66 publications from this institution
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.
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.
The vibration time series are analyzed using methods for periodically non-stationary random processes (PNRP). Band-pass filtering and Hilbert transform are used to extract quadrature components. The cross-covariance structure of quadratures is considered. It was shown that cross-covariances of different order quadratures result in periodical non-stationarity of the vibration signal.
Theoretical and experimental results of time series modeling are summarized. Special attention is given to periodically correlated random processes (PCRP). It is suggested to use the parametric modeling methods on the basis of PCRP decomposition on stationary processes for construction of the process model. Proposed parametrical model is helpful for veriflcation the efficiency of devices and systems with periodical character of sources.
A new approach for the fault detection of the turbo-set friction bearings, based on the investigation the periodically non-stationary properties of vibration signals, is analyzed.
An analysis of the covariance and spectral structure of the Hilbert transform of biperiodically non-stationary random processes, which are a model of signals with double rhythmicity, are provided. The obtained relations for the cross-covariance and cross-spectral characteristics of the signal and its Hilbert transform. Наведено аналіз кореляційної та спектральної структури перетворення Гільберта біперіодично нестаціонарних випадкових процесів, які є моделлю сигналів із подвійною ритмічністю. Отримано співвідношення для взаємокореляційних та взаємоспектральних характеристик сигналу та його перетворення Гільберта.
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.
The model of vibration signal of gearbox pair in the form of periodically correlated non-stationary random process is considered. It is shown that hidden periodicities in biperiodic correlated random process mean and covariance function, characterizing the vibrations of gearbox pair can be detected using the component and least square methods. Seven particular cases of the bi-rhythmic hidden periodicity for different modulation modes are analyzed.
Технологічно-природничий університет.85796, Польща, Бидгощ, алея проф
Discrete estimators of the deterministic part for a biperiodically nonstationary signal obtained by the least square method (LSM) are analysed.It was shown that LSM-estimation allows avoiding the leakage effects.The conditions of consistency for the discrete estimators are obtained.The formulae for variance estimators, which describe their dependencies on a realization length, sampling interval and signal covariance components, are analysed.
Publication in the conference proceedings of EUSIPCO, Poznan, Poland, 2007
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.
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.
