Study On Fault Feature Extraction For Nonlinear Nonstationary Signals Based On General Local Frequency

Feature extraction of vibration signal has always been the frontier in conditionmonitoring and fault diagnosis of equipment. Particularly, there exist greatdifficulties in feature extraction of nonlinear nonstationary signal of early fault, weakfault and multiple faults for large and complex equipment. It has become the mostchallenging problem in the field. Based on the re-examining and re-understanding offrequency, a novel concept of general local frequency is proposed. The research onfault feature extraction of nonlinear nonstationary signal is investigated andsuccessfully applied to the multi-source impact vibration signal of reciprocatingcompressor. This study has important scientific significance in development ofspectrum analysis and time-frequency analysis. It also has broad application prospectin other nonlinear nonstationary engineering fields.The concept of global frequency (i.e., the reciprocal of periodic) andinstantaneous frequency (i.e. the derivative of phase) has been widely used inspectrum analysis and time-frequency analysis respectively. They play an importantrole in describing the overview and detail of signals. However, there are also somelimitations in feature extraction of nonlinear nonstationary signal. To solve thisproblem, a novel concept of general local frequency is proposed, which presentsboth the advantage of global frequency and instantaneous frequency according to theexpression in frequency domain and time-frequency domain. It not only overcomethe limitation of global frequency which is meaningful for period signal and can notdescribe the non-period signal with varying frequency and amplitude, but also solvethe problem of instantaneous frequency which is defined for narrow-band signal andlack of many large-scale frequency information. In addition, some simulations aretaken as example to verify the applicability of general local frequency, whichdemonstrate the accuracy of general local frequency.Time-frequency analysis techniques, such as short time Fourier transform, wavelet transform Wigner-Ville distribution, chirplet transform, empirical modeldecomposition and local mean decomposition, have been played an effective role infault diagnosis of rotating machinery. However, with the extension of fault diagnosistoward large and complex equipment, whose vibration signal presents complexcharacteristics of nonlinearity, nonstationarity and non-Gaussian. Its time-frequencydistribution will become very complicated. Between the frequency band and faultfeature is lack of mapping. The physical meaning of some frequency components isnot clear, and it is difficult to extract useful feature information. To solve thisproblem, a novel time-frequency analysis method of general local frequency basedon adaptive waveform decomposition is presented for extracting the time-frequencyfeatures of multi-component nonstationary signal. The proposed method has gottenrid of the thought that signal is composed by seriers of basis function which rely onsome priori knowledge, and it still has a well self-adaptive. In addition, a fusionnoise reduction technology based on adaptive waveform decomposition and mutualinformation is investigated and the simulation results verify its effectiveness.The phenomenon that power spectrum contains the continuous peaks and noisebackground is often an important basis for recognizing system in chaotic state.However, the power spectrum is based on the stationary assumption, which is noteffective in analyzing the nonlinear nonstationary time series. Therefore, a novelfrequency domain analysis method based on general local frequency is proposed.The Duffing system is taken as example, the bifurcation phenomenon in frequencydomain of Duffing system is investigated. The method not only can over come thefalse frequency information generated by the power spectrum, but also caneffectively describe the structure and distribution of nonlinear signal in frequencydomain. In addition, the modulation characteristic and modulation similarity ofchaos time series are found by general local frequency analysis based on adaptivewaveform decomposition.Although the essential information of nonlinear nonstationary signals can be described by the features in frequency-domain and time-frequency domain ofgeneral local frequency, their values are seriously influenced by noise and sampleselection. There are great differences in magnitude order for various signals. Thecomparability, repeatability and stability of results are poor. In order to compensatethese deficiencies, the Lempel-Ziv complexity is applied to analyze thetime-frequency complexity of general local frequency. Comparing the time domainanalysis, the structure of time-frequency is simpler, the physical meaning is moreclearly and the type of signal is identified more accurately. Vibration signals ofrolling bearing are taken as examples, and the effectiveness of complexity analysisof time-frequency feature extracted by general local frequency is verified.Multiple source impact signals of reciprocating compressor present typicalnonlinear nonstationary characteristics. It is difficult to extract feature informationby existing time-frequency analysis methods. According to the theoretical research inthis paper, the method of spectrum analysis and time-frequency analysis based ongeneral local frequency is applied to describe the overview and detail of vibrationsignals for gas valve in different states, which can supply more rich and meaningfulfeatures for fault diagnosis of reciprocating compressor. In addition, the Lempel-Zivcomplexity is also applied to feature analysis in time domain and time-frequencydomain of gas valve signal. The results indicate that the structure of time-frequencyis simpler than time domain structure, and the proposed method can reduce theinterference of randomness brought by noise in some extent. So it is more effectivelyin describing the nonlinear relationship of gas valve in different states. In addition,the standard of LZC feature for gas valve in different states is given, which can beused as the auxiliary reference of fault diagnosis for reciprocating compressor.