Yuzefovych R.M.

Pelypets R.I.

Lychak O.V.

Sliepko R.T.

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A harmonic model of a bi-periodic non-stationary random process is presented for describing complex vibration signals. Methods based on periodic and bi-periodic non-stationary random processes (PNSP and BPNSP) can be applied to analyze vibration oscillations of rotating mechanism assemblies. It is shown that the use of the least mean square (LSM) methods for detecting hidden first and second order periodicities allows estimating the bi-rhythmic properties of a vibration signal modeled using BPNSP. Expressions for the mean function and correlation function are obtained by superposing harmonics with combination frequencies. It is shown, that only the exact correspondence of the data analysis methods to the oscillation model ensures the reliability of the obtained results and is the basis for their correct interpretation. Using DFT, STFT and WT, researchers suppose that time series under investigation are segments of some deterministic oscillations, and when supplying WCD or WVD for analyzing signals - as realizations of the stochastic processes. WCD describes the power spectral density of a stationary random process, while WVD characterizes the properties of the instantaneous spectral density for a non-stationary random process. The periodogram analysis method was proposed by Schuster as a way to search for periodic signals observed against the background of stochastic oscillations. Hilbert transform can be used to analyze both deterministic and stochastic modulations. In opposite to these, vibrations of machines consisting of several rotating units have a complex polyrhythmic structure, which is primarily caused by different speeds of rotation of individual elements. In the general case, these oscillations can be described by polyperiodically nonstationary random processes, which belong to the class of almost periodically nonstationary processes.

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