The Theory Of Adaptive Morphological Filter And Local Wave Decomposition And Roller Bearings Fault Diagnosis

Vibration signal is the information carrier of rolling bearing of running state. Periodicallyrepeated impact and amplitude modulation are important characteristics of defects and fault inrolling bearings. They have a common characteristic that is not only related to time but alsoclosely related to frequency. It is difficult to obtain all of the signal characteristics if we splitthe time-frequency features and only analyze this kind of signals from the viewpoint of timeor frequency domain. On the contrary, it will undoubtedly improve the diagnostic accuracyand reliability if we identify the signal from the angle of the joint time-frequency domain. Inaddition, strong background noise and shock vibration are also characteristics of rollingbearing vibration signal that can not be ignored. So this paper adopts the method of adaptivemorphological filtering that filter out background noise and extract shock signal throughsetting up adaptive multi-structural and multi-scale morphological filter with the criterion ofrolling bearing fault characteristic frequency. Based on this, the method of local wavedecomposition is employed to process vibration signals of rolling bearing. Then thecharacteristic parameters of related scale entropy are extracted and finally the running statesof rolling bearing are identified with the method of fuzzy clustering. The main work is asfollows:(1) Mathematical morphology abandons the view of traditional numerical modeling andanalysis. It depicts and analyzes signal from set. The “probe” named as a structure elementwas designed to collect the information of signal. It achieved signal matching, signalextracting, details keeping and noise suppression by moving the probe constantly. Accordingto the measurement principle of frequency response function in the vibration signalprocessing, the quantitative relationship between filtering characteristic and the width ofstructure the elements, sampling frequency, analysis point number was studied. A quantitativedescription of the mathematical morphological filter was given. The method of multi-scalemulti-structural adaptive mean filter was proposed. The construction of adaptive multi-scalemulti-structural element was discussed in detail. With frequency intensity coefficient ascriterion, the adaptive multi-scale multi-structural mean filter was constructed by using sensitive structure elements, which realized better extraction effects of the low-frequencysignal.(2) Local wave method is an adaptive variable decomposition algorithm based on localsignal characteristics. The method decomposes signal into numbers of IMF and a trend term.Because the basis functions were generated by adaptive signal processing, it has good localcharacterization capabilities. By detailed analysis of the mechanism of the endpoint effect, amethod of endpoint effect suppression that is based on the endpoint matching characteristicwave extension was put forward. In the process of wave matching, the characteristics of thesignal at the endpoints were taken into full consideration. With the signal at the endpoint asbasic matching element, the unconstrained situation at the endpoint was changed whicheffectively suppressed the end effect according to the simulation test results.(3) The completeness of the local wave decomposition, the nature of energyconservation and the false component of local wave decomposition was employed forinspection and removal of false component, offset error component in the dominant modalcomponent. The method of anti-false component based on conservation of energy and relatedanalysis was put forward and the principle of false component attribute discrimination andmodal updating was proposed by using correlation analysis discriminant signal first dominantmode component combining with the principle of conservation of energy.(4) According to different generation mechanisms of the mode mixing, the paperproposed anti-mode mixing method of using morphological operations and frequency shift.Morphological operation was an effectively powerful tool to extract the intermittent signaland interfere with pulse. Therefore, on the basis of the morphological operations, the methodof anti-mode mixing caused by abnormal incidents was proposed. The simulation results showthat morphological operations had a great effect on mode mixing caused by pulse interferenceand intermittent signals; Frequency shift effectively solved the problem of mode mixing dueto interaction between signals. When the second sufficient condition of the local wavedecomposition was satisfied, the First sufficient condition can be up to120.95. Withthe method proposed in this paper, the local wave decomposition process, extracting IMFcomponents matching the original component, could be realized successfully.(5) By analyzing rolling bearing vibration signals measured under different conditionswith the method of adaptive morphological filter and the local wave decomposition and by using fuzzy clustering method. The feature scale entropy of the local wave extracted wastransformed into fuzzy equivalence relation matrix by the normalization processing andcalibration and then underwent clustering analysis. The method proved to be simple, practicaland with great detection precision, being an effective method of rolling bearing faultdiagnosis.The study above, to a great extent, enriched and improved the morphological filteringand local wave decomposition method. Diagnostic applications indicated the methodsproposed in the paper could distinguish between different working conditions and solvepractical problems.