Research On Parameter Optimization Of Empirical Mode Decomposition

The trend of time series is a kind of additive component which contains the global change.In many fields,the trend extraction problem has practical significance.In recent years,the methods of signal processing have been widely concerned for the trend extraction.However,most of the traditional trend extraction algorithms based on signal processing methods are based on Fourier transform.It is well-known that,Fourier transform is limited to smooth and linear data processing.For processing non-stationary nonlinear signals,it is inevitable to destroy the original attributes of the data,and difficult to reveal its real physical significance.Empirical mode decomposition algorithm is a time-frequency analysis method,which can adapt to non-linear and non-stationary signal analysis according to the characteristics of the signal itself.Now,more and more researchers have introduced it into trend extraction.The core of the algorithm is to select which eigenmode functions to construct the signal trend.However,due to the existence of mode aliasing,signals of different scales are decomposed into the same inherent mode component,resulting in crosstalk between different modes,which makes the decomposition result lose its clear physical significance.Therefore,how to obtain meaningful eigen modal function is very important for trend extraction.In this paper,we review the decomposition principles and algorithm flow of ensemble empirical mode decomposition algorithm for solving modal aliasing,including analyzing two main problems affecting the reconstruction error and computational efficiency of ensemble empirical mode decomposition algorithm,namely how to determine the amplitude of white noise and how to determine the average number of sets required.White noise is added to eliminate or suppress the problem of mode aliasing.In the process of signal reconstruction,the influence of white noise must be offset by the average of a certain number of times.On one hand,adding small value noise can suppress the influence of mode aliasing and reduce the reconstruction error;on the other hand,adding large value white noise will increase the required average times of collection and reduce the computational efficiency.T solve the problem of modal aliasing phenomenon and adaptively selecting of the amplitude of added white noise amplitude and the number of ensemble averaging,a parameter optimization method for empirical mode decomposition is proposed in this thesis,which is based on ensemble empirical mode decomposition.The amplitude of white noise is determined by calculating the relative root mean square error between the original signal and the selected intrinsic mode components.Then,the parameter optimization method is implemented by limiting the range of the error values and under the constraints of ensemble averaging number and the amplitude of white noise.The experimental results show that the proposed algorithm can effectively extract the signal trend componentGrating ruler has attracted much attention as a precise positioning measuring device in the high-end equipment manufacturing industry of fine processing.How to further improve the measuring accuracy of grating ruler has been studied by many researchers.The proposed empirical mode decomposition with parameter optimization is used to analyze the error data of the grating ruler.It extracts the trend component of the error data to eliminate the inherent error of the error measurement data.Experimental results show that the proposed method can effectively improve the measuring accuracy of grating ruler.