The Theory And Application Of Intrinsic Time Scale Decomposition

As an important research content of signal processing discipline,time-frequency analysis of nonlinear non-stationary signals has been rapidly developed and widely applied in various fields in recent years.Intrinsic time-scale decomposition(ITD)is one of the novel analytical tools that processes on this type of signals.It has been rapidly developed in theory and applied research,and it has received the attention of many scholars.ITD has been widely used in mechanical fault detection,however,the application field of this method is relatively limited.Therefore,the theoretical research of this method needs to be developed.How to effectively choose the ITD components and avoid losing the components containing useful information is still an important research content.Therefore,this thesis is mainly based on the theory and application of ITD.An improved intrinsic time-scale decomposition(IITD)components selection method based on matching pursuit(MP)algorithm is proposed.The main purpose of this method is to choose the useful components of the resulting signal,and finally extend the components selection method to applied research.The following work is carried out :(1)This thesis proposes a selection method of IITD components based on MP algorithm,which can effectively choose the IITD components.The main problem to be solved is how to choose effective components among the finite components,while requiring the number of components to be as small as possible.As the selection of the components are binary,and the total number of the components to be selected should be as small as possible.Therefore,this selection problem is expressed as the L0 norm binary programming problem.On the other hand,due to the requirement that the selected components retain the useful information of the original signal as much as possible.This is a L infinite norm constraint.That means,the formulated optimization problem is a binary sparse optimization problem with a L0 norm objective function subject to a L infinite norm constraint.Since the above problem is non-convex and non-smooth,the thesis will solve the problem based on the inspiration of matching pursuit algorithm.As a novel non-stationary nonlinear time-frequency analysis method,IITD overcomes many limitations of classical methods such as empirical mode decomposition,Fourier analysis and wavelet analysis.MP is an efficient greedy algorithm for solving sparse optimization,which is extremely computationally intensive.Therefore,the components selection method that combines them has the advantages of both methods.And this is also the innovation of this thesis.(2)In order to verify the feasibility of the components selection method proposed above,this thesis will apply this method to signal denoising and signal underlying trend extraction.This thesis choses these two applications for feasibility verification mainly because these two applications are more extensive and basic signal processing applications.The application results in signal denoising show that the proposed method has better signal and noise separation effects in artificial noise signals.The obtained denoising signals have a relatively high signal to noise ratio(SNR).Compared with several classical decomposition methods and sparse optimization methods,the underlying trend extraction results applied to the two actual signals show that the underlying trend extracted by the proposed method of this thesis obtains better results and can better track the changes of the original signal.The above simulation results fully verify the feasibility and practicability of the components selection method proposed in this thesis.