scholarly journals NOISE CORRUPTION OF EMPIRICAL MODE DECOMPOSITION AND ITS EFFECT ON INSTANTANEOUS FREQUENCY

2010 ◽  
Vol 02 (03) ◽  
pp. 373-396 ◽  
Author(s):  
DANIEL N. KASLOVSKY ◽  
FRANÇOIS G. MEYER
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Poor Performance ◽  
Specific Mechanism ◽  
Time Frequency ◽  
Seismic Waveform ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Transition Modes ◽  
Nonstationary Data

Huang's Empirical Mode Decomposition (EMD) is an algorithm for analyzing nonstationary data that provides a localized time-frequency representation by decomposing the data into adaptively defined modes. EMD can be used to estimate a signal's instantaneous frequency (IF) but suffers from poor performance in the presence of noise. To produce a meaningful IF, each mode of the decomposition must be nearly monochromatic, a condition that is not guaranteed by the algorithm and fails to be met when the signal is corrupted by noise. In this work, the extraction of modes containing both signal and noise is identified as the cause of poor IF estimation. The specific mechanism by which such "transition" modes are extracted is detailed and builds on the observation of Flandrin and Goncalves that EMD acts in a filter bank manner when analyzing pure noise. The mechanism is shown to be dependent on spectral leak between modes and the phase of the underlying signal. These ideas are developed through the use of simple signals and are tested on a synthetic seismic waveform.

SMOOTHING EMPIRICAL MODE DECOMPOSITION: A PATCH TO IMPROVE THE DECOMPOSED ACCURACY

2010 ◽  
Vol 02 (04) ◽  
pp. 521-543 ◽  
Author(s):  
SUN-HUA PAO ◽  
CHIEH-NENG YOUNG ◽  
CHIEN-LUN TSENG ◽  
NORDEN E. HUANG
Keyword(s):  
Empirical Mode Decomposition ◽  
Cubic Spline ◽  
Nonstationary Processes ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Functional Forms ◽  
Nonstationary Data ◽  
Nonlinear Decomposition ◽  
Cubic Spline Function ◽  
Smoothing Procedure

Hilbert-Huang Transformation (HHT) is designed especially for analyzing data from nonlinear and nonstationary processes. It consists of the Empirical Mode Decomposition (EMD) to generate Intrinsic Mode Function (IMF) components, from which the instantaneous frequency can be computed for the time-frequency Hilbert spectral Analysis. Currently, EMD, based on the cubic spline, is the most efficient and popular algorithm to implement HHT. However, EMD as implemented now suffers from dependence on the cubic spline function chosen as the basis. Furthermore, due to the various stoppage criteria, it is difficult to establish the uniqueness of the decomposition. Consequently, the interpretation of the EMD result is subject to certain degree of ambiguity. As the IMF components from the classic EMD are all approximations from the combinations of piece-wise cubic spline functions, there could also be artificial frequency modulation in addition to amplitude modulation. A novel Smoothing Empirical Mode Decomposition (SEMD) is proposed. Although SEMD is also an approximation, extensive tests on nonlinear and nonstationary data indicate that the smoothing procedure is a robust and accurate approach to eliminate the dependence of chosen spline functional forms. Thus, we have proved the uniqueness of the decomposition under the weak limitation of spline fittings. The natural signal length-of-day 1965–1985 was tested for the performance in nonstationary and nonlinear decomposition. The resulting spectrum by SEMD is quite stable and quantitatively similar to the optimization of EMD.

ENSEMBLE EMPIRICAL MODE DECOMPOSITION FOR HYPERSPECTRAL IMAGE CLASSIFICATION

2012 ◽  
Vol 04 (01n02) ◽  
pp. 1250003 ◽  
Author(s):  
MIN ZHANG ◽  
YI SHEN
Keyword(s):  
Empirical Mode Decomposition ◽  
Hyperspectral Image ◽  
Ensemble Empirical Mode Decomposition ◽  
Classification Performance ◽  
Finite Amplitude ◽  
Support Vector ◽  
Time Frequency ◽  
Original Dataset ◽  
Mode Decomposition ◽  
Nonstationary Data

