Research on the order selection of the autoregressive modelling for rolling bearing diagnosis

The article does a research on the order selection of the autoregressive (AR) model for the rolling element bearings. First, the model of the signal that matches the one introduced by McFadden is considered. To clearly describe it, here it is called the resonance damping model. It is shown that the impulses generated by a fault will cause structure resonance and soon decay with a periodic mode. As the AR process based on the prediction theory has an ability to recognize the periodic (quasi-periodic) part, it is possible to pick out the damping part that is a quasi-periodic component. Because of the background noise, the damping part cannot be recognized if the component decays to be buried into noise absolutely. Hence the optimal order should be the number of points contained by the process, which is the maximum length of the periodic damping part that the AR model can recognize. That is to say, the process should last until the resonance damping part is buried into noise completely. Then an experiment to validate the method is carried out and success is achieved in the fault diagnosis of real rolling bearings. In the end, it is concluded that the optimal order has a high ability for noise cancellation for rolling element bearing diagnosis.