Trend Extraction Via Improved Hilbert-Huang Transform And Its Applications

Trend is usually defined as the smooth additive component containing information about the global change of time series.The identification and estimation of trends are of vital importance to many fields,such as econometrics,power systems,plant industries and biomedical sciences.Thus,extracting the trend is an important procedure of time series analysis.Nowadays many trend extraction methods have been proposed and applied in many fields,which include model based approaches,nonparametric trend prediction methods and signal processing methods.Among them,signal processing methods are the most promising approaches.However,the traditional signal processing based methods for trend extraction are basicly based on the Fourier analysis,which make the assumption that the signal is linear and stationary.So the traditional signal processing method for trend extraction would fails to extract the trend of the signal effectively since most of the signals in the real world are nonlinear and nonstationary.As the key part of the Hilbert Huang Transform(HHT)method,empirical mode decomposition(EMD)is an effective method for time-frequency analysis,which is a powerful tool for analyzing nonlinear and nonstationary signals and applied in many areas.Recently,many researchers has successful introduced the EMD into the trend extraction problem.The key problem for the EMD based trend extraction method is to select the candidate intrinsic mode functions(IMFs)for extracting the trend.However,due to the mode mixing,the decomposition results of the EMD would lose physical significance.In order to effectively extract the trend,the mode mixing problem must be avoided.In this thesis,traditional noise-assisted ensemble empirical mode decomposition methods are reviewed,which include ensemble empirical mode decomposition(EEMD),complementary ensemble empirical mode decomposition(CEEMD)and optimal ensemble empirical mode decomposition(OEEMD).To reduce the error of reconstruction,the decomposition via CEEMD uses a pair of positive and negative noises added to the signal,which is superior to the EEMD method.Both EEMD and CEEMD methods have achieved good results on fixing the mode mixing problem.Althought the above methods have achieved good performances,two problems still remain to be solved,which are high computational cost and the determination of two critical parameters(the amplitude of the added white noise and the number of ensemble trials).Essentially,in the EEMD,the aim of adding white noise is to homogenize the extrema distribution of the original signal for eliminating the mode mixing.Ideally,it seems that the smaller the noise amplitude can be the better.But if the noise amplitude is too small,it could not lead to enough change of extrema distribution that the EMD relies on.Hence the amplitude of the added white noise should not be too small.Under this condition,a few hundred of ensemble trials are necessary for eliminating the effect of residue noise,which will inevitably lead to high computational cost.In this thesis,an adaptive complementary ensemble empirical mode decomposition(ACEEMD)is proposed based on relative root-mean-square error that is employed for the selection of the proper amplitude of the added white noises,in which the IMFs with physical significance can be decomposed from the data.Then a novel Hilbert marginal spectrum(HMS)analysis scheme is proposed to select the candidate IMFs for trend extraction,which is based on the energy distribution of HMSs.The analysis results indicate that the proposed trend extraction method represents a sound improvement over the original EMD method,and has strong practicability.To further verify the effectiveness of the proposed method,two applications are presented,which include error compensation of the absolute optical encoder and T wave alternans detection.Absolute optical encoders have emerged as a preferable choice of accurate positioning measurement for high-end manufacturing.To further improve the measurement accuracy of the absolute optical encoder,a novel error compensation method is proposed based on the Hilbert Huang Transform(HHT).When the trend of the measurement error is extracted,the inherent error component can be eliminated from the measurement error.Experimental results indicate that the proposed compensation method extracts the underlying trend of the measurement error very well and improves the measurement accuracy of the absolute optical encoder.Recent studies have shown the repolarization alternans,also known as T-wave alternans(TWA),as a risk stratifier for sudden cardiac death.TWA has been considered as an indicator to detect anomalies in ventricular repolarization and ventricular arrhythmias.It consists of a beat-to-beat variation in amplitude,waveform,and duration of the ST–T complex.Most commonly,the variation is so small and subtle that visual assessment becomes impractical and unfeasible.In this thesis,the proposed trend extraction method is used to estimation ST–T complex from the noisy signal.Further,combine the proposed mehtod with the spectrum method to improve the detection performance.Experimental results indicate that the proposed method can effectively improve the detection performance for TWA as well as eliminate the noise.