Detection of distributed and localized faults in rotating machines using periodically non-stationary covariance analysis of vibrations

Abstract The covariance structure for vibrations of the noising mechanism for a port crane and a wind turbine with gear tooth breakage are studied on the basis of their models in the form of periodically non-stationary random processes (PNRPs). The investigation is performed by the authors using PNRP statistical analysis methods. The estimations of the basic frequencies of the vibration’s deterministic components and the time changes of the power for the stochastic part (the PNRP variance) are the key issues of this analysis. In the present paper, the basic frequency estimators are obtained using the least squares technique which are characterized by the maximum of the signal-to-noise ratio as compared with techniques known in the literature. Using the basic frequency, values for the Fourier coefficients for the mean and covariance functions are calculated and the dependencies of the forenamed moment functions on time and lag are ascertained. The amplitude spectra of the deterministic oscillations and the time changes of the power of the stochastic part are presented. These spectra are considered as the symptomatic features of the mechanism’s state of health. It is revealed that the high-frequency modulation of PNRP carrier harmonics is narrow-band for both distributed and localized faults. Using bandpass filtering and Hilbert transform, the quadratures for each high-frequency component are separated and analyzed. It is shown that the auto- and cross-covariance structure of the high-frequency component quadratures characterizes the specific features of the different types of faults. Using the cross-covariance map for high-frequency components, the peculiarities of the bandpass filtering of vibrations for a damaged wind turbine’s gearbox as a PNRP’s is considered. It is shown that the filtering bandwidth cannot be narrower than 14 times the basic frequency. This bandwidth essentially exceeds that recommended in the literature (two to three times the basic frequency).