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.
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.
Technical Diagnostics and Non-Destructive Testing, 2021, №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.
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.
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
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.
