Grouping Theory And Application Of Singular Spectrum Analysis Based On Empirical Mode Decomposition

The study of non-linear and non-stationary signal processing methods is an important branch of signal processing research,and it has achieved rapid development in recent years.Singular spectrum analysis(SSA)is one of the innovative time-frequency analysis tools that acts on this type of signals.It has attracted the attention of many researchers in recent years.SSA has been proved to play an important role in many applications,h owever,the theoretical research aspect of SSA is lack of attention,resulting in the lack of theoretical support for this method.Therefore,it is urgent to speed up the theoretical research.Nowadays,most of the theoretical studies of SSA are focused on the selection of parameters,especially the grouping relates to the effect of the whole SSA algorithm.At present,the mainstream methods of grouping divide SSA components into two groups,but there are some limitations in these methods.There are few theories and methods which can divide SSA components into many groups,and there is no general method.Thus,this thesis first proposes a method to divide SSA components into multiple groups by combining empirical mode decomposition,and extends the improved algorithm to applied research.The following work is carried out:(1)This thesis first proposed a SSA grouping theory combined with empirical mode decomposition.The principle of the grouping theory is as follows,the total number of groups of the SSA components is selected to be the same as the total number of the intrinsic mode functions(IMFs)of the signal.And then,the SSA components are assigned to the group where the absolute correlation coefficient between the IMF and the SSA component is the highest.This grouping method is imp lemented using the matching pursuit(MP)algorithm.The grouping theory proposed in this thesis has three advantages compared with other theories.First,many SSA grouped components based on this grouping theory are more conducive to analysis.From the gro uping simulation experiments,it can be seen that the IMFs and the SSA grouped components obtained using this grouping theory have similarities in both the time domain and the frequency domain,that is,the obtained grouped components can have the analysis characteristics of the two methods simultaneously.Second,this kind of grouping theory can automatically determine the number of groups,so that the grouping can maintain stronger stability without human interference.Third,the grouping principle of the theory is simple and easy to understand,and the computation is small.(2)In order to verify the feasibility of the new SSA grouping theory,this thesis carries out experimental verification of signal denoising according to the grouping theory.This thesis choses signal denoising for experimental verification because it is one of the most extensive and basic application studies.The method of selecting group ed components in signal denoising experiment refers to the EMD method based on continuous mean square error criterion.Using this method,some SSA grouped components are selected to form the denoised signal.If the denoised signal has a relatively high signal-to-noise ratio(SNR),it can proved that the proposed SSA grouping theory is feasible.This method is compared with other four common denoising methods on three different structural signals.Computer numerical simulation results show that the SNR of several signals denoised by our proposed method are higher than those denoised by the existing common denosing methods.In addition,the theoretical method proposed in this thesis can maintain excellent noise reduction effect when the S NR of the original signal spans a wide range.It is demonstrated that the theoretical method is robust to the original noisy signals with a large SNR coverage and the signals with different structure.