Improved Empirical Mode Decomposition Method Research Articles

Improved empirical mode decomposition method based on amplitude-frequency characteristic of vortex signals.

The vortex flowmeter occupies a vital position in flow measurement with its unique advantages. It is essentially a fluid vibration instrument, and its measurement process is susceptible to interference, which seriously affects measurement accuracy. In particular, at low flow rates, it is an urgent problem to extract vortex signals from the complex noise. Among many signal processing methods, Empirical Mode Decomposition (EMD) is a time-frequency analysis method suitable for nonlinear, non-stationary signals. EMD can adaptively decompose noisy signals into noise and useful signal components arranged from high frequency to low frequency. For the above problems, an innovative, improved EMD method is proposed in this paper. The digital filter is designed according to the amplitude-frequency characteristic of vortex signals. After filtering, the vortex signal is adjusted to a fixed value, and high-frequency noise is filtered. According to the consistency of the filtered signal's amplitude, we design a decomposition stop criterion for EMD to process the output signal of the vortex sensor. This method not only maintains the characteristic of adaptive decomposition in EMD but also completes the automatic extraction of the vortex signal under complex noise. It provides a new comprehensive method for realizing high-precision and anti-interference vortex flowmeters.

An Improved Empirical Mode Decomposition Algorithm Based on Frequency Rotation Factor and Vector Operation in Complex Plane

In order to overcome the phenomenon of aliasing mode in empirical mode decomposition (EMD), an improved EMD method based on frequency rotation factor and vector operation is proposed. First, fast Fourier transform (FFT) is used to determine the frequency components contained in the original signal. Second, Hilbert transform is applied to transform the real plane analysis into complex plane analysis, then the amplitude frequency product of the signal is satisfied with adaptive full decomposed by frequency inversion and vector operation. Third, the traditional EMD algorithm is used to extract the lowest frequency mode in the complex frequency domain while it is the highest frequency in the time domain (because the frequency inversion operation is performed in the previous step), and finally the original mode of the real plane is restored by forward frequency rotation and inverse vector operation, so as to complete all modal decomposition through this loop algorithm. The simulation results show that the method can effectively separate the aliasing problem and extract the useful signals with low time cost.

Electrocardiogram signal reconstruction based on mode component identification by heartbeat physical feature in improved empirical mode decomposition domain

Electrocardiogram (ECG) diagnosis is based on the waveform, duration and amplitude of characteristic wave, which are required to have a high accuracy for ECG signal reconstruction. As an effective nonlinear signal processing method, empirical mode decomposition (EMD) has been widely used for diagnosing and reconstructing the ECG signal, but there are two problems arising here. One is the mode mixing, and the other is that the mode components used in reconstruction are identified by experience. Therefore, the method of reconstruction is not adaptive and universal, and reconstructed ECG signal loses accuracy. Firstly, we propose an improved EMD method, which is called integral mean mode decomposition (IMMD). The analysis of 5000 samples of Gaussian white noise shows that IMMD has better multi-resolution analysis ability than EMD, and it can effectively alleviate mode mixing consequently. Secondly, based on the inherent physical characteristics of ECG signal, cardiac cycle or heart rate (HR), it has practical physical significance to identify the mode components used in ECG signal reconstruction. The cardiac cycle feature acts as the intrinsic mode function (IMF) component through two modes. 1) For the low-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as the amplitude modulation. The envelope of the IMF component has the characteristics of the cardiac cycle, and the frequency corresponding to the maximum amplitude in the spectrum of the envelope is equal to HR. 2) For the high-order IMF that belongs to the ECG signal, the cardiac cycle feature acts as frequency modulation. Those IMF components have the harmonic characteristics of periodic heartbeats, and the maximum amplitude in the spectrum corresponds to an integral multiple of HR (usually 1－3 times). The noise attributed to IMF component cannot show the above two cardiac cycle characteristics. Thus the proposed method is adaptive and universal. The 47 ECG signals with baseline drift and muscle artifact noise are tested. The results show that the proposed method is more effective than the variational mode decomposition (VMD), Haar wavelet with soft threshold, ensemble empirical mode decomposition (EEMD) and EMD. Among the 47 correlation coefficients between reconstructed and original ECG signals, the proposed method has 31 better than VMD, 33 better than Haar wavelet, 42 better than EEMD and 45 better than EMD. The mean of 47 correlation coefficients from the proposed method is 0.8904, and the variance is 0.0071, which shows that the proposed method has good performance and stability.

