A CRITERION FOR SELECTING RELEVANT INTRINSIC MODE FUNCTIONS IN EMPIRICAL MODE DECOMPOSITION

2010 ◽  
Vol 02 (01) ◽  
pp. 1-24 ◽  
Author(s):  
ALBERT AYENU-PRAH ◽  
NII ATTOH-OKINE
Keyword(s):  
Empirical Mode Decomposition ◽  
Numerical Experiments ◽  
Numerical Procedure ◽  
Basis Functions ◽  
Natural Phenomena ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Numerical Errors ◽  
Mode Decomposition ◽  
Study Results

Information extraction from time series has traditionally been done with Fourier analysis, which use stationary sines and cosines as basis functions. However, data that come from most natural phenomena are mostly nonstationary. A totally adaptive alternative method has been developed called the Hilbert–Huang transform (HHT), which involves generating basis functions called the intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD). The EMD is a numerical procedure that is prone to numerical errors that may persist in the decomposition as extra IMFs. In this study, results of numerical experiments are presented, which would establish a stringent threshold by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors. The threshold is dependent on the correlation coefficient between the IMFs and the original signal. Finally, the threshold is applied to IMFs of earthquake signals from five accelerometers located in a building.

scholarly journals Texture Feature Extraction Method for Ground Nephogram Based on Hilbert Spectrum of Bidimensional Empirical Mode Decomposition

2014 ◽  
Vol 31 (9) ◽  
pp. 1982-1994 ◽  
Author(s):  
Xiaoying Chen ◽  
Aiguo Song ◽  
Jianqing Li ◽  
Yimin Zhu ◽  
Xuejin Sun ◽  
...  
Keyword(s):  
Empirical Mode Decomposition ◽  
Recognition Rate ◽  
Texture Feature ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Feature Extraction Method ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Marginal Spectrum ◽  
Bidimensional Empirical Mode Decomposition

Abstract It is important to recognize the type of cloud for automatic observation by ground nephoscope. Although cloud shapes are protean, cloud textures are relatively stable and contain rich information. In this paper, a novel method is presented to extract the nephogram feature from the Hilbert spectrum of cloud images using bidimensional empirical mode decomposition (BEMD). Cloud images are first decomposed into several intrinsic mode functions (IMFs) of textural features through BEMD. The IMFs are converted from two- to one-dimensional format, and then the Hilbert–Huang transform is performed to obtain the Hilbert spectrum and the Hilbert marginal spectrum. It is shown that the Hilbert spectrum and the Hilbert marginal spectrum of different types of cloud textural images can be divided into three different frequency bands. A recognition rate of 87.5%–96.97% is achieved through random cloud image testing using this algorithm, indicating the efficiency of the proposed method for cloud nephogram.

WEIGHTED SLIDING EMPIRICAL MODE DECOMPOSITION

2011 ◽  
Vol 03 (04) ◽  
pp. 509-526 ◽  
Author(s):  
R. FALTERMEIER ◽  
A. ZEILER ◽  
A. M. TOMÉ ◽  
A. BRAWANSKI ◽  
E. W. LANG
Keyword(s):  
Time Series ◽  
Empirical Mode Decomposition ◽  
Sampling Rate ◽  
Computational Effort ◽  
Intrinsic Mode Functions ◽  
Weighted Version ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Reconstruction Quality ◽  
Spectral Transform

The analysis of nonlinear and nonstationary time series is still a challenge, as most classical time series analysis techniques are restricted to data that is, at least, stationary. Empirical mode decomposition (EMD) in combination with a Hilbert spectral transform, together called Hilbert-Huang transform (HHT), alleviates this problem in a purely data-driven manner. EMD adaptively and locally decomposes such time series into a sum of oscillatory modes, called Intrinsic mode functions (IMF) and a nonstationary component called residuum. In this contribution, we propose an EMD-based method, called Sliding empirical mode decomposition (SEMD), which, with a reasonable computational effort, extends the application area of EMD to a true on-line analysis of time series comprising a huge amount of data if recorded with a high sampling rate. Using nonlinear and nonstationary toy data, we demonstrate the good performance of the proposed algorithm. We also show that the new method extracts component signals that fulfill all criteria of an IMF very well and that it exhibits excellent reconstruction quality. The method itself will be refined further by a weighted version, called weighted sliding empirical mode decomposition (wSEMD), which reduces the computational effort even more while preserving the reconstruction quality.

