A Novel Gaussian Window Approach for Empirical Mode Decomposition

2012 ◽  
Vol 457-458 ◽  
pp. 274-277
Author(s):  
Shuen De Wu ◽  
Chiu Wen Wu ◽  
Cha Lin Liu ◽  
Yan Hao Huang ◽  
Kung Yen Lee
Keyword(s):  
Numerical Analysis ◽  
Empirical Mode Decomposition ◽  
Averaging Method ◽  
Intrinsic Mode Functions ◽  
Gaussian Window ◽  
Mode Decomposition ◽  
The Mean ◽  
Algorithmic Construction ◽  
Window Approach ◽  
Mode Mixing

Empirical mode decomposition (EMD) is an algorithmic construction for decomposing multi-component signals into a series of intrinsic mode functions (IMFs). However, traditional EMD may encounter the difficulty of mode mixing when a signal contains intermittency. To solve the difficulty, a Gaussian window averaging method is proposed to construct the mean envelope of a given signal in each sifting process. The numerical analysis also demonstrates promising reliability with the proposed algorithm.

scholarly journals An Improved Empirical Mode Decomposition Based on Local Integral Mean and Its Application in Signal Processing

2021 ◽  
Vol 2021 ◽  
pp. 1-30
Author(s):  
Xiao-dong Niu ◽  
Li-rong Lu ◽  
Jian Wang ◽  
Xing-cheng Han ◽  
Xuan Li ◽  
...  
Keyword(s):  
Empirical Mode Decomposition ◽  
Real Data ◽  
Ensemble Empirical Mode Decomposition ◽  
Mean Value ◽  
Orthogonal Decomposition ◽  
Intrinsic Mode Functions ◽  
Improved Method ◽  
Mode Decomposition ◽  
The Mean ◽  
Mode Mixing

Empirical mode decomposition (EMD) is an effective method to deal with nonlinear nonstationary data, but the lack of orthogonal decomposition theory and mode-mixing are the main problems that limit the application of EMD. In order to solve these two problems, we propose an improved method of EMD. The most important part of this improved method is to change the mean value by envelopes of signal in EMD to the mean value by the definite integral, which enables the mean value to be mathematically expressed strictly. Firstly, we prove that the signal is orthogonally decomposed by the improved method. Secondly, the Monte Carlo method of white noise is used to explain that the improved method can effectively alleviate mode-mixing. In addition, the improved method is adaptive and does not need any input parameters, and the intrinsic mode functions (IMFs) generated from it is robust to sifting. We have carried out experiments on a series of artificial and real data, the results show that the improved method is the orthogonal decomposition method and can effectively alleviate mode-mixing, and it has better decomposition performance and physical meaning than EMD, ensemble EMD (EEMD), and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). In addition, the improved method is generally more time-consuming than EMD, but far less than EEMD and CEEMDAN.

scholarly journals The Measurement and Elimination of Mode Splitting: From the Perspective of the Partly Ensemble Empirical Mode Decomposition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Bin Liu ◽  
Peng Zheng ◽  
Qilin Dai ◽  
Zhongli Zhou
Keyword(s):  
Spectral Analysis ◽  
White Noise ◽  
Empirical Mode Decomposition ◽  
Ensemble Empirical Mode Decomposition ◽  
Permutation Entropy ◽  
Intrinsic Mode Functions ◽  
Mode Splitting ◽  
Mode Decomposition ◽  
Microseismic Signal ◽  
Mode Mixing

The problems of mode mixing, mode splitting, and pseudocomponents caused by intermittence or white noise signals during empirical mode decomposition (EMD) are difficult to resolve. The partly ensemble EMD (PEEMD) method is introduced first. The PEEMD method can eliminate mode mixing via the permutation entropy (PE) of the intrinsic mode functions (IMFs). Then, bilateral permutation entropy (BPE) of the IMFs is proposed as a means to detect and eliminate mode splitting by means of the reconstructed signals in the PEEMD. Moreover, known ingredient component signals are comparatively designed to verify that the PEEMD method can effectively detect and progressively address the problem of mode splitting to some degree and generate IMFs with better performance. The microseismic signal is applied to prove, by means of spectral analysis, that this method is effective.

scholarly journals A New Islanding Detection Technique using Ensemble Empirical Mode Decomposition

2020 ◽  
Vol 9 (3) ◽  
pp. 461-466
Keyword(s):  
Empirical Mode Decomposition ◽  
Distributed Generation ◽  
Gaussian White Noise ◽  
Ensemble Empirical Mode Decomposition ◽  
Islanding Detection ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Signal Processing Methods ◽  
Mixing Problem ◽  
Mode Mixing

Penetration of distributed generation (DG) is rapidly increasing but their main issue is islanding. Advanced signal processing methods needs a renewed focus in detecting islanding. The proposed scheme is based on Ensemble Empirical Mode Decomposition (EEMD) in which Gaussian white noise is added to original signal which solves the mode mixing problem of Empirical mode decomposition (EMD) and Hilbert transform is applied to obtained Intrinsic mode functions(IMF). The proposed method reliably and accurately detects disturbances at different events