Feature extraction method of cavitation acoustic emission signals of hydraulic turbines based on improved EMD

The cavitation of hydraulic turbine is one of the most difficult problems in the world. Empirical mode decomposition (EMD) is capable of decomposing the cavitation signals in an adaptive way. Because the traditional EMD has a special end effect, an improved EMD method was erected and applied to extract the features of cavitation acoustic emission (AE) signals of hydraulic turbines in this paper. Comparison of the mirror extension method and the average extremum extension method was carried out on the base of their ability to reduce the end effect, and the better mirror extension was adopted to deal with the cavitation AE signals. The measured AE signals generating from the cavitation were processed and the features were extracted by the improved EMD. Spectrogram can be drawn from cavitation inception to cavitation intensifies. In combination with the energy ratio of the intrinsic mode function (IMF) and the cavitation coefficient, it is found that the absolute energy ratio varies sharply under the cavitation conditions. The results show clearly that the improved EMD method can solve the defects of the end effect and is effective in the feature extraction of the cavitation acoustic emission signals of hydraulic turbines. The findings can be used as a technical basis for the identification of the cavitation conditions of Francis turbines.

An improved empirical mode decomposition method using second generation wavelets interpolation

Empirical mode decomposition (EMD) may generate undesirable intrinsic mode functions (IMFs) under low sampling rate, which can significantly affect the results of decomposition. In this paper, an improved EMD method using second generation wavelets interpolation is presented which can eliminate undesirable IMFs and reduce the scale mixing effectively under low sampling rate. Firstly, the original signal under low sampling rate is reconstructed by inverse process of second generation wavelets lifting algorithm. Secondly, the location algorithm of extrema using second generation wavelets is given to obtain the accurate position of extrema. Finally, five examples are demonstrated to justify the effectiveness. Numerical simulation and experimental results are attained to show the effectiveness of the proposed method in eliminating undesirable IMFs and reducing the scale mixing, thereby making the proposed improved EMD a promising method for improving the performance of EMD under low sampling rate.

An improved EMD method with modified envelope algorithm based on C2 piecewise rational cubic spline interpolation for EMI signal decomposition

In this paper, we propose an improved empirical mode decomposition (EMD) method, termed IEMD, with modified envelope algorithm based on C2 piecewise rational and C2 monotone piecewise rational cubic spline interpolations, for the decomposition of nonlinear and non-stationary EMI signals. In the sifting procedure, we first construct the upper and lower envelopes employing C2 piecewise rational cubic spline interpolation (PRCSI) technique. Considering the existence of undershoots, we further modify the original envelopes iteratively with C2 monotone piecewise rational cubic spline interpolation (MPRCSI) technique, for the elimination of undershoots as accurate as possible. Experiments on synthetic and real signals, compared with three improved versions of EMD, three for ensemble EMD (EEMD) and TL-SVD, demonstrate that the proposed method is more valid and flexible when applied to the decomposition of synthesis harmonic signals and real EEG signals, signifying it also can be applied to the decomposition of EMI signals which are known to be extremely nonlinear and non-stationary.

An improved empirical mode decomposition method based on the cubic trigonometric B-spline interpolation algorithm

Empirical mode decomposition (EMD) is a new method presented recently for analyzing nonlinear and non-stationary signals. Its basic idea is to decompose the signal into a series of complete orthogonal intrinsic mode functions (IMFs) based on the local characteristics of the signal in time domain. The key step of EMD is to use the cubic spline interpolation to connect the maximum and minimum values of the signals into upper and lower envelopes respectively, and then calculate the mean values of upper and lower envelopes. Based on the cubic trigonometric B-spline interpolation algorithm, a new improved method for EMD is proposed named CTB-EMD in this paper. In this method, the interpolation curve is more flexible because of the adjustability of shape of the cubic trigonometric B-splines curve. Thus, the overshoot and undershoot problems in the cubic spline interpolation curve can be avoided, and then the decomposition of the signal is more accurate and effect. Through numerical experiments, we compare the effect of this method with other methods on decomposing simulation signals and real signals. Experimental results show that this method can decompose signals more effectively and accurately.

