Applications of Fractional Lower Order Frequency Spectrum Technologies to Bearing Fault Analysis

Abstract

The traditional spectral analysis method is used to study the characteristics of bearing fault signals in frequency domain, which is reasonable and effective in general cases. However, it is proved that the fault signals have heavy tails in this paper, which are α stable distribution, and 1<α<2, and even the noises belong to α stable distribution. Then the conventional spectral analysis methods degenerate and even fail under α stable distribution environment. Several improved frequency spectral analysis methods are proposed employing fractional lower order covariation or fractional lower order covariance in this paper, including fractional lower order Blackman-Tukey covariation spectrum (FLOBTCS), fractional lower order periodogram covariation spectrum (FLOPCS), and fractional lower order welch covariation spectrum (FLOWCS). In order to suppress side lobe and improve resolution, we present novel fractional lower order autoregression (FLO-AR) and fractional lower order autoregressive moving average (FLO-ARMA) parameter model frequency spectrum methods, and the calculation steps are summarized. The proposed spectrum methods are compared with the existing methods based on second-order statistics under Gaussian and SαS distribution environments, and the results show that the new algorithms have better performance than the traditional methods. Finally, the improved methods are applied to estimate frequency spectrums of the normal and outer race fault signals, and it is demonstrated that they are effective for fault diagnosis.

Applications of Fractional Lower Order Synchrosqueezing Transform Time Frequency Technology to Machine Fault Diagnosis

“…]e − j2πfτ dt. (27) e right side of (27) is converted from the time domain to the frequency domain based on Plancherel's theorem and Fourier transform; then we obtain…”

“…Recently, it is verified that probability density function (PDF) of the mechanical bearing fault signals has an obvious trail, which is a nonstationary and non-Gaussian distribution and belongs to α stable distribution (0 < α < 2); even the noises are also α stable distribution [25][26][27][28].…”

Fractional lower order linear chirplet transform and its application to bearing fault analysis

“…Due to the repeated transient characteristics caused by local damage, it is easy to be drowned by various interference components and strong noise, so early identification and diagnose of the rolling bearing faults is still difficult. Recently, it is verified that probability density functions (PDFs) of the mechanical bearing fault vibration signals have obviously trailing process, they belong to non-stationary and non-Gaussian distribution α stable distribution (1<α<2), even the strong noises are also α stable distribution [24][25][26]. The performance of the above-mentioned methods based on second-order statistics degenerates under α stable distribution environment, even which fails.…”

Fault Characteristic Extraction by Fractional Lower-Order Bispectrum Methods

“…e adaptive cumulative distribution detector and blind estimation of frequency hopping parameters methods were proposed based on α-stable distribution model in [32,33]. Several improved frequency spectrum analysis methods have been introduced for α-stable distribution environment in [34], and the improved time frequency representation algorithms are proposed in [35], which have been applied to mechanical fault signal analysis.…”