Kalman filtering using trigonometric polynomials for gear fault diagnosis under a variable speed condition


It is well known that the presence of cracks on a gear tooth is manifested by an amplitude modulation (AM) as well as by a phase modulation (PM). And their estimation is crucial for the diagnosis and the prognostic of the gearboxes state. In this paper, a new demodulation technique for the gear fault diagnosis is proposed. It is based on the Kalman filtering combined with a polynomial basis function of the rotating speed. First, the problem of the demodulation is formulated in term of the state space modeling of the vibration signal. This is achieved by approximating the modulations by orthogonal trigonometric polynomials function of the rotating speed. Then, the Kalman filtering is used to estimate the coefficients of the polynomials in order to reconstruct the modulation signals. This approach is different from the classical ones such as the narrow-band demodulation technique (NBDT) or the time synchronous averaging (TSA).

The advantages of the proposed approach over the latter are discussed in this paper. Also, its efficiency is evaluated using both synthetic and real gearbox vibration signal.