An improved EMD method for modal identification and a combined static-dynamic method for damage detection

Empirical mode decomposition (EMD) is a highly adaptable signal processing method. However, the EMD approach has certain drawbacks, including distortions from end effects and mode mixing. In the present study, these two problems are addressed using an end extension method based on the support vector regression machine (SVRM) and a modal decomposition method based on the characteristics of the Hilbert transform. The algorithm includes two steps: using the SVRM, the time series data are extended at both endpoints to reduce the end effects, and then, a modified EMD method using the characteristics of the Hilbert transform is performed on the resulting signal to reduce mode mixing. A new combined static-dynamic method for identifying structural damage is presented. This method combines the static and dynamic information in an equilibrium equation that can be solved using the Moore-Penrose generalized matrix inverse. The combination method uses the differences in displacements of the structure with and without damage and variations in the modal force vector. Tests on a four-story, steel-frame structure were conducted to obtain static and dynamic responses of the structure. The modal parameters are identified using data from the dynamic tests and improved EMD method. The new method is shown to be more accurate and effective than the traditional EMD method. Through tests with a shear-type test frame, the higher performance of the proposed static-dynamic damage detection approach, which can detect both single and multiple damage locations and the degree of the damage, is demonstrated. For structures with multiple damage, the combined approach is more effective than either the static or dynamic method. The proposed EMD method and static-dynamic damage detection method offer improved modal identification and damage detection, respectively, in structures.

An improved EMD method based on the multi-objective optimization and its application to fault feature extraction of rolling bearing

An improved Empirical Mode Decomposition (EMD) method based on the multi-objective optimization is proposed in this paper and is applied to extract the fault feature of rolling bearing with inner and outer race fault. Firstly, a new rational spline interpolation which has a shape controlling parameter is introduced based on cubic spline interpolation. Secondly, the selection criterion concluding time domain objective and frequency objective are considered simultaneously rather than separately. Then, the Particle Swarm Optimization (PSO) is used to find out the optimal IMF and determine the optimal shape controlling parameter. The procedure of the improved EMD based on multi-objective optimization (MO-EMD) is described in this paper. The effectiveness of MO-EMD is validated by the simulation signal and the robustness of MO-EMD to noise is also investigated. At last, the MO-EMD is employed to process the vibration signals of rolling bearing with fault. By comparison with original EMD, EEMD and improved CEEMDAN, it can be found that the MO-EMD has better decomposition capability and can restrain the mode mixing apparently. Combined with envelope spectrum analysis, more fault feature information can be extracted by MO-EMD.

An efficient method for analysis of EMG signals using improved empirical mode decomposition

In this paper, a simple technique with improved empirical mode decomposition (IEMD) in conjunction with four different features is used for the analysis of amyotrophic lateral sclerosis (ALS) and normal EMG signals. EMG signals consist of noise from various sources, such as electronic instruments, moving artifacts and electrical instruments. The empirical mode decomposition (EMD) method followed by median filter (MF) has been employed to remove the impulsive noise from intrinsic mode function (IMF) components generated through EMD. The filtered IMF components are summed together to generate a new signal. EMD process is further applied to new EMG signal to generate improved IMFs called as improved EMD method. In the IEMD algorithm for the first time, a new technique is proposed to choose the window size of median filter. For this, the features namely amplitude modulation bandwidth (BAM), frequency modulation bandwidth (BFM), spectral moment of power spectral density (SMPSD), and first derivative of instantaneous frequency (MFDIF) extracted from the improved IMFs are used to discriminate between ALS and normal EMG signals. Finally, it is observed that IEMD method increases the discrimination ability of these features as compared to the EMD method and the adaptively fast ensemble empirical mode decomposition (AFEEMD) method.

Modelling the volatility of the tanker freight market based on improved empirical mode decomposition

ABSTRACTIn this article, a method based on empirical mode decomposition (EMD) and BEKK–Multivariate GARCH (MVGARCH) is developed to analyse the volatility of the tanker freight market. First, the initial time series of tanker freight rates is decomposed into several independent intrinsic mode functions (IMFs). Next, the IMFs are composed as three components by an improved EMD: the long-term trend time series that represents the benchmark freight rates of the tanker freight market, the high-frequency time series that reflects the short-term supply–demand relation and the low-frequency time series caused by extreme events. Based on the results of EMD, the volatility spillover effects between the freight rates of Aframax, Suezmax and Very Large Crude Carrier (VLCC) markets are tested by the BEKK–MVGARCH model. The results indicate that there are volatility spillover effects between the reconstructed components, although the volatility spillover effects between the original freight series are not significant. The improved EMD method contributes to the retention of the economic characteristics of the original time series, thereby providing a vital approach for tanker freight market analysis. Furthermore, the potential volatility spillover among different sub-markets can be investigated through the integration of EMD and the BEKK–MVGARCH.

