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 α -stable distribution ( 1 < α < 2 ); even the background noises are also α -stable distribution process. Then it is difficult to obtain reliable conclusion by using the traditional bispectral analysis method under α -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 α 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.
Highlights
Bispectral analysis based on high-order statistics is an effective tool to solve nonlinear phase coupling and nonGaussian fault diagnosis [1, 2]. e traditional bispectrum methods include nonparametric bispectrum [3, 4], parametric AR bispectrum [5, 6], parametric ARMA bispectrum [7], and their improved bispectrum methods [8]. e bispectrum of the signal contains the amplitude information and the phase information
In view of the performance degradation of the conventional bispectrum methods in α-stable distribution environment, the improved fractional low-order direct bispectrum and fractional low-order indirect bispectrum methods have been proposed for α-stable distribution environment in this paper, and the improved fractional lowerorder autoregression model bispectrum and fractional lower-order autoregressive moving average model bispectrum methods are presented for decreasing the estimate variance and increasing the bispectral flatness. We summarize their calculation steps. e improved bispectrum methods and the traditional bispectrum methods employing second-order statistics are compared under Gaussian and α-stable distribution environments; the simulation results show that the improved bispectrum methods have performance advantages compared to the traditional methods
In order to further verify the pulse characteristics of the bearing fault signals, we use α-stable distribution statistical model to estimate the parameters of the inner race fault, ball fault, and outer race fault signals, and the results are given in Table 1 [37, 38]
Summary
Bispectral analysis based on high-order statistics is an effective tool to solve nonlinear phase coupling and nonGaussian fault diagnosis [1, 2]. e traditional bispectrum methods include nonparametric bispectrum [3, 4], parametric AR bispectrum [5, 6], parametric ARMA bispectrum [7], and their improved bispectrum methods [8]. e bispectrum of the signal contains the amplitude information and the phase information. Several improved bispectrum analysis methods based on fractional lower-order statistics are proposed for mechanical bearing fault diagnosis in Gaussian or α-stable distribution noise environment. In order to further verify the pulse characteristics of the bearing fault signals, we use α-stable distribution statistical model to estimate the parameters of the inner race fault, ball fault, and outer race fault signals, and the results are given in Table 1 [37, 38]. As it can be seen, the characteristic index of the normal signals is equal to 2, which is Gaussian distribution. SαS distribution is a more concise and accurate statistical model for the bearing fault signals
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