Theory, Methodology Of Parameterized Time-frequency Analysis And Its Application In Engineering Signal Processing

Assuming that a signal to be analyzed is stationary, its Fourier transform obtains an explicitfrequency spectrum. The frequency spectrum reveals the overall frequency contents contained bythe signal, though it cannot indicate the localized frequency contents at any specific time.However, widely studied non-stationary signal in various research fields usually contains thetime-varying frequency contents, known as instantaneous frequency, so that Fourier transform isnot suitable to analyze such signals. Recently, plenty of time-frequency methods have beenproposed. By providing a time-frequency representation, they are powerful to analyzenon-stationary signals. According to whether the parameters are related to the signal, thetime-frequency methods can be categorized into non-parameterized time-frequency method andparameterized time-frequency method. While analyzing non-stationary signal, the former methodusually leads to a blur time-frequency representation since they use signal-independenttime-frequency resolution. On the other hand, with adopting a matched kernel function for apre-defined signal model, the latter method is much more effective in characterizing the realtime-frequency pattern of non-stationary signal.The content of this thesis overall involves three aspects: the theory, methodology of theparameterized time-frequency analysis (PTFA) and its application in engineering signalprocessing.The thesis started with chirplet transform, a classical PTFA method. With defining frequencyrotate-operator and frequency shift-operator, a new insight of the chirplet transform was proposed.The new insight provided the basis to explore the general PTFA. With an arbitrary continuous integrable kernel function, we constructed more general frequency rotate-operator and frequencyshift-operator. Therefore, a general definition of PTFA was proposed by using the above twooperators. According to the definition, we derived several properties of PTFA, i.e., time-shift,frequency-shift and scale transform, et al.Secondly, the thesis proposed three new PTFA methods, i.e., polynomial chirplet transform,spline chirplet transform and generalized warblet transform. Based on the proposed generaldefinition, they used the kernel function of polynomial function, spline function and Fourier series,respectively. It has been proved that they are powerful to analyze non-stationary signals withrapid time-varying instantaneous frequency. Since kernel function determines the performance ofa PTFA method, so it is critical to select proper parameters for the kernel function. Therefore, weproposed a kernel parameter estimation method with curve fitting for the ridge of thetime-frequency representation. The analysis results verified that the proposed method could selectproper parameters for the above three PTFA methods, even when the considered signal is heavilycontaminated by noise.Thirdly, the thesis focused on how to use PTFA to process multi-component signal. When thecomponents exhibit great differences, the existing PTFA methods fail to analyze directly by usingone kernel function. To overcome this deficiency, we proposed a time-frequency representationfusion method by integrating with image processing method. The study results proved that itcould be an effective way to improve the energy concentration and time-frequency resolution forthe aforementioned multi-component signal. Meanwhile, from signal decomposition point of view,we proposed a signal decomposition method to facilitate the usage of standard PTFA methods.With optimizing a frequency concentration index that is derived from the general definition ofPTFA, a multi-component signal is decomposed into several mono-component signals. In suchcase, the standard PTFA method could obtain a time-frequency representation with improvedenergy concentration for the multi-component signal.Lastly, the thesis applied PTFA methods in two fields, i.e., the characteristic signal processingof rotary machine and Lamb wave signal processing. Before using the above PTFA methods, weevaluated their performance and adaptability when they are used to estimate the instantaneous frequency of noisy signal. Then, for the vibration signal collected from a rotor test rig and ahydraulic turbine machine during non-stationary stage, we adopted the developed PTFA methodsto estimate the instantaneous speed and provide a refined time-frequency analysis, respectively.The analysis results demonstrated that the spline chirplet transform and the signal decompositionmethod were suitable to deal with the mono/multi-component vibration signal. On the other hand,Lamb wave characterizes the frequency dispersion feature, i.e., the localized frequency delayvaries with the frequency nonlinearly. To analyze such signal, we proposed a complementarydefinition in frequency domain for the PTFA’s general definition. Meanwhile, the kernel ofpolynomial function and Fourier series were used to develop polynomial frequency delaytransform and Fourier series frequency delay transform. Then, the thesis studied the groupvelocity estimation for the Lamb wave based on the above transforms. The simulation andexperiment results verified that the proposed methods could effectively analyze dispersive Lambwave signal, and accurately estimate the group delay of its single mode.