Gearbox Fault Detection Using Empirical Mode Decomposition

2004 ◽  
Author(s):  
Xianfeng Fan ◽  
Ming J. Zuo
Keyword(s):  
Fault Detection ◽  
Empirical Mode Decomposition ◽  
Vibration Signal ◽  
Original Data ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Stationary Vibration ◽  
Non Stationary Signal ◽  
Envelope Spectrum

Local faults in a gearbox cause impacts and the collected vibration signal is often non-stationary. Identification of impulses within the non-stationary vibration signal is key to fault detection. Recently, the technique of Empirical Mode Decomposition (EMD) was proposed as a new tool for analysis of non-stationary signal. EMD is a time series analysis method that extracts a custom set of bases that reflects the characteristic response of a system. The Intrinsic Mode Functions (IMFs) within the original data can be obtained through EMD. We expect that the change in the amplitude of the special IMF’s envelope spectrum will become larger when fault impulses are present. Based on this idea, we propose a new fault detection method that combines EMD with Hilbert transform. The proposed method is compared with both the Hilbert-Huang transform and the wavelet transform using simulated signal and real signal collected from a gearbox. The results obtained show that the proposed method is effective in capturing the hidden fault impulses.

Empirical Mode Decomposition and Robust Pitch Detection Based on Recurrence Analysis

2013 ◽  
Vol 303-306 ◽  
pp. 1035-1038
Author(s):  
Jing Fang Wang
Keyword(s):  
Empirical Mode Decomposition ◽  
Pitch Detection ◽  
Intrinsic Mode Functions ◽  
Noisy Environment ◽  
Method Performance ◽  
Recurrence Analysis ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Band Filter ◽  
Better Than

A new pitch detection method is designed by the recurrence analysis in this paper, which is combined of Empirical Mode Decomposition (EMD) and Elliptic Filter (EF). The Empirical Mode Decomposition (EMD) of Hilbert-Huang Transform (HHT) are utilized tosolve the problem, and a noisy voice is first filtered on the elliptic band filter. The two Intrinsic Mode Functions (IMF) are synthesized by EMD with maximum correlation of voice, and then the pitch be easily divided. The results show that the new method performance is better than the conventional autocorrelation algorithm and cepstrum method, especially in the part that the surd and the sonant are not evident, and get a high robustness in noisy environment.

SIMULATION OF EARTHQUAKE RECORDS BY MEANS OF EMPIRICAL MODE DECOMPOSITION AND HILBERT SPECTRAL ANALYSIS

2014 ◽  
Vol 08 (01) ◽  
pp. 1450002 ◽  
Author(s):  
ABDOLLAH BAGHERI ◽  
AMIR A. FATEMI ◽  
GHOLAMREZA GHODRATI AMIRI
Keyword(s):  
Spectral Analysis ◽  
Empirical Mode Decomposition ◽  
Time History ◽  
Response Spectra ◽  
Frequency Function ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Earthquake Records ◽  
Mode Decomposition ◽  
Time Histories

One of the most important problems in the design of earthquake resistance structures at sites with no strong ground motion data is the generation and simulation of earthquake records. In this paper, an effective method based on Hilbert–Huang transform for the simulation of earthquake time histories is presented. The Hilbert–Huang transform consists of the empirical mode decomposition and Hilbert spectral analysis. Earthquake time histories decompose via empirical mode decomposition to obtain the intrinsic mode functions of earthquake time history. Any of intrinsic mode functions is simulated based on the proposed method for simulation. The ground frequency function of the presented model is estimated using Hilbert spectral analysis for the simulation of earthquake accelerograms. The proposed method has been applied to three earthquake records to demonstrate the efficiency and reliability of the approach. The obtained results of simulating method by comparison between pseudo-acceleration and pseudo-velocity response spectra of actual and the average of simulated time histories for these three earthquakes reveal that the simulated earthquake time histories well preserve the significant properties and the nonstationary characteristics of the actual earthquake records. The results indicated that there is a good accord between the response spectra of simulated and genuine time histories.

Feature Extraction of the Crack AE Signal Using HHT Transform

2013 ◽  
Vol 340 ◽  
pp. 441-444
Author(s):  
K.F. He ◽  
Z.J. Zhang ◽  
X.J. Li
Keyword(s):  
Acoustic Emission ◽  
Empirical Mode Decomposition ◽  
Crack Depth ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Mode Function ◽  
Mode Decomposition ◽  
Marginal Spectrum ◽  
Ae Signal

The use of Hilbert-Huang transform (Hilbert-Huang transform, HHT) on crack AE signal study, through empirical mode decomposition (empirical mode decomposition, EMD) AE signal is decompose into a number of intrinsic mode functions (Intrinsic mode Function, IMF), Hilbert spectrum and Hilbert marginal spectrum are calculated. The results show that crack depth structure bearing of acoustic emission are detected accurately by the number of acoustic emission events, time and crack the degree from Hilbert spectrum and Hilbert marginal spectrum.