Ensemble Noise-Reconstructed Empirical Mode Decomposition for Mechanical Fault Detection

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Jing Yuan ◽  
Zhengjia He ◽  
Jun Ni ◽  
Adam John Brzezinski ◽  
Yanyang Zi
Keyword(s):  
Fault Detection ◽  
Empirical Mode Decomposition ◽  
Measured Signal ◽  
Accelerometer Data ◽  
Intrinsic Mode Functions ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Mixing Problem ◽  
Emd Method ◽  
Mode Mixing

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

A fast online bandwidth empirical mode decomposition scheme for avoidance of the mode mixing problem

2017 ◽  
Vol 232 (20) ◽  
pp. 3652-3674 ◽  
Author(s):  
SH Momeni Massouleh ◽  
Seyed Ali Hosseini Kordkheili ◽  
H Mohammad Navazi
Keyword(s):  
Empirical Mode Decomposition ◽  
Low Frequency ◽  
Dominant Frequency ◽  
Auxiliary Function ◽  
Intrinsic Mode Functions ◽  
Online Data ◽  
Decomposition Scheme ◽  
Mode Decomposition ◽  
Mixing Problem ◽  
Mode Mixing

The main objective of this work is to propose a scheme to extract intrinsic mode functions of online data with an acceptable speed as well as accuracy. For this purpose, an individual block framework method is firstly employed to extract the intrinsic mode functions. In this method, buffers are selected such that they overlap with their neighbors to prevent the end effect errors with no need for the averaging process. And in order to avoid the mode mixing problem, a bandwidth empirical mode decomposition scheme is developed to effectively improve the results. Through this scheme, an auxiliary function made of both high- and low-frequency components corresponding to noise and dominant frequency is added to data for the strengthening of the components for the better extraction of intrinsic mode functions during sifting process. An index criterion as well as a threshold limit is also introduced to separate high- and low-frequency parts of data at desired frequency range. Advantages of the proposed scheme are assessed and comparisons with the available methods are presented. Solution of different types of examples and experimentally generated data for two faulty ball bearings reveals that the present easily implemented scheme achieves results with lower computational efforts and accuracy.

NOISE-MODULATED EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 02 (01) ◽  
pp. 25-37 ◽  
Author(s):  
PO-HSIANG TSUI ◽  
CHIEN-CHENG CHANG ◽  
NORDEN E. HUANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
The Core ◽  
Mode Decomposition ◽  
Threshold Amplitude ◽  
The Mean ◽  
Mixing Problem ◽  
Emd Method

The empirical mode decomposition (EMD) is the core of the Hilbert–Huang transform (HHT). In HHT, the EMD is responsible for decomposing a signal into intrinsic mode functions (IMFs) for calculating the instantaneous frequency and eventually the Hilbert spectrum. The EMD method as originally proposed, however, has an annoying mode mixing problem caused by the signal intermittency, making the physical interpretation of each IMF component unclear. To resolve this problem, the ensemble EMD (EEMD) was subsequently developed. Unlike the conventional EMD, the EEMD defines the true IMF components as the mean of an ensemble of trials, each consisting of the signal with added white noise of finite, not infinitesimal, amplitude. In this study, we further proposed an extension and alternative to EEMD designated as the noise-modulated EMD (NEMD). NEMD does not eliminate mode but intensify and amplify mixing by suppressing the small amplitude signal but the larger signals would be preserved without waveform deformation. Thus, NEMD may serve as a new adaptive threshold amplitude filtering. The principle, algorithm, simulations, and applications are presented in this paper. Some limitations and additional considerations of using the NEMD are also discussed.

A Novel Gaussian Window Approach for Empirical Mode Decomposition

2012 ◽  
Vol 457-458 ◽  
pp. 274-277
Author(s):  
Shuen De Wu ◽  
Chiu Wen Wu ◽  
Cha Lin Liu ◽  
Yan Hao Huang ◽  
Kung Yen Lee
Keyword(s):  
Empirical Mode Decomposition ◽  
Gaussian Window ◽  
Mode Decomposition ◽  
Window Approach

The use of ensemble empirical mode decomposition to improve bispectral analysis for fault detection in rotating machinery

2010 ◽  
Vol 224 (8) ◽  
pp. 1759-1769 ◽  
Author(s):  
Y Lei ◽  
M J Zuo ◽  
M Hoseini
Keyword(s):  
Empirical Mode Decomposition ◽  
Reconstruction Algorithm ◽  
Ensemble Empirical Mode Decomposition ◽  
Rotating Machinery ◽  
Intrinsic Mode Functions ◽  
Vibration Signals ◽  
Physical Experiments ◽  
Mode Decomposition ◽  
Mixing Problem ◽  
Mode Mixing

Empirical mode decomposition (EMD) has been widely applied to analyse signals for the detection of faults in rotating machinery. However, sometimes, it cannot reveal signal characteristics accurately because of the mode mixing problem. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate the mode mixing problem of EMD. With EEMD, components that are physically meaningful can be extracted from the signals. Bispectrum, a third-order statistic, helps identify phase coupling effects, which are useful for detecting faults in rotating machinery. Utilizing the advantages of EEMD and bispectrum, this article proposes a joint method for detecting such faults. First, original vibration signals collected from rotating machinery are decomposed by EEMD and a set of intrinsic mode functions (IMFs) is produced. Then, the IMFs are reconstructed into new signals using the weighted reconstruction algorithm developed in this article. Finally, the reconstructed signals are analysed via bispectrum to detect faults. The simulation experiments and the physical experiments of two gears with a chipped tooth and a cracked tooth, respectively, demonstrate that the proposed method can detect faults more clearly than can directly performing bispectrum on the original vibration signals.