Railway Wheel Flat Detection Based on Improved Empirical Mode Decomposition

This study explores the capacity of the improved empirical mode decomposition (EMD) in railway wheel flat detection. Aiming at the mode mixing problem of EMD, an EMD energy conservation theory and an intrinsic mode function (IMF) superposition theory are presented and derived, respectively. Based on the above two theories, an improved EMD method is further proposed. The advantage of the improved EMD is evaluated by a simulated vibration signal. Then this method is applied to study the axle box vibration response caused by wheel flats, considering the influence of both track irregularity and vehicle running speed on diagnosis results. Finally, the effectiveness of the proposed method is verified by a test rig experiment. Research results demonstrate that the improved EMD can inhibit mode mixing phenomenon and extract the wheel fault characteristic effectively.

Output-Only Modal Analysis Based on Improved Empirical Mode Decomposition Method

The output-only modal analysis for bridge structures based on improved empirical mode decomposition (EMD) is investigated in this study. First, a bandwidth restricted EMD is proposed for decomposing nonstationary output measurements with close frequency components. The advantage of bandwidth restricted EMD to standard EMD is illustrated by a numerical simulation. Next, the modal parameters are extracted from intrinsic mode function obtained from the improved EMD by both random decrement technique and stochastic subspace identification. Finally, output-only modal analysis of a railway bridge is presented. The study demonstrates the mode mixing issues of standard EMD can be restrained by introducing bandwidth restricted signal. Further, with the improved EMD method, band-pass filter is no longer needed for separating the closely spaced frequency components. The modal parameters extracted based on the improved EMD method show good agreement with those extracted by conventional modal identification algorithms.

An Improved EMD Method for Time–Frequency Feature Extraction of Telemetry Vibration Signal Based on Multi-Scale Median Filtering

We hereby propose an Empirical Mode Decomposition (EMD) method improved with a multi-scale median filtering for extraction of the time---frequency feature of telemetry vibration signals under interference from impulse noise. The signal is decomposed into a series of intrinsic mode functions (IMF) by EMD roughly. Median filtering is then performed on each IMF with filter window length varying with the IMF's frequency, respectively. This maneuver will allow effective impulse noise suppression with minimal loss of signal integrity. A new signal can then be reconstructed by adding up each component after the median filtering and treated with a repeat EMD to obtain new IMFs as a final result. This method overcomes the filtering window length selection problem in the median filtering, which can obtain better time---frequency feature extraction performance under the impulse noise interference condition. Data processing results from both a simulation signal and a telemetry vibration signal of a test showed the effectiveness of this method.

Signature Analysis Based on Improved EMD with High-order Spline Interpolation

Empirical mode decomposition (EMD) is proved to be an effective tool for the nonlinear and non-stationary signals.  Many researchers have studied the application of EMD in a variety of fields. But few in-depth studies are related to the improvement of EMD. A new signal analysis approach based on improved EMD method is introduced in this paper. Firstly, the basic principle of EMD is introduced. Then the influence of spline interpolation’s EC to the EMD is investigated. In addition, the EMD based on high-order spline interpolation is used to improve the precision of the algorithm. Furthermore, the fast EMD is developed in order to improve the computation efficiency and precision. From what has been discussed above, we may safely draw the conclusion :(a) The EMD algorithm based on high-order spline interpolation can improve the precision remarkably while the calculation time is increased. (b) As the order of spline interpolation increasing, the precision of algorithm is not proportionable. The precision will not be improved when the order is up to certain order.

