Research On Adaptive Time-Frequency Analysis And Its Application To Fault Diagnosis

Running conditions of machine are diverse and the changes of these conditions would result in non-stationary signals occurring. Some non-stationary signals also appear with the occurring and developing of faults in operating a machine. So the non-stationary characteristics can be taken as the tokens of some faults. The frequencies change with time for non-stationary signals, thus the signals can't be described sufficiently in time domain or frequency domain. But time-frequency analysis as a powerful tool for analyzing non-stationary signals can represent the frequencies of signals changing with time.The researches in this dissertation are supported by the National Natural Science Foundation of China(No.5067209), and the Key Science and Techanology Project of Henan Province(No,0122022000), and the Innovation Fund for Outstanding Schalar of Henan Province(No,0621000500). This dissertation studies the limitations of time-frequency analysis and aims to improve time-frequency resolution based on different constructs. The contents of the dissertation are as follows:1. This dissertation analyzes the deficiencies of the fixed kernel and the characteristics of signal auto-terms and cross-terms. And then the adaptive time-frequency analysis based on the radial parabola kernel(RPK) is proposed to suppress these cross-terms while retaining the auto-terms as much as possible; the definition of RPK is given and the algorithm is studied. The RPK can adopt the optimizing method to filter cross-terms adaptively according to the signal distribution. Compared with traditional fixed -kernel functions, such as Wigner-Ville distribution, Choi-Williams distribution and Cone-kernel distribution, the superiority of the RPK function is obvious. The RPK can avoid the ringing introduced by the cutoff of 0/1 rectangle kernel, shorten the distance between passband and stopband. And thus the fine time-frequency resolution can be obtained. The RPK time-frequency distribution not only suppresses the cross-terms preferably but also removes the noise of signals due to the adaptive filtering of the kernel function. Another advantage of the adaptive RPK time-frequency distribution is that without any hypotheses for signals, it offers improved time-frequency distribution for a large class of signals.2. Because orthogonal harmonic wavelets provide a complete set of complex exponential functions whose spectrums are confined to adjacent and non-overlapping bands of frequency. The harmonic wavelet packet decomposition is proposed and the algorithm is presented. Then, combining the harmonic wavelet packet decomposition with the maximum projection theory, this paper proposes an adaptive decomposing method. This method decomposes signal into linearity combination of a series of harmonic wavelet base atoms. The adaptive decomposing method based on harmonic wavelet packet can avoid the inherent cross interference in the Cohen class time-frequency distribution, eliminate the spurious components introduced by energy leakage in wavelet packet decomposition and in matching pursuit based on wavelet packet. In the proposed method, the time-frequency atoms can be adaptively selected according to the analyzed signal from the harmonic wavelet packet dictionary; non-stationary signal is decomposed into a number of independent frequency sub-bands, and the frequency overlapping and leakage are avoided. The simulation results show that the proposed approach can depict signal features preferably and fine time-frequency resolution can be obtained.3. The adaptive chirplet decomposition is studied in order to depict the time-varying features of non-stationary signals better. With the increase of parameter number, the number of atoms in dictionary becomes numerous when using matching pursuit dictionary. If the atoms in dictionary cannot fit the signal well, the signal will need to be approximated by several atoms, thus the signal features cannot be represented best. Furthermore, these methods generally assume a signal model without noise, and hence their efficiency under low SNR conditions cannot be rigorously demonstrated. Because parameter selection is the key in chirplet decomposition, a new algorithm of parameter estimation is proposed.Firstly, the fractional Fourier transform (FRFT) is investigated, and the chirp rate is searched by FRFT. Compared with Radon-Wigner transform, the estimation method not only reduces searching load but also weakens the influence of noise. The detection of chirp rate by FRFT is efficient for single-component signals or multi-component signals which the components are close in energy. But for multi-component signals in which component energy is dramatically diverse, the components with strong energy would cover up the components with weak energy. In the proposed method, when a component is decomposed, the signal will subtract the component, and the next detection of chirp rate is processed for the residual signal. In this way, the problem that the weak components might be covered up is solved using the decomposing method. Time center and frequency center are estimated using short-time Fourier transform after the chirp rate parameter is estimated. Then quasi-Newton maximization and expectation maximization (EM) algorithm are employed to refine the estimate accuracy. The algorithm which combines the EM with the maximum projection decomposition takes noise into account in complete data, using the parameter estimates obtained by quasi-Newton maximization as the initial value to decompose the observed data. And thus the accurate estimation are obtained. The simulation results indicate the proposed method obtains fine time-frequency resolution and is robust in low SNR conditions.The adaptive chirplet decomposition and the proposed parameter estimation method ensure that the base functions perfectly match the analyzed signal and realize the sparse description of the signal. Another advantage of this method is its utility as a classifier in intelligent diagnosis. The signal whose type is the same as base type can be represented efficiently when the decomposition number is coincident with the component number. When the signal type is not coincident with base, the signal would be approximated by several bases and the time-frequency distribution can still reflect the time-frequency features.4. Time-varying autoregressive(TVAR) model of non-stationary signal is studied. Using this method, the time-varying parametric identification of non-stationary signal can be translated into a linear time-invariant problem by introducing a set of basis functions. Then, the parameters are estimated by using recursive least square algorithm with a forgetting factor and adaptive time-frequency distribution is achieved. Next, a new TVAR parametric model based on wavelet functions is proposed, and its algorithm is inferred. The feasibility and the performance analysis are carried on using synthetic signals. The simulation results illustrate that the proposed approach is superior to the common time-frequency analysis. Comparing the method that assumes signal is stationary in intervals, the TVAR model has the better capacity to track the time-varying signals. The time-frequency analysis based on TVAR model may overcome the limitation of heavy computation load. Another advantage of this method is that time-frequency resolution does not rely on the relationship between sampling frequency and sampling points. The time-frequency analysis based on TVAR model relies on the base type to some degree. We employ wavelet base function to represent the time-varying parameters of the model because of its good performance in capturing localized variations of the model. Compared with other general expansion such as Fourier or Polynomial, wavelet base is also provided to show that the proposed method is very suited for modeling and identifying the model parameters. Recursive least square algorithm is employed to avoid inverse matrix operation. Moreover, the use of recursive algorithm significantly reduces the computational time, which is relevant to real time implementation. But the performance of the algorithm is influenced strongly by noise because of using least square criterion, so the robustness of the method need to be improved in the future.5. In rotating machinery, rotor and its components, such as rolling element bearings, are key components in mechanical systems. Their failures account for a large percentage of breakdowns in rotating machinery. Some of these breakdowns can be catastrophic. Conducting diagnosis and prognosis on rotor and bearings is therefore fundamental to maintaining the integrity of mechanical systems. The vibration signals caused by faulty bearing are typical non-stationary. So the experiments are conducted and the data are acquired. Then we analyze the data using proposed methods, and accordingly obtain the time-frequency features. Compared with the common time-frequency analysis, the proposed adaptive time-frequency analysis are more efficient in representing the signal features, especially the adaptive parabola kernel and adaptive chirplet decomposition. They not only provide high time-frequency resolution but also possess fine de-noising capability in low SNR conditions. At last, the proposed adaptive methods are compared according to the experiment results. Their characteristics and application situations are summarized. The validity of proposed methods is confirmed by these experiment results.