Ensemble empirical mode decomposition (EEMD) is a novel adaptive time-frequency analysis method, which is particularly suitable for extracting useful information from noisy nonlinear or nonstationary data. This paper presents the utilization of EEMD for hyperspectral images to extract signals from them, generated in noisy nonlinear and nonstationary processes. First, EEMD is applied to each hyperspectral image band and defines the true intrinsic mode function (IMF) components as the mean of an ensemble of trials, each consisting of the signal plus a white noise of finite amplitude. After EEMD is performed to each band, new bands are reconstructed as the sum of IMFs and the trend, and classification is executed over these new bands. Finally, the hyperspectral image with new bands was classified with support vector machine (SVM) to show the classification performance of the proposed approach. Experimental results show that the utilization of the EEMD significantly increases the classification accuracy compared to the dataset processed by empirical mode decomposition (EMD) and the original dataset.

scholarly journals Ensemble EMD based Time-Frequency Analysis of Continuous Adventitious Signal Processing

2018 ◽  
Vol 7 (4.10) ◽  
pp. 896
Author(s):  
B. B Shankar ◽  
D. Jayadevappa
Keyword(s):  
Empirical Mode Decomposition ◽  
Instantaneous Frequency ◽  
Ensemble Empirical Mode Decomposition ◽  
Sound Waves ◽  
Lung Sound ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Marginal Spectrum ◽  
Frequency Components ◽  
Nonlinear Signal

The importance of lung sound analyses is increasing day by day very rapidly. In this paper, we present a new method for analysis of two classes of lung signals namely wheezes and crackles. The procedure used in this article is based on improved Empirical Mode Decomposition (EMD) called Ensemble Empirical Mode Decomposition (EEMD) to analyze and compare continuous and discontinuous adventitious sounds with EMD. These two proposed procedures decompose the lung signals into a set of instantaneous frequency components. Function (IMF). The continuous and discontinuous adventitious sounds are present in an asthmatic patient, produces a non-stationary and nonlinear signal pattern. The empirical mode decomposition (EMD) decomposes such characteristic signals. The instantaneous frequency and spectral analysis related to dual techniques specified above are utilized by IMF to investigate and present the outcome in the time-frequency distribution to investigate the qualities of inbuilt properties of lung sound waves. The Hilbert marginal spectrum has been used to represent total amplitude and energy contribution from every frequency value. Finally, the resultant EEMD analysis is better for wheezes that solves mode mixing issues and improvisation is seen over the EMD method.   

Applications of the synchrosqueezing transform in seismic time-frequency analysis

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. V55-V64 ◽  
Author(s):  
Roberto H. Herrera ◽  
Jiajun Han ◽  
Mirko van der Baan
Keyword(s):  
Wavelet Transform ◽  
Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Seismic Signals ◽  
Time Frequency ◽  
Trade Offs ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Synchrosqueezing Transform ◽  
Instantaneous Frequencies

Time-frequency representation of seismic signals provides a source of information that is usually hidden in the Fourier spectrum. The short-time Fourier transform and the wavelet transform are the principal approaches to simultaneously decompose a signal into time and frequency components. Known limitations, such as trade-offs between time and frequency resolution, may be overcome by alternative techniques that extract instantaneous modal components. Empirical mode decomposition aims to decompose a signal into components that are well separated in the time-frequency plane allowing the reconstruction of these components. On the other hand, a recently proposed method called the “synchrosqueezing transform” (SST) is an extension of the wavelet transform incorporating elements of empirical mode decomposition and frequency reassignment techniques. This new tool produces a well-defined time-frequency representation allowing the identification of instantaneous frequencies in seismic signals to highlight individual components. We introduce the SST with applications for seismic signals and produced promising results on synthetic and field data examples.

Research on Fault Diagnosis Method Based on Empirical Mode Decomposition & Time-Frequency Reassignment

2012 ◽  
Vol 433-440 ◽  
pp. 6256-6261
Author(s):  
Zhi Hua Hao ◽  
Zhuang Ma ◽  
Hao Miao Zhou
Keyword(s):  
Empirical Mode Decomposition ◽  
Simulation Analysis ◽  
Intrinsic Mode Function ◽  
Time Frequency ◽  
Mode Function ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Cross Terms ◽  
Decomposition Time ◽  
The Cross

