Analysis Of Local Wave Decomposing Methods, Characteristics And Its Application Study

With the development of science and technology, Non-stationary signal processing and its application in engineering gain more and more attention. As we all know, non-stationary signal processing is a very difficult problem not only in signal processing field but also in fault diagnosis. Many technologies have appeared to meet the need of processing non-stationary signal. Local wave method is one of them. After several years' research and application it is approved that Local wave method is a wonderful way in non-stationary signal processing. But Local wave method is a new technology, and has many research to be done for testifying it's validity. Base on the opinion and National Nature Science Fund Project. "Research on Local Wave method and its Engineering Application" (No.50475155 ), the dissertation deeply study the local wave method both in theory and application in engineering. The main contents as follows:1. Since Local wave decomposition and wavelet decomposition have many similarities, detail researches have been done to compare their similarities and differences both in theory and in application — one and two dimension decomposition, singularity detection, data compression and time-frequency analysis, which offers an new idea for further study on local wave.2. The decomposition ability of current Local wave methods are given, which involves the relation of sample frequency and decomposition error, relation of two distinguishable sins, and the indistinguishability reason of sin/cos amplitude modulation with two sin/cos addition. And also it indicates that the higher frequency components may not meet the condition of Hilbert transformation, suggestion is given to be careful to use Hilbert transformation in higher frequency components. At the same time, The reasons of excessive decomposition and false components are also discussed, the relation coefficient of components and the original signal is used to solve the problem.3. For most noise has higher frequency, the firstly decomposed components which have little relation with original signal maybe are noise. Addition to the characteristics of noise, anew denoise method based on local wave decomposition is brought forward. The signal is denoised with this method and proved wonderful in non-stationary signal denoise.4. Accurate trend of a signal can be got through Local wave decomposition. So the criterion of trend judgment is established. The component whose normalized mean value is far from zero is stained by the non-zero trend. So this component and all the posterior components as well as the residual are added to become the slow-change trend. The trend gotten from Local wave decomposition is proved a new method in estimation of probability...