A system dynamic approach to bearing fault identification with the application of Kalman and H∞ filters

Abstract

This work attempts to examine the scope of applying Kalman filter and H∞ filter individually on the vibration signal acquired for identifying local defects in a rolling element bearing. This is essentially a system dynamic approach, which is another choice, examined to be a better one in comparison with few other signal analysis approaches reported in the literature. Kalman and H∞ filters are optimal state estimators; Kalman filter is the minimum variance estimator while H∞ filter minimizes the worst case estimation error. States, displacement and velocity, of a rotor shaft system are obtained from its equations of motion, which are written by including the process noise and measurement noise to take into account modeling inaccuracies and vibration from other sources. Experiments have been carried out to investigate the performance of Kalman and H∞ filters each with the Envelope Analysis technique, a popular one for identification of bearing faults, in a noisy environment. Envelope Analysis is performed by taking a Hilbert transform of the band pass filtered signal, whose centre frequency and bandwidth are to be properly selected for satisfactory performance of the algorithm. Signals from test bearings running nearly at constant speed and having a single defect on the inner race and outer race have been acquired for different operating speeds of the test rig in the presence of extraneous vibration (noise) generated by running a nearby compressor. The signal obtained after the application of Kalman and H∞ filter demonstrates a significant enhancement in signal to noise ratio resulting in a clear identification of defect frequencies in the vibration spectrum. Therefore, Kalman or H∞ based state estimation approach may be used with confidence to extract bearing signals from noisy vibration signals.