Order-frequency analysis of machine signals

Latest researches have asserted the eligibility of angle/time cyclostationarity in analyzing machine signals when operating under variable speed conditions. A core descriptor in this framework is the order-frequency spectral correlation (OFSC), basically estimated by the averaged cyclic periodogram (ACP), being able to jointly decode (i) the angle-dependent modulations related to the machine kinematics and (ii) the time-dependent carriers related to the machine dynamics. The present paper comes into this context with the aim of enriching this framework with new tools excerpted from cyclostationarity. In particular, a new estimator of the OFSC based on the cyclic modulation spectrum (CMS) is proposed and compared with the ACP in terms of resolution, statistical performance and computational cost. In addition, two related tools are theoretically addressed and their estimators are derived through the ACP and CMS. Specifically, the optimality of the order-frequency spectral coherence (the normalized/whitened form of the OFSC) in revealing cyclic components according to their SNR is demonstrated. Also, the improved envelope spectrum is derived from the latter by integrating over the spectral frequency variable, evidencing considerable enhancement over the squared envelope spectrum. The potentiality of the proposed tools and the adequacy of the related estimators are experimentally investigated on simulated and real-world vibration signals.