Publications

Обґрунтовано вибір моделі вібраційного процесу при її статистичному аналізі. Розглянуто і обґрунтовано використання методу “краплі дощу” для виділення послідовності циклів складних стохастичних навантажень. Розроблено відповідні алгоритм і програмне забезпечення, наведено результати їх застосування для виявлення циклів напружень у реальних сигналах вібрації від нормального та пошкодженого підшипників. The choice of vibration signal model for stochastical analysis is proved in this paper. The selection of cycles sequency of complex stochastic loads based on the “rain-flow counting” method is shown. Special algorithm and software are developed. The results of their usage for real vibration signal from defective and normal rolling bearing are presented.

Publication in the conference proceedings of EUSIPCO, Poznan, Poland, 2007

Modeling of the Earth magnetic field variations as periodically non-stationary random process (PNRP) is represented. Results of processing real-life time-series by PNRP methods are analyzed and model of magnetic field daily variations in the form of superposition of stochastically amplitude and phase-modulated harmonics with daily frequency and its multiples is proposed. The covariance and spectral structures of the quadratures for the individual components wich was separated using Hilbert transform are considered. It is show that individual component are jontly PNRP. Obtained results can be usefull for parameterization and computer simulation of the daily variations of Earth magnetic field.

The estimators of parameters of bi-periodic nonstationary vibration signal deterministic part, obtained with using the least squares method (LSM), are analyzed. LSM estimation allows avoiding aliasing effects. The formulas for estimators of variance and bias, which describe their dependences on realization length and signal covariance components, are derived. The results are specified for the quadrature model of the signal. LSM has shown its efficiency for separation of harmonics with close frequencies, so it should be considered as the main method for vibration signals analysis. It is shown that its usage allows one to obtain unbiased estimators of bi-periodic nonstationary vibration signal deterministic part regardless of realization length and harmonic frequencies.

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 random processes is discussed. 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.

Представлена розроблена у Фізико-механічному інституті ім. Г.В. Карпенка НАН України віброакустична система
\nдля виявлення та діагностики дефектів обертових вузлів механізмів на ранніх стадіях їх розвитку, основою якої є теорія і методи статистики періодично нестаціонарних випадкових процесів та їх узагальнень. Описано функціональні
\nможливості системи. Розглянуто приклад її застосування при виявленні та ідентифікації дефектів підшипників ковзання турбоагрегатів ТЕС.

The periodical non-stationary random signal (PNRS), which is a superposition of amplitude and phase stochastically modulated harmonics with multiple frequencies, is considered. It is assumed that the modulation spectrum is concentrated in a band width of which is less than the basic frequency of the signal. In vibrodiagnostics determining of the modulation parameters for the vibration signals from damaged mechanisms makes it possible to identify defects and extract their characteristic features on the early stages of their initiation. The covariance and spectral properties of multicomponent narrow-band PNRS and its Hilbert transform are considered. Formulae for Fourier series coefficients of auto- and cross-covariance functions, spectral densities and their Hilbert transforms are obtained, relationships between them are found. The covariance and spectral structure of the analytical signal are analyzed. It is shown that, in contrast to a monocomponent narrow-band signal, the analytical signal is a periodically non-stationary random process. The number of harmonics of its covariance function is twice less than that of the covariance function of the signal. It is established that the amplitudes of the harmonics of the covariance function of a multicomponent narrow-band signal are determined only by correlations between the quadratures of harmonics with different orders.

The covariance functions and the power spectral densities of the quadrature components for narrowband periodically non-stationary random signal are analysed. The expressions which describe their dependencies on the covariance and spectral components of the signal are obtained. The comparision of the dependencies with a stationary case is carried out.

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.