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 New Spectral Representation of Earthquake Recordings Using an Improved Hilbert-Huang Transform

2011 ◽  
Vol 255-260 ◽  
pp. 1671-1675
Author(s):  
Tian Li Huang ◽  
Wei Xin Ren ◽  
Meng Lin Lou
Keyword(s):  
Empirical Mode Decomposition ◽  
Spectral Representation ◽  
Low Frequency ◽  
Accurate Information ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Marginal Spectrum

A new spectral representation method of earthquake recordings using an improved Hilbert-Huang transform (HHT) is proposed in the paper. Firstly, the problem that the intrinsic mode functions (IMFs) decomposed by the empirical mode decomposition (EMD) in HHT is not exactly orthogonal is pointed out and improved through the Gram-Schmidt orthogonalization method which is referred as the orthogonal empirical mode decomposition (OEMD). Combined the OEMD and the Hilbert transform (HT) which is referred as the improved Hilbert-Huang transform (IHHT), the orthogonal intrinsic mode functions (OIMFs) and the orthogonal Hilbert spectrum (OHS) and the orthogonal Hilbert marginal spectrum (OHMS) are obtained. Then, the IHHT has been applied for the analysis of the El Centro earthquake recording. The obtained spectral representation result shows that the OHS gives more detailed and accurate information in a time–frequency–energy presentation than the Hilbert spectrum (HS) and the OHMS gives more faithful low-frequency energy presentation than the Fourier spectrum (FS) and the Hilbert marginal spectrum (HMS).

ENTROPIC INTERPRETATION OF EMPIRICAL MODE DECOMPOSITION AND ITS APPLICATIONS IN SIGNAL PROCESSING

2010 ◽  
Vol 02 (04) ◽  
pp. 429-449 ◽  
Author(s):  
CHIH-YUAN TSENG ◽  
HC LEE
Keyword(s):  
Empirical Mode Decomposition ◽  
Filter Design ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Noise Filter ◽  
Mode Decomposition ◽  
Analysis Strategy ◽  
Low Pass ◽  
The Hilbert Transform

The Hilbert-Huang transform (HHT) method, which is designed to analyze nonstationary and nonlinear time-dependent data, is attracting lots of attention. The HHT first applies the empirical mode decomposition (EMD) to decompose data into intrinsic mode functions (IMF). The Hilbert transform then is applied to the IMFs to reveal its instantaneous frequency spectrum. However, because the EMD lacks analytical interpretation, the meaning of IMFs is unclear. This work proposes an entropic analysis strategy to provide an information-based interpretation. Based on this strategy, three applications in data analysis are demonstrated: (1) studies of characteristic of white noise, (2) determination of minimum sampling rates to generate sufficient numbers of realizations, and (3) a low pass noise filter design.

scholarly journals Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages

2019 ◽  
Vol 9 (13) ◽  
pp. 2587 ◽  
Author(s):  
Chun-Yao Lee ◽  
Kuan-Yu Huang ◽  
Yu-Hua Hsieh ◽  
Po-Hung Chen
Keyword(s):  
Empirical Mode Decomposition ◽  
Electrical Discharge Machining ◽  
Detection System ◽  
Detection Accuracy ◽  
Intrinsic Mode Functions ◽  
Noise Interference ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Lower Complexity ◽  
Motor Bearing

This paper proposes a model which uses the greedy algorithm to select the optimal intrinsic mode functions (IMFs) of the empirical mode decomposition (EMD), namely the greedy empirical mode decomposition (GEMD) model. The optimal IMFs can more sufficiently represent the characteristics of damage bearings since the proposed GEMD model effectively selects some IMFs not affected by noise. To validate the superiority of the proposed GEMD model, various damage types of motor bearings were shaped by electrical discharge machining (EDM) in this experiment. The measured motor current signals of various types were decomposed to IMFs by using EMD. Then the optimal IMFs can be obtained by using the proposed GEMD model. The results show that the Hilbert–Huang transform (HHT) spectrums when using the optimal IMFs become easier in the detection system than when using all IMFs. Simultaneously, the detection accuracy of motor bearing damages is increased by using the features extracted from the lower complexity HHT spectrum. The average detection accuracy can be also improved from 69.5% to 74.6% by using the features extracted from the GEMD-HHT spectrum even in a noise interference 10dB

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