66 publications from this institution
Hilbert transform of a narrowband periodically non-stationary random signal (PNRS) is considered.The relations for the covariance components of PNRS and its Hilbert transform are obtained.The dependencies of the covariance properties of Hilbert transform on covariance damping coefficients of modulating processes are analyzed on the basis of the simulated realizations.
Publication in the conference proceedings of EUSIPCO, Poznan, Poland, 2007
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.
An analysis of the covariance and spectral structure of the Hilbert transform of biperiodically nonstationary random processes, which model signals with double rhythmicity, is presented here. The obtained relations connect the cross-covariance and cross-spectral characteristics of the signal and its Hilbert transform with the characteristics of the signal itself. We examine the properties of the analytic signal and present characteristic special cases determined by the spectral features of carrier-harmonic modulation.
A narrow-band high frequency amplitude modulation as a model of vibration signal is considered. Use of Hilbert transform for the demodulation of periodically non-stationary random signal (PNRS) is discussed. Relations for spectral and covariance components of model signal, its Hilbert transform and cross-covariance components are obtained. Quadratures for modulation signal are extracted and analyzed. It is shown, that the Fourier coefficients of the auto-covariance functions of a signal and its Hilbert transform are the same and its cross-covariance functions differ only by a sign. The square of the modulus of the analytical signal is not a “squared envelope” in the known sense. A “squared envelope” in this case is a random process, whose mathematical expectation is equal to twice the variance of the raw signal. This results in an identity of cyclic spectrums of variances for analytic and raw signals. Thus, the Hilbert transform cannot be used directly as a demodulation procedure, and the “squared envelope” can be analyzed only as the implementation of a random process using PNVP methods. It is shown that band-pass filtering and the Hilbert transform can be used for extraction of modulating signal quadratures.
Using Hilbert transform for the analysis of periodically non-stationary random signals (PNRS), is discus-sed. The narrow-band high frequency amplitude modulation is considered. It is shown that, the auto-covariance functions of a signal and its Hilbert transform are the same and its cross-covariance functions differ only by a sign, which results in an identity of cyclic spectrums of variances for analytic and raw signals. It is shown that band-pass filtering can reduces both the number of signal variance cyclic harmonics and their amplitudes.
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.
Предложен новый подход к многомерной вибрационной диагностике вращающихся узлов машинных комплексов, основанный на использовании методов теории нестационарных случайных процессов и корреляционного тензорного анализа. Разработаны методы верифицированы при проведении натурных испытаний на вибрационном стенде и промышленных объектах Украины. На основе разработанной методики построено портативную диагностическую систему многомерного контроля.
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 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.
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 estimation of the instantaneous spectral density of periodically random processes (PCRP) and its Fourier coefficients in continuous and discrete cases is considered. The formulae for calculation of the mean square error dependencies on parameters of processing and signals are obtained. The aliasing effects are analyzed. The example of estimation of PCRP spectral function for vibration signal of defect rotary unit is given.
