Kalman Filtering using Trigonometric Polynomials for Gear Fault Diagnosis Under a Variable Speed Condition

Abstract : It is well known that the presence of cracks on a gear tooth is manifested by both amplitude modulation (AM) and phase modulation (PM) and their estimation is crucial for the diagnosis and prognosis of the state of the gearbox. In this paper, a new demodulation technique for gear fault diagnosis is proposed based on Kalman filtering combined with a polynomial basis function of the rotating speed. First, the problem of demodulation is formulated in terms of the state-space modelling of the vibration signal. This is achieved by approximating the modulations using the orthogonal trigonometric polynomial function of the rotating speed. Kalman filtering is then used to estimate the coefficients of the polynomials in order to reconstruct the modulation signals. This approach is different from classic approaches such as the narrowband demodulation technique (NBDT) or time-synchronous averaging (TSA). The advantages of the proposed approach over the latter are discussed in this paper and the efficiency of the new approach is also evaluated using both synthetic and real gearbox vibration signals.