Studies On Ensemble Empirical Mode Decomposition With Complementary Adaptive Noises

Hilbert-Huang transform (HHT) is a new time-frequency analysis method which was proposed by Norden E. Huang in 1998. This algorithm has been proved to be a powerful approach to analyze non-linear and non-stationary signals. Thus, it has been widely adopted in many fields and valuable to be further studied. Hilbert-Huang transform mainly consists of two parts:the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). The EMD, the key part of HHT, can adaptively decompose a signal into a series of intrinsic mode functions (IMFs) according to the characteristics of the signal. However, the EMD suffers from the mode-mixing problem that can makes the decomposition results lose physical significance when some fast intermittent signals ride on a slow-oscillating wave.This thesis studies the fundamental principles of some traditional noise-assisted empirical mode decomposition methods, which are ensemble empirical mode decomposition (EEMD), complementary ensemble empirical mode decomposition (CEEMD) and ensemble empirical mode decomposition with adaptive noise (EEMDAN). The EEMDAN method proposed by Torres M E et al. reduces the reconstruction errors and the number of sifting iterations, and achieves good IMFs. There are two improvements in the EEMDAN. First, this algorithm adds the IMFs of the noises decomposed by the EMD instead of adding standard white noises directly to the signal in the process of decomposition. Second, this algorithm calculates the ensemble mean immediately when the previous IMF is shifted before the next one. However, there still exists the residual noise in each intrinsic mode function in the EEMDAN.Although these traditional algorithms can more or less suppress the mode mixing problem, there exist some other inherent problems, such as lack of rigorous mathematical theories. To solve these problems, this thesis attempts to mathematically analyze the reconstruction errors and deduce the formulae of the residual noises step by step.In order to suppress the residual noises in IMFs obtained by the EEMDAN especially when the ensemble size is not large enough, this thesis proposes an improved algorithm by adding pairs of positive and negative noises, which is termed as ensemble empirical mode decomposition with complementary adaptive noise (EEMDCAN). The experimental results indicate that the proposed method can obviously reduce the residual noise in each intrinsic mode function compared to the EEMDAN.In addition, this thesis employs the EEMDCAN in the fields of electrocardiogram (ECG) signal processing. To solve the problem of the ECG baseline wander that greatly affects the normal medical diagnosis, a new ECG baseline wander correction method is proposed based on the EEMDCAN. This improved method decomposes the noised ECG signal by the EEMDCAN. Then, the baseline wander signal is adaptively selected according to zero-crossing rates of IMFs. The experimental results from MIT-BIH Normal Sinus Rhythm Database indicate that the proposed method can remove the baseline wander signal from the ECG signal effectively.