AR pole trajectory in condition monitoring studies

In this paper a novel approach is proposed for vibration based fault detection studies by the tracking of pole movements in the complex z domain. Vibration signals obtained from the ball bearings from a High Vacuum (HV) and Low Vacuum (LV) ends of a dry vacuum pump run in normal and fault conditions are modeled as time variant AR (Autoregressive) series. The positions of the poles which are the roots of the AR coefficient polynomial vary for every frame of vibration data. It is a known fact that as defects such as spalls and cracks start to appear on the ball bearings, the amplitude of the vibrations of characteristic defect frequencies increase. Faults can be predicted by movement of poles in the complex plane as the pole positions are expected to move closer to the unit circle as the severity of the defect increases. The area of the region swept by the migratory poles loci and their distances from the unit circle can be useful fault indicators. From the position of the poles inside the unit circle, classification and quantification of the main spectral peak of defect frequencies can be easily performed, leading to the possibility of having frame to frame monitoring of spectral parameters of interest. The AR pole positions also allow an easier quantitative estimation of the spectral parameters. The pole representation facilitates the easier understanding of the spectral characteristics of the process because of the one-to-one correspondence between the poles and the AR spectral peaks. This method has interesting potential applications in condition monitoring and diagnostic applications. The description of the movement of the poles is shown to be particularly important for the study of harmonic components of the signal. This analysis has been validated with actual data obtained from the pump and initial results obtained are very promising.