

Hilbert transform of a periodically non-stationary random signal: Low-frequency modulation

Diagnostics of gear pair damage using the methods of biperiodically correlated random processes. Part 1. Theoretical aspects of the problem

Technical Diagnostics and Non-Destructive Testing, 2022, №04. TEKHNICHESKAYA DIAGNOSTIKA I NERAZRUSHAYUSHCHIY KONTROL Quarterly scientific-technical and production journal. ISSN: 0235-3474. Established in 1989. Subscription index: 74475. State Registration Certificate KV 4787 of 09.01.2001. All rights reserved Publisher: B.E.Paton Electric Welding Institute, National Academy of Sciences of Ukraine. Main topics of the magazine: theoretical and practical articles on technical diagnosing and non-destructive testing; flaw detection, residual life of structures. Each issue features: scientific articles; manufacturing experiences; reviews; exhibitions, conferences; advertisements.

Coherent covariance analysis of periodically correlated random processes for unknown non-stationarity period

The covariance analysis of the periodically non-stationary random signal with narrow-band modulation of carrier harmonics

The periodically non-stationary random signals (PNRSs), whose carrier harmonics are mo-dulated by jointly stationary high-frequency random processes are analyzed. A representation of the signal in the form of a superposition of high-frequency components is obtained and it is shown that these components are jointly periodically non-stationary random processes. The random process is periodically non-stationary of the second order only in the case when some of the cross-covariance functions of its modulation processes are not equal to zero. The correlations of the PNRP spectral harmonics and the correlations of the modulating processes in series representation are equivalent. Evaluating the specific features of the auto- and cross-covariances for modulating processes as well as contribution of each pair to the covariance component values allows us to detect defects at early stages.

Correlation Matrix for Analysis of the Covariance and Spectral Structures of PNRP

Methods of Hidden Periodicity Discovering for Gearbox Fault Detection

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.

Methods of indication and operative detection of underground communication elements

Indication methods and technical means of functionally important sections and elements of underground engineering communication are considered.

Component covariance analysis for periodically correlated random processes

Linear filtration methods for statistical analysis of periodically correlated random processes—Part I: Coherent and component methods and their generalization

A Corelation-Based Analysis of the Spectral Composition of Vibrations for a Gas-Turbine Engine with Unbalanced Rotor

Forced oscillations of cracked beam under the stochastic cyclic loading

Periodically correlated random processes: Application in early diagnostics of mechanical systems

Hilbert transform for covariance analysis of periodically nonstationary random signals with high-frequency modulation

We discuss the use of the Hilbert transform for the analysis of periodically non-stationary random signals (PNRSs), whose carrier harmonics are modulated by jointly stationary high-frequency narrow-band random processes. PNRS of this type are suitable models for numerous natural and man-made phenomena, including the vibration of a damaged mechanism. We show that the auto-covariance function of the signal and its Hilbert transform are the same, and that their cross-covariance functions differ only in their sign, meaning that the sum of squares of the signal and its Hilbert transform cannot be considered a 'squared envelope' and no new information is contained compared with the variance of the raw signal. A representation of the signal in the form of a superposition of high-frequency components is obtained and it is shown that these components are jointly periodically non-stationary random processes. The properties of the band-pass filtered signals are examined, and it is shown that band-pass filtering can reduce both the number of signal variance cyclic harmonics and their amplitudes. We show that it is possible to extract the quadratures of narrow-band high-frequency modulation processes using the Hilbert transform. The results obtained here theoretically substantiate the use of the Hilbert transform for the analysis of high-frequency modulation which occurs when a fault appears. They offer a new way to consider the traditional approach to vibration diagnosis. A processing technique that can be considered an alternative to envelope analysis is described, and its use in the analysis of a vibration signal is discussed.

Hilbert Transform for Analysis of Amplitude Modulated Wide-band Random Signals

Hilbert transform of the wide-band high frequency amplitude modulation is considered. It is shown that its covariance function is the same as covariance function of the raw signal and cross-covariance functions of them differ only by a sign. It results in an identity of cyclic spectrums of variances for analytic and raw signals. The properties of band-pass filtered signals are examined and it is shown that band-pass filtering can reduce both the number of signal variance cyclic harmonics and their amplitudes. Relationships linking the covariance components of analytical signals and auto-covariance and cross-covariance functions of their quadratures are ascertained.

The Coherent and Component Estimation of Covariance Invariants for Vectorial Periodically Correlated Random Processes and Its Application

Statistical analysis of periodically non-stationary oscillations for unknown period

The strict characteristic and the comparative analysis of the developed by authors the coherent and the component methods for statistical analysis of periodically correlated random processes (PCRP) — the mathematical models of the stochastic oscillations — for unknown period of the non-stationarity is given. The comparison of efficiencies of the proposed methods for period estimation with the given in literature for individual cases of PCRP is provided.