A smoothness index-guided approach to wavelet parameter selection in signal de-noising and fault detection

Gabor wavelet transform can be used for de-noising impulsive signals measured from faulty bearings. However, it has been a challenging task to select proper wavelet parameters. This paper reports a method to guide the selection process by a smoothness index. The smoothness index is defined as the ratio of the geometric mean to the arithmetic mean of the wavelet coefficient moduli of the vibration signal. For the signal contaminated by Gaussian white noise, we have shown that the modulus of the wavelet coefficients follows Rician distribution. Based on this observation, we then prove that the smoothness index converges to a constant number (0.8455…) in the absence of mechanical faults or for very low signal to noise ratio. This result provides a dimensionless smoothness index upper bound corresponding to the most undesirable case. We have also shown that the smoothness index value decreases in the presence of impulses with properly selected parameters. The proposed method has been successfully used to de-noise both simulated and experimental signals.