Revealing Parameters of Hidden Periodicities by Parametric DFT Method in Functional Diagnostics of Machines and Mechanisms

The purpose of the study is to develop a new method for monitoring the technical condition and functional diagnostics of machines and mechanisms for various purposes based on the spectral analysis of the vibroacoustic signal generated by them. The developed new method for monitoring the technical condition and functional diagnostics of machines and mechanisms for various purposes is based on a generalization of classical discrete Fourier transform (DFT) in the form of parametric DFT (DFT-P). The paper reveals and formulates the problems that arise when using the classical DFT to identify the parameters of hidden periodicities in a vibroacoustic signal generated by machines and mechanisms for various purposes. These are the aliasing effect, the scalloping effect, the picket fence effect. The advantages of DFT-P over DFT in solving the fundamental problems of dynamics and vibroacoustics, solving the problems of noise and vibration are studied in detail. Theoretical foundations for measuring the parameters of a discrete harmonic signal based on parametric discrete Fourier transform have been developed. The reasons for the occurrence of non-invariance of the energy spectrum of a discrete harmonic signal given on a finite interval are investigated by the method of parametric discrete Fourier transform. A technique for determining (estimating) the errors in measuring the amplitude of a harmonic signal by the method of parametric discrete Fourier transform is proposed. An experimental verification of the theoretical results obtained in the work on revealing the parameters of hidden periodicities by parametric DFT method in the functional diagnostics of machines and mechanisms using a vibroacoustic signal was carried out by numerical simulation.