A Study On Non-stationary Of Bearing’s Fault Signal Based On Alpha Stable Distribution

Rolling bearing is the most commonly used also the most vulnerable part inrotating machinery components, The rolling-bearing’s normal operation is the necessaryfor normal operation of the rotary machinery and equipment, so making a diagnosis tothe rolling bearing has important practical significance. At present, the method based onthe equipment’ vibration signal is the most common and valid method in the faultdiagnosis. Generally, Most of the vibration signal in reality is random andnon-stationary. And the rolling bearing’s vibration by the runtime signal is classic cyclicstationary random signal one kind of non-stationary. There is modulation phenomenon,when the fault in inner ring and roll. Especially the early failure fault vibrationamplitude is smaller, these cases the property of cycle stationary is obvious. Themethods center on FFT, such as Envelopment analysis and spectrum analysis becomedisabled, when the property of non-stationary is serious. So how to extract the fault traitfrom the vibration signal is very important. Even though the time-frequency analysissuch as Wavelet analysis, short time Fourier transform method maybe also disabled insome non-stationary condition.This paper, which is based on mechanical vibration theory, probability andmathematical statistics and signal processing technology, used the mechanical faultdiagnosis’s methods. In this paper, the research object is the vibration signal of faultedrolling-bearing. From the definition of non-stationary signal, I research the rollingbearing fault mechanism of non-stationary, the influencing factor and the non-stationaryperformance. And use the Wold-Cramer decomposition to transform the non-stationarydiscrete random signal to the signal’s complex envelop. And we can get the ideal resultof fault frequency of a bearing fault non-stationary signal. The fault rolling bearing’svibrating signal is non-Gaussian and the probability distribution is more fit with Alphastable distribution. For the two factors I apply the concept of alpha stable distribution.Alpha stable distribution’s order is less than two, which is also called fractional lowerorder moment. It is the only kind of conform to the generalized center limit theorem ofprobability density distribution. And It can be a good description has obviouscharacteristics of shock pulses signal. The normalized Fractional Lower Order Momentof Alpha stable distribution can represent the degree of the bearing fault signal pulsesize. Also it can represent the character of signal’s stationary. Based on the two characters above, we can select the most optimal complex envelop.The method in this paper is verified through the simulation experiment and othermethods. Using the program development software LabVIEW and NI equipment, I cancollect the fault rolling bearing’s vibration signal from the gear dynamic simulationsystem. And use the MATLAB to analyze the Acquisition data, I can get the faultcharacter frequency by the above mentioned method. The tree structure of filter bankand complex analytic filter algorithm is adopted to generate the signal complexenvelope in this paper. Then use the normalized Fractional Lower Order Moment toIdeal complex envelop of fault signal. In order to be more persuasive, I make ananalysis using the public data. The Comparing the results also show that the method isaccuracy and superiority.