Research On Wavelet Ridge Extraction Method And Its Applications

The extraction of wavelet ridges is an important part of the time-frequency analysis ofnon-stationary signals. By the use of information contained in the wavelet ridges, the transientcharacteristics of signals can be estimated, the signals can be decomposed, reconstructed and filtered,and the modal parameter of systems can be identified. Currently, the ridge extraction algorithms basedon the modulus maxima and phase information of wavelet coefficients have their own flaws, therefore,in order to reduce the redundancy of the wavelet transform, improve the efficiency of ridge extractionand achieve precise ridge results of multi-ridge signals, this paper studied the ridge extractionalgorithm based on the partial differential equations of the wavelet transform, discussed how eachprocess can be achieved and the impact of various parameters on the results, this algorithm has beensuccessfully applied to the signal decomposition and reconstruction and system modal parameteridentification, simulation results verified the validity and accuracy of the algorithm.The main contents of this paper are as follows:(1) This paper did research on the principles of the continuous wavelet transform and itsimplementation process, theoretical research in terms of the concept, methods and applications ofwavelet ridges and wavelet skeletons was made, and the parameter of the basis function of the wavelettransform was changed to improve.(2) We realized a ridge extraction algorithm based on the partial differential equations of thewavelet transform. Begin from the modulus maxima definition of wavelet ridges and the partialdifferential equations of the wavelet transform, the principle of the algorithm was derived in detail andthe numerical implementation steps of the algorithm are designed. Combining this algorithm and theimproved Morlet wavelet, the selection of multiple parameters in this algorithm were studied in detail,and the basic principles of how to choose the parameters were given. Implementation on the waveletridge extraction and each component reconstruction of signals using this algorithm has been achievedsuccessfully.(3) The ridge extraction algorithm was applied to the system modal parameter identification. Therelationship between wavelet ridge and modal parameters were studied, and the calculation formula toidentify modal parameters using wavelet ridges was deduced. We used simulation system of threedegrees and modal experiment of the arc structure to verify the effectiveness of the algorithm.Identification results of simulated signals had high accuracy, the modal frequency identification of the arc structure had high accuracy, and the reasons for poor precision of damping ratio were analysed.(4) A wavelet time frequency ridge analysis software was developed based on the MATLABGraphical User Interface. The overall design and demand analysis of the software was done first. Themain interface of the software was designed, and reasonable arrangements for the layout of eachfunction module were made. Each function module was designed in detail. By choosing simple andpractical controls, using structured programming, each function of the algorithm was implemented.The main function modules of the software were tested in simulation, and the effectiveness of thealgorithm and the technical utility of the software were verified.