Extracting Rolling Element Bearing Faults From Noisy Vibration Signal Using Kalman Filter

Vibration analysis has been widely accepted as a common and reliable method for bearing fault identification, however, the presence of noise in the measured signal poses the maximum amount of difficulty. Therefore, for the clearer detection of defect frequencies related to bearing faults, a denoising technique based on the Kalman filtering algorithm is presented in this paper. The Kalman filter yields a linear, unbiased, and minimum mean error variance recursive algorithm to optimally estimate the unknown states of a dynamic system from noisy data taken at discrete real time intervals. The dynamics of a rotor bearing system is presented through a linear model, where displacement and velocity vectors are chosen as states of the system. Process noise and measurement noise in the equations of motion take into account the modeling inaccuracies and vibration from other sources, respectively. The covariance matrix of the process noise has been obtained through the transfer function approach. The efficiency of the proposed technique is validated through experiments. Periodic noise and random noises obeying the white Gaussian, colored Gaussian and non-Gaussian distribution have been simulated and mixed with a clean experimental signal in order to study the efficiency of the standard Kalman filter under various noisy environments. Additionally, external vibrations to the test rig have been imparted through an electromechanical shaker. The results indicate an improvement in the signal to noise ratio, resulting in the clear identification of characteristic defect frequencies after passing the signal through the Kalman filter. The authors find that there is sufficient potential in using the Kalman filter as an effective tool to denoise the bearing vibration signal.