The spectral analysis of cyclo-non-stationary signals

Condition monitoring of rotating machines in speed-varying conditions remains a challenging task and an active field of research. Specifically, the produced vibrations belong to a particular class of non-stationary signals called cyclo-non-stationary: although highly non-stationary, they contain hidden periodicities related to the shaft angle; the phenomenon of long term modulations is what makes them different from cyclostationary signals which are encountered under constant speed regimes. In this paper, it is shown that the optimal way of describing cyclo-non-stationary signals is jointly in the time and the angular domains. While the first domain describes the waveform characteristics related to the system dynamics, the second one reveals existing periodicities linked to the system kinematics. Therefore, a specific class of signals – coined angle-time cyclostationary is considered, expressing the angle-time interaction. Accordingly, the related spectral representations, the order-frequency spectral correlation and coherence functions are proposed and their efficiency is demonstrated on two industrial cases.