The reassignment method is a technique for sharpening a time-frequency representation by mapping the data to time-frequency coordinates that are nearer to the true region of support of the analyzed signal. The reassignment method has been proved to produce a better localization of the signal components and improve the readability of the time-frequency representation by concentrating its energy at a center of gravity. But there are still few cross-terms. Then, the empirical mode decomposition is introduced to the reassignment method to suppress the interference of the cross-term encountered in processing the multi-component signals. The multi-component signal can be decomposed into a finite number intrinsic mode function by using EMD. Then, the reassignment method can be calculated for each of the intrinsic mode function. Simulation analysis is presented to show that this method can improve the localization of time-frequency representation and reduce the cross terms. The vibration signals measured from diesel engine in the stage of deflagrate were analyzed with the reassignment method. Experimental results indicate that this method has good potential in mechanical fault feature extraction.

scholarly journals Fault diagnosis of gearbox based on improved polynomial adaptive chirp mode decomposition algorithm

2021 ◽  
Author(s):  
Lingli Cui ◽  
Yuchuan Peng ◽  
Tongtong LIU
Keyword(s):  
Fault Diagnosis ◽  
Instantaneous Frequency ◽  
Variable Speed ◽  
Vibration Signals ◽  
Planetary Gearbox ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Frequency Representation ◽  
Study Results ◽  
Gearbox Vibration

Abstract The adaptive chirp mode decomposition (ACMD) has good time-frequency representation results in analyzing chirp signals, while there is a time-frequency ambiguity problem in the analysis of variable speed planetary gearbox vibration signals. To address this problem, a planetary gearbox fault diagnosis method based on improved polynomial adaptive chirp mode decomposition wavelet is proposed (IPACMD). Using Adaptive chirp mode decomposition, the amplitude and instantaneous frequency of multiple signal components are estimated; To avoid over-decomposition to generate spurious signal components, the similarity conditional entropy is used to optimize the adaptive chirp mode decomposition threshold ;The polynomial chirp transform (PCT) using a polynomial function instead of the linear chirp kernel in the chirp transform to improve the time-frequency aggregation of the instantaneous frequency curve of each signal component and output high-resolution time-frequency representation results. Compared with the original method, the proposed method has better time-frequency aggregation and is more effective for the analysis of variable speed planetary gearbox vibration signals. The simulation and experimental study results show that the method can effectively identify the frequency components and time-frequency characteristics of the variable-speed planetary gearbox vibration signal and realize the fault diagnosis of the planetary gearbox.

scholarly journals Bearing Fault Classification Using Ensemble Empirical Mode Decomposition and Convolutional Neural Network

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1248
Author(s):  
Rafia Nishat Toma ◽  
Cheol-Hong Kim ◽  
Jong-Myon Kim
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Empirical Mode Decomposition ◽  
Vibration Signal ◽  
Ensemble Empirical Mode Decomposition ◽  
Fault Classification ◽  
Original Signal ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Reconstructed Signal

Condition monitoring is used to track the unavoidable phases of rolling element bearings in an induction motor (IM) to ensure reliable operation in domestic and industrial machinery. The convolutional neural network (CNN) has been used as an effective tool to recognize and classify multiple rolling bearing faults in recent times. Due to the nonlinear and nonstationary nature of vibration signals, it is quite difficult to achieve high classification accuracy when directly using the original signal as the input of a convolution neural network. To evaluate the fault characteristics, ensemble empirical mode decomposition (EEMD) is implemented to decompose the signal into multiple intrinsic mode functions (IMFs) in this work. Then, based on the kurtosis value, insignificant IMFs are filtered out and the original signal is reconstructed with the rest of the IMFs so that the reconstructed signal contains the fault characteristics. After that, the 1-D reconstructed vibration signal is converted into a 2-D image using a continuous wavelet transform with information from the damage frequency band. This also transfers the signal into a time-frequency domain and reduces the nonstationary effects of the vibration signal. Finally, the generated images of various fault conditions, which possess a discriminative pattern relative to the types of faults, are used to train an appropriate CNN model. Additionally, with the reconstructed signal, two different methods are used to create an image to compare with our proposed image creation approach. The vibration signal is collected from a self-designed testbed containing multiple bearings of different fault conditions. Two other conventional CNN architectures are compared with our proposed model. Based on the results obtained, it can be concluded that the image generated with fault signatures not only accurately classifies multiple faults with CNN but can also be considered as a reliable and stable method for the diagnosis of fault bearings.

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