Transform Operator Pair Assisted Hilbert–Huang Transform for Signals With Instantaneous Frequency Intersections

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Yuxin Sun ◽  
Chungang Zhuang ◽  
Zhenhua Xiong
Keyword(s):  
A Priori ◽  
Low Frequency ◽  
Ensemble Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Start Up ◽  
Instantaneous Frequencies

Due to low frequency resolution for closely spaced spectral components, i.e., the instantaneous frequencies (IFs) lie within an octave or even have intersections, the Hilbert–Huang transform (HHT) fails to separate such signals and consequently generates inaccurate time–frequency distribution (TFD). In this paper, a transform operator pair assisted HHT is proposed to improve the capability of the HHT to separate signals, especially those with IF intersections. The two operators of a pair are constructed to remove the chosen component that is clearly observed in the TFD of the signal, and then recover it from intrinsic mode functions (IMFs). With this approach, the components can be clearly separated and the intersections can also be identified in the TFD. Since a priori knowledge of the transform operator is usually not available in real applications, an iterative algorithm is presented to obtain a global transform operator. The effectiveness of the proposed algorithm is demonstrated by analysis of numerical signals and a real signal collected from a cracked rotor–bearing system during the start-up process. Moreover, the proposed approach is shown to be superior to the normalized Hilbert transform (NHT) as well as the ensemble empirical mode decomposition (EEMD).

scholarly journals Common Crossing Structural Health Analysis with Track-Side Monitoring

2019 ◽  
Vol 21 (3) ◽  
pp. 77-84
Author(s):  
Mykola Sysyn ◽  
Olga Nabochenko ◽  
Franziska Kluge ◽  
Vitalii Kovalchuk ◽  
Andriy Pentsak
Keyword(s):  
Gaussian Process Regression ◽  
Ensemble Empirical Mode Decomposition ◽  
Frequency Resolution ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Structural Health ◽  
Rolling Surface ◽  
Mode Decomposition ◽  
Inertial Measurements ◽  
Common Crossing

Track-side inertial measurements on common crossings are the object of the present study. The paper deals with the problem of measurement's interpretation for the estimation of the crossing structural health. The problem is manifested by the weak relation of measured acceleration components and impact lateral distribution to the lifecycle of common crossing rolling surface. The popular signal processing and machine learning methods are explored to solve the problem. The Hilbert-Huang Transform (HHT) method is used to extract the time-frequency features of acceleration components. The method is based on Ensemble Empirical Mode Decomposition (EEMD) that is advantageous to the conventional spectral analysis methods with higher frequency resolution and managing nonstationary nonlinear signals. Linear regression and Gaussian Process Regression are used to fuse the extracted features in one structural health (SH) indicator and study its relation to the crossing lifetime. The results have shown the significant relation of the derived with GPR indicator to the lifetime.

scholarly journals A Reservoir Information Extraction Method Based on Improved Hilbert-Huang Transform

2019 ◽  
pp. 85-90
Author(s):  
Qingmi Yang
Keyword(s):  
Signal Processing ◽  
Seismic Signal ◽  
Ensemble Empirical Mode Decomposition ◽  
Processing Technique ◽  
Intrinsic Mode Functions ◽  
Signal Processing Technique ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Non Stationary Signal

Hilbert-Huang transform (HHT) is a nonlinear non-stationary signal processing technique, which is more effective than traditional time-frequency analysis methods in complex seismic signal processing. However, this method has problems such as modal aliasing and end effect. The problem causes the accuracy of signal processing to drop. Therefore, this paper introduces the method of combining the Ensemble Empirical Mode Decomposition (EEMD) and the Normalized Hilbert transform (NHT) to extract the instantaneous properties. The specific process is as follows: First, the EEMD method is used to decompose the seismic signal to a series of Intrinsic Mode Functions (IMF), and then The IMFs is screened by using the relevant properties, and finally the NHT is performed on the IMF to obtain the instantaneous properties.

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).

Spatiotemporal Trend and Variability of Precipitation in Taiwan Based on Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD)

2021 ◽  
Author(s):  
Chun-Hsiang Tang ◽  
Christina W. Tsai
Keyword(s):  
Time Series ◽  
Empirical Mode Decomposition ◽  
Ensemble Empirical Mode Decomposition ◽  
Intrinsic Mode Functions ◽  
Short Term ◽  
Time Frequency ◽  
Spatial Locality ◽  
Temperature And Precipitation ◽  
Mode Decomposition ◽  
Climatic Scenarios

<p>Abstract</p><p>Most of the time series in nature are nonlinear and nonstationary affected by climate change particularly. It is inevitable that Taiwan has also experienced frequent drought events in recent years. However, drought events are natural disasters with no clear warnings and their influences are cumulative. The difficulty of detecting and analyzing the drought phenomenon remains. To deal with the above-mentioned problem, Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD) is introduced to analyze the temperature and rainfall data from 1975