Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods

Abstract

The generated signals generally contain a large amount of background noise when the mechanical bearing fails, and the fault signals present nonlinear and non-Gaussian feature, which have heavy tail and belong to $\alpha$ -stable distribution ( $1<\alpha <2$ ); even the background noises are also $\alpha$ -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under $\alpha$ -stable distribution environment. Two improved bispectrum methods are proposed based on fractional lower-order covariation in this paper, including fractional low-order direct bispectrum (FLODB) method, fractional low-order indirect bispectrum (FLOIDB) method. In order to decrease the estimate variance and increase the bispectral flatness, the fractional lower-order autoregression (FLOAR) model bispectrum and fractional lower-order autoregressive moving average (FLOARMA) model bispectrum methods are presented, and their calculation steps are summarized. We compare the improved bispectrum methods with the conventional methods employing second-order statistics in Gaussian and $S\alpha S$ distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods. Finally, we use the improved methods to estimate the bispectrum of the normal and outer race fault signal; the result indicates that they are feasible and effective for fault diagnosis.