Research On The Problems Of Nonstationary Random Signal Analysis And Processing Based On Local Wave Method

A recently developed theoretical and computational method by Huang [1998] is especially well suited for analyzing time-series data that represent nonstationary and nonlinear processes. The key part of the method is the local wave ,decomposition method with which any complicated data set can be decomposed into a finite and often small number of intrinsic mode functions that admit well-behaved Hilbert transforms. With the Hilbert transform, the intrinsic mode functions yield instantaneous frequencies as functions of time that give sharp identifications of imbedded structures. The final presentation of the results is an energy frequency-time distribution, designated as the Hilbert spectrum. This decomposition method is adaptive and, therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and non-stationary processes. The main innovations embodied in this method are the introduction of the intrinsic mode functions based on local properties of the signal, which make the instantaneous frequency meaningful; and the introduction of the instantaneous frequencies for complicated data sets, which eliminate the need for spurious harmonics to represent nonlinear and non-stationary signals. This method is designated as local wave method.This paper does further research into local wave method, and on this basis it studies several problems about nonstationary random signal analysis and processing, and puts forward several new methods to solve the problems. It includes the following:The local wave method is further studied. Some factors related are studied, and measures to raise working efficiency of the method are put forward. The measures are very important for the applications of local wave method. Using Hilbert spectrum and its marginal spectrum, new ways to solve machinery fault diagnosis problems are found. The related problems that need further study in this field are pointed out, too.On the basis of local wave method, a new method for suppressing the cross-term of Wigner-Ville distribution is presented. It is designated as local wave decomposition and its Wigner-Ville distribution. First, this method preprocesses the signal: using local wave decomposition method, a complicated signal is decomposed into a finite and often small number of intrinsic mode functions, and then, Wigner-Ville distribution is calculated in any of the intrinsic mode functions. This presented method can suppress the cross-term interference efficiently, and will not create the smooth portions of auto-terms. Even though each pair of auto-terms is relatively close in time-frequency plane, the presented method can suppress the cross-term interference efficiently and meanwhile, keep all the fine qualities of Wigner-Ville distribution.The local wave decomposition method is extended, and a general method for analyzing variance-stationary random signal is presented. It is designated as signal decomposition method. Using a method of signal decomposition, the trend component series can be obtained from the variance-stationary random signal; the rest of it is zero-mean stationary random signal that can be studied with the parametric model of stationary random signal. This method, simple and commonly used, is the general method to process the signals, and any priori knowledge of the trend component is not need. The trend component series derived in this way can near more exactly the trend component curve of the variance-stationary random signal.Based on local wave method, a new method for time-varying parametric model of analyzing nonstationary signals designated as the local wave decomposition and its time-varying parametric model is presented. It includes two procedures. First, using local wave decomposition method, we can decompose any complicated nonstationary signal into a finite and often small number of intrinsic mode functions. Second, a time-varying parametric model is established in any of these intrinsic mode functions, and gets their t...