Signal Extraction Based on an Improved EMD Method

The main purpose of this paper is to propose an improved empirical mode decomposition (EMD) approach based on principal component analysis (PCA). EMD is a time-frequency analytical method used to deal with non-linear and non-stable signals. But it generally fails to separate IMFs from primordial signal consisting of several adjacent frequencies,especially when noise is strong.In this papar the PCA is introduced to solve this problem.First,PCA is used to pro-process sample signal to get principal components. Then several signals are reconstructed by principal components.Reconstructing signals can separate adjacent frequencies and depress noise.With the EMD method again,right characteristic information is obtained from intrinsic mode functions (IMFs). Simulated signal is analyzed by the proposed method, as shown by example. Compared to the EMD method, this improved method is proved to be superior to the traditional EMD method in extracting the characteristics of signal,which consisting adjacent frequencies and interfered by strong noise.

New Algorithm to Identify Inrush Current Based on Improved EMD

Empirical mode decomposition (EMD), which is the core mechanic of the Hilbert-Huang transform(HHT), is a local, fully data driven and self-adaptive analysis approach. It is a powerful tool for analyzing multi-component signals. Aiming at the reduction of scale mixing and artificial frequency components, an improved scheme was proposed for analysis and reconstruction of nonstationary and multicomponent signals. The improved EMD method uses the wavelet analysis method and normalized correlation coefficient to deal with the problems. Because the inrush current is a peaked wave with nonstationary component, a new algorithm based on improved EMD is presented for fast discrimination between inrush current and fault current of power transformers. Theoretical analysis and dynamic simulation results show that the method is effective and reliable under various fault conditions and simple to be applied.

An Improved EMD Method and its Application in Nonstationary Signals Analysis

Empirical mode decomposition (EMD) method based on HHT has exhibited unique advantages such as adaptability and highly efficiency in many nonlinear, nonstationary signals processing applications. It breaks the uncertainty principle limit, but the traditional EMD still has its deficiencies. In this article, we construct a new wavelet which has excellent decomposing-frequency performance and energy concentration, and then an improved EMD method based on this wavelet is presented. Results of numerical simulation show the validity and efficiency of the method proposed in paper are better than traditional one. Furthermore, some foreseeable trends of time-frequency distribution technologies are described. The systems in reality, strictly speaking, tend to non-linear, so most practical signals are non-stationary random signals. Nonlinear, nonstationary signals analysis is a very significant and difficult problem in almost all technical fields such as automation, communication, aerospace- engineering, biomedicine, structural fault diagnosis and so on. Owed to the rapid development of large scale integrated circuit technology and artificial intelligence, the exploration of signal processing theories have got a sharply impetus. A series of new modern signal processing theories and methods have appeared to meet the need of time-frequency joint analysis of nonlinear, non-Gaussian and non-stationary signals, including discrete short-time Fourier transform, wavelet transform, Hilbert-Huang transform and so on. Time-frequency joint analysis can observe the evolution of the signal in the time domain and the frequency domain simultaneously, provide local time-frequency characteristics of the signal.

Sifting process of EMD and its application in rolling element bearing fault diagnosis

Among the vibration-based fault diagnosis methods for rolling element bearing, the shock pulse method (SPM) combined with the demodulation method is a useful quantitative technique for estimating bearing running state. However, direct demodulation often misestimates the shock value of characteristic defect frequency. To overcome this disadvantage, the vibration signal should be decomposed before demodulation. Empirical mode decomposition (EMD) can be an alternative for preprocess bearing fault signals. However, the trouble with this method’s application is that it is time-consuming. Therefore, a novel method that can improve the sifting process’s efficiency is proposed, in which only one time of cubic spline fitting is required in each sifting process. As a consequence, the time for EMD analysis can be evidently shortened and the decomposition results simultaneously maintained at a high precision. Simulations and experiments verify that the improved EMD method, combined with SPM and demodulation analysis, is efficient and accurate and can be effectively applied in engineering practice.

Signal feature extraction based on an improved EMD method

Empirical mode decomposition (EMD) is a powerful tool for analyzing composite, nonlinear and non-stationary signals. Intrinsic mode functions (IMFs) obtained by EMD are band-limited, which can represent the features of signal and reserve the local information. Because of lacking theoretical foundation, EMD has many problems in scale mixing, stop criterion, etc. In this paper, we use an improved EMD method for signal feature extraction. Optimal envelopes mean is obtained by an inverse EMD filter scheme in the improved method. A new sifting stop criterion is proposed to guarantee the orthogonality of the sifting results. And finally, two different methods are utilized for performance evaluation of the decomposition results. Numerical simulation and experimental result demonstrate the validity of the improved method.