Restoring statistical cyclicity in rotating machinery vibrations using the oscillatory almost-cyclostationary model

Speed fluctuations will affect the statistical characteristics of rotating machinery vibrations, resulting in fuzzy fault features that are difficult to extract. This type of feature ambiguity can be interpreted as the vibrations are warped in time, and the related signal model is described as a time-warped almost-cyclostationary (ACS) process. By employing this sophisticated model in a de-warping procedure, the regular statistical properties of the signal are restored. In this paper, we propose a novel de-warping method for restoring fault features of rotating machinery under fluctuating speed conditions. Notice that the time-warped ACS process belongs to a subclass of the oscillatory ACS signal model. More specifically, under moderate speed fluctuation conditions, rotating machinery signals are further characterized as modulated cyclical signals. Therefore, the de-warping can be achieved by demodulating the time-varying autocorrelation function. The proposed approach avoids directly estimating the warping function by the complex non-convex optimization problem. Meanwhile, the accuracy of the solution is guaranteed. More clustered features lead to a more efficient diagnosis. In addition, the rotating speed can also be derived from the warping function without using a tachometer. Case studies of the experiments on a conventional bearing and a turbopump bearing with a large DN-value confirm the feasibility of the oscillatory ACS signal model. Furthermore, the superiority of the de-warping method is corroborated by the enhanced fault features in the classical cyclic spectrum analysis.