A New Singular Spectrum Decomposition Method Based on Cao Algorithm and Amplitude Aware Permutation Entropy

Abstract

Singular spectrum decomposition (SSD) is relatively affected by noise. The singular spectrum component (SSC) obtained in a strong noise environment not only contains a lot of noise, but also has over-decomposition phenomenon. One reason is that the selection of the SSD embedding dimension is subjective and cannot adapt well to signals with higher complexity. Another reason is that the iterative termination condition of the SSD is based on the normalized mean square error of the residual signal and the original signal. This will cause the SSD to produce a lot of pseudo components when SSD processes strong noisy signal. In order to enhance the decomposition performance of the SSD in strong noise environment, this paper starts from the selection of embedding dimension and the improvement of iteration termination conditions, and proposes an improved singular spectrum decomposition (ISSD) based on Cao algorithm and amplitude aware permutation entropy (AAPE). Firstly, the DC of the signal to be decomposed is taken out. Secondly, Cao algorithm is used to calculate the optimal embedding dimension of the signal to be decomposed, and then SSD is performed to obtain a SSC and a residual signal. Finally, the normalized AAPE value (NAAPE) of the SSC is calculated. If it is greater than the threshold, the residual signal at this time is considered to be a noise component, the decomposition is stopped, and the residual signal is output as the last SSC. Otherwise, the residual signal is used as the signal to be decomposed, and it continues to decompose. After the decomposition, the validity of the DC (Direct component) is determined by energy comparison. If the DC is a valid component, it will be output as the first SSC. Otherwise, the DC is discarded. The completeness of ISSD through theoretical analysis and equation derivation is proved. Its effectiveness is verified by analog signal, Lorenz signal and sunspot activity data. The comparative experiment of EMD, EEMD, VMD, SSD and ISSD is used to prove the advanced nature of ISSD. The simulation results show that ISSD has the ability to identify noise and can effectively avoid over-decomposition. At the same time, ISSD can accurately extract the DC contained in the original signal to avoid energy loss. In addition, ISSD can use Cao algorithm to select the appropriate embedding dimension to improve the quality of SSC. Finally, the rank sum test is used to prove the advanced nature of ISSD from a statistical point of view.