Study On Two-dimensional Plane Express Based On Cyclostationarity For Weak Fault Features Extraction Of Rolling Element Bearings

With the development of technology, rotating machinery possesses more and morecomplex structure, which asks for accurate operation situation to ensure long-term saferunning. As vital parts of rotating machinery, rolling element bearing plays a veryimportant role in the normal running of overall system. Their any deviation from thenormal situation that is caused by defects, no matter how light they are, will disturb therunning of connected components. Consequently, more components will be involved inand the performance of the system will deteriorate gradually together with a series of faults.Therefore, picking up fault characters of rolling element bearing as early as possibleguarantees the normal operation of overall system. But, it is not an easy task. Early faultsof them are weak, and fault information always buries under environment noise.Monitoring their occurrence and evolution is an arduous challenge. Parameters of rotatingmachinery are periodically time-varying, especially for those under failure situation.Periodical time-variance implies cyclostationarity. Therefore, studying the cyclostationarycharacters of rolling element bearing could clarify the fault essence and has easier access topicking up weak fault information.To realize the early feature extraction of bearing faults, fault bearing signal model andcyclic statistics theories are investigated, the cyclostationary nature of bearing vibrationsignals is analyzed. Fault feature signal is separated from background noise and otherinterferences through the second order and third order cyclostationary analysis, thus theearly and weak fault signatures are identified objectively and effectively. The contents areas follows:(1) The characteristics of incipient fault of rolling element bearing are analyzed, andits fault signal model is introduced. The signal model has two components, deterministicand random, whose frequency characteristics are studied: the deterministic part has discretespectrum while the random one has continuous spectrum. It is analyzed that the uncertaintyof impulse period, which is caused by variation of rotation speed or contact angle of rollingelements, can cause the decrease of discrete spectrum and make it very difficult tohighlight the fault characteristic frequency in power spectrum of rolling element bearings.(2) Cyclostationary phenomena and basic concepts of cyclic statistics are brieflytalked about. Based on the theories of cyclic statistics, the second order cyclostationaryfeature is obtained for the rolling element bearing fault signal model. The methods basedon spectral correlation density function and cyclic autocorrelation function analysis forearly fault detecting of bearing is investigated. And both the methods are focus on thecyclic frequency-frequency plane or cyclic frequency-time lag plane. (3) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. And statistical properties of the signals change periodically with time. Theaccurate analysis of time-varying signals is an essential pre-request for the fault diagnosisand hence safe operation of rolling element bearings. The Wigner distribution (WD) isprobably most widely used among the Cohen’s class in order to describe how the spectralcontent of a signal changes over time. However, the basic nature of such signals causessignificant interfering cross-terms, which do not permit a straightforward interpretation ofthe energy distribution. To overcome this difficulty, the Wigner-Ville distribution based onthe cyclic spectral density is discussed in this paper. It is shown that the improvedWigner-Ville distribution, which based on cyclic spectral density of a long time series, canrender the time-frequency distribution less susceptible to noise, and restrain the cross-termsin the time-frequency domain. Simulation and experiment of the rolling element bearingfault diagnosis are performed, and the results indicate the validity of the Wigner-Villedistribution based on cyclic spectral density in time-frequency analysis for bearing faultdetection.(4) The vibration signals of rolling element bearings are random cyclostationary whenthey have faults. However, because the background noise is very heavy when the earlyfault occurs, it is difficult to disclose the latent periodic components successfully evenusing the second order cyclostationary analysis. To overcome this difficulty, the cyclicbispectrum (CBS), an alternative approach based on third-order cyclostationarity analysis,is discussed in this paper. Furthermore, the slice spectrum analysis of the CBS is proposed.The CBS is a third-order cyclic statistical parameter, in the frequency domain. TheCBS gives full play to the advantage which is provided from the higher order cyclicstatistical methods. It can restrain noise and provide more information than classicalmethods such as amplitude spectrum analysis and envelope analysis when the fault at anearly stage. However, the CBS is four-dimensional. So, the Slices Spectrum Analysis of theCBS is introduced to fault diagnosis. According to the algorithm by C.T. Yiakopoulos andI.A. Antoniadis, the actual CBS analysis is a set of specific values for cyclic frequency α.And, each of them corresponds to a specific cyclic frequency α. We called each of them tothe once slice of the CBS. That is, the once slice of the CBS, which is3D structure, issliced along the cyclic frequency axis firstly. The CBS corresponding one cyclic frequencyis called the once slice of the CBS. Simulation and experiment of the rolling elementbearing fault diagnosis are performed, and the results indicate the feasibility and validity ofthe once slice of the CBS analysis in rolling element bearing early fault diagnosis.However the information in the once slice is redundant and indirect for fault diagnosis.So the twice slice of the CBS, as the horizontal slice of the once slice (HSCBS), thevertical slice of the once slice (VSCBS) and the diagonal slice of the once slice (DSCBS), which is sliced along one frequency axis in the once slice is studied. By analysis, thehorizontal slice of the once slice of the CBS (HSCBS) which is at a special given cyclicfrequency is proposed to resolve the contradiction. Additionally, the less computation ofHSCBS is also appealing.