Hilbert transform of the wide-band high frequency amplitude modulation is considered. It is shown that its covariance function is the same as covariance function of the raw signal and cross-covariance functions of them differ only by a sign. It results in an identity of cyclic spectrums of variances for analytic and raw signals. The properties of 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. Relationships linking the covariance components of analytical signals and auto-covariance and cross-covariance functions of their quadratures are ascertained.
The results of the processing of the wind turbine gearbox vibration signals are presented. The least square estimators of the periods of the deterministic part of the vibration signal and time variations power of stochastic part are obtained. The amplitude spectra of the deterministic and stochastic oscillations for different degrees of the gearbox damage are analyzed. The covariance structure of stochastic part of vibration was analyzed. The efficient indicator for practical evaluation of gear teeth damage, formed on the basis of amplitude spectra was proposed.
The estimators of deterministic part parameters for biperiodically nonstationary vibration signal, obtained by the least squares method (LSM), are analyzed. The formulae for LSM-estimator variances and bias, which describe their dependencies on realization length and signal covariance components, are obtained. It is shown that LSM allows to avoid leakage effects and to obtain unbiased estimators of biperiodic nonstationary vibration signal deterministic part for arbitrary realization length and harmonic frequencies.