Improved Vancouver Raman Algorithm Based on Empirical Mode Decomposition for Denoising Biological Samples

2019 ◽  
Vol 73 (12) ◽  
pp. 1436-1450 ◽  
Author(s):  
Fabiola León-Bejarano ◽  
Martin O. Méndez ◽  
Miguel G. Ramírez-Elías ◽  
Alfonso Alba
Keyword(s):  
Empirical Mode Decomposition ◽  
Raman Spectra ◽  
Biological Samples ◽  
Biological Material ◽  
Noise Levels ◽  
Synthetic Material ◽  
High Noise ◽  
Mode Decomposition ◽  
Mean Filter ◽  
The Mean

A novel method based on the Vancouver Raman algorithm (VRA) and empirical mode decomposition (EMD) for denoising Raman spectra of biological samples is presented. The VRA is one of the most used methods for denoising Raman spectroscopy and is composed of two main steps: signal filtering and polynomial fitting. However, the signal filtering step consists in a simple mean filter that could eliminate spectrum peaks with small intensities or merge relatively close spectrum peaks into one single peak. Thus, the result is often sensitive to the order of the mean filter, so the user must choose it carefully to obtain the expected result; this introduces subjectivity in the process. To overcome these disadvantages, we propose a new algorithm, namely the modified-VRA (mVRA) with the following improvements: (1) to replace the mean filter step by EMD as an adaptive parameter-free signal processing method; and (2) to automate the selection of polynomial degree. The denoising capabilities of VRA, EMD, and mVRA were compared in Raman spectra of artificial data based on Teflon material, synthetic material obtained from vitamin E and paracetamol, and biological material of human nails and mouse brain. The correlation coefficient (ρ) was used to compare the performance of the methods. For the artificial Raman spectra, the denoised signal obtained by mVRA ([Formula: see text]) outperforms VRA ([Formula: see text]) for moderate to high noise levels whereas mVRA outperformed EMD ([Formula: see text]) for high noise levels. On the other hand, when it comes to modeling the underlying fluorescence signal of the samples (i.e., the baseline trend), the proposed method mVRA showed consistent results ([Formula: see text]. For Raman spectra of synthetic material, good performance of the three methods ([Formula: see text] for VRA, [Formula: see text] for EMD, and [Formula: see text] for mVRA) was obtained. Finally, in the biological material, mVRA and VRA showed similar results ([Formula: see text] for VRA, [Formula: see text] for EMD, and [Formula: see text] for mVRA); however, mVRA retains valuable information corresponding to relevant Raman peaks with small amplitude. Thus, the application of EMD as a filter in the VRA method provides a good alternative for denoising biological Raman spectra, since the information of the Raman peaks is conserved and parameter tuning is not required. Simultaneously, EMD allows the baseline correction to be automated.

Ensemble Empirical Mode Decomposition and Sparsity Measurement as Tools Enhancing the Gear Diagnostic Capabilities of Time Synchronous Averaging

2017 ◽  
Vol 09 (02) ◽  
pp. 1750004 ◽  
Author(s):  
Pawel Rzeszucinski ◽  
Michal Juraszek ◽  
James R. Ottewill
Keyword(s):  
Empirical Mode Decomposition ◽  
Ensemble Empirical Mode Decomposition ◽  
Diagnostic Information ◽  
Optimal Parameters ◽  
Vibration Data ◽  
Mode Decomposition ◽  
Ultrasound Signal ◽  
Diagnostic Capabilities ◽  
Mixing Problem ◽  
Mode Mixing

The paper introduces the concept of exploring the potential of Ensemble Empirical Mode Decomposition (EEMD) and Sparsity Measurement (SM) in enhancing the diagnostic information contained in the Time Synchronous Averaging (TSA) method used in the field of gearbox diagnostics. EEMD was created as a natural improvement of the Empirical Mode Decomposition which suffered from a so-called mode mixing problem. SM is heavily used in the field of ultrasound signal processing as a tool for assessing the degree of sparsity of a signal. A novel process of automatically finding the optimal parameters of EEMD is proposed by incorporating a Form Factor parameter, known from the field of electrical engineering. All these elements are combined and applied on a set of vibration data generated on a 2-stage gearbox under healthy and faulty conditions. The results suggest that combining these methods may increase the robustness of the condition monitoring routine, when compared to the standard TSA used alone.

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