Improved EEMD Denoising Method Based on Singular Value Decomposition for the Chaotic Signal

Abstract

Chaotic data analysis is important in many areas of science and engineering. However, the chaotic signals are inevitably contaminated by complicated noise in the collection process which greatly interferes with the analysis of chaos identification. The chaotic vibration is extremely nonlinear and has a broad range of frequencies; linear filtering methods are not effective for chaotic signal noise reduction. Then an improved ensemble empirical mode decomposition (EEMD) based on singular value decomposition (SVD) and Savitzky-Golay (SG) filtering method was proposed. Firstly, the noise energy of first level intrinsic mode function (IMF) was estimated by “3σ” criterion, and then SVD was used to extract the signal details from first IMF, and the singular value was selected to reconstruct the IMF according to noise energy of the first IMF. Secondly, the remaining IMFs are divided into high frequency and low frequency components based on consecutive mean square error (CMSE), and the useful signals of high frequency components and low frequency components are extracted based on SVD and SG filtering method, respectively. The superiority of the proposed method is demonstrated with simulated signal, two-degree-of-freedom chaotic vibration signals, and the experimental signals based on double potential well theory.