Application Of Higher-order Statistics In The Fault Features Of Bearings

This thesis uses higher-order statistics, especially the properties that high-ordercumulant and higher-order spectra can restrain Gaussian noise, to research on faultdiagnosis method of rolling bearing based on higher-order statistics, and also to studythe fault feature method of rolling bearing based on high-order cyclic statistics.Firstly, the thesis introduces the basic theory of high-order statistics.(1) Discussesthe bispectrum which is the lowest order in higher-order cumulant spectrum, and pointsout that the bispectrum can completely restrain Gaussian noise in theory;(2) the thesisdiscusses the definition, basic properties, estimation algorithm and slice demodulationperformance of cyclic autocorrelation function, points out that cyclic autocorrelationfunction demodulation can extract fault feature.(3) On this basis, the theory ofhigher-order cyclic statistics is studied, focuses on the definition and basic properties ofcyclic bispectrum(three-order cyclic cumulant spectrum) which is the lowest order inhigher-order cyclic cumulant, improves the estimation algorithm of cyclic bispectrum,and points out that the cyclic bispectrum could handle the cyclostationary signal andrestrain Gaussian noise and non-Gaussian noise.Secondly, after simulation and experimental research, the thesis points out that thebispectrum especially two-dimensional contour map of bispectrum is divisible, whichcan distinguish different fault type of rolling bearing. But because bispectrum analysiscould not effectively extract fault characteristic frequency and the vibration signal isassumed to be stable. The thesis introducs the slice analysis method of cyclicautocorrelation function into the cyclic bispectrum analysis, puts forward to apply thepeak frequency slice spectrum of cyclic bispectrum spectral method for featureextraction of fault. The results shows that the method can extract fault characteristicfrequency and the frequency of two times peak at both sides of slice spectrum will beevenly distributed between fault passing frequency harmonics.The thesis also researches on the four-order cumulant—kurtosis, pointed out thatthe kurtosis has high value for bearing faultpointed out that the kurtosis has high valuefor bearing fault feature component, and puts forward the kurtosis analysis method and the kurtosis analysis method is applied to the frequency range selection of FIR filter.The experimental results shows: using this method to determine the parameters andfilter the vibration signal, the time-domain index after calculation can clearly distinguishthat the rolling bearing is faulty or not.