A Study On Morlet Wavelet Transform Theory And Application With Software Implementation

In recent years, wavelet analysis as a new kind of time-frequency representation technique, has obtained rapid development and widespread application in different engineering field. Based on non-orthogonal Morlet wavelet, its analysis characteristic in time-frequency domain and application in modal parameter identification are studied deeply and systemically in this dissertation. In addition, on the foundation of theory and algorithm research, N-DTAS software has been developed based on LabVIEW platform. The main content is as follows:The relation between the change of dilatation factor a and translation factor b and the resolution of time and frequency domain is investigated in detail. Fast, simple and practical computational approach of non-orthogonal wavelet coefficient is presented from both convolution and Parseval theorem point of view.For the identification of modal parameters with input and output data, the method using the free response of analysed system based on tradional and modified Morlet wavelet is researched. Modal frequency and damping ratio can be obtained by fitting the wavelet transform coefficient's modulu and phase. Especially the idendification of mode shape based on least square and the condition satisfyied between wavelet center frequency f0 and wavelet factor N are proposed. The result of three degree of freedom simulation system and GARTEUR aircraft model shows that the modified Morlet wavelet is very suitable for modal parameters identification with closed mode frequency.The method substituting not random decrement function but correlation function for time response function is presented for the identification of modal parameters with only output data. In contrast to the traditional method extracting system free response via RDT, the obvious advantage is that, the unbiased cross-correlation estimation based on FFT has faster computing speed and average technique in frequency domain can enhance SNR level, and the identification result especially damping ratio has the higher precision. The efficency of the method has been demonstrated by two-storey building and Chao-bai bridge example results.N-DTAS software for data acquisition and signal processing, which has the function based on not only traditional FFT but also wavelet analysis for modal parameter identification, is developed based on LabVIEW platform. In this dissertation, the key LabVIEW advanced programming technique such as GPIB driver, Multithread, DLL, Queue, GUI, VI Sever, file management and software installer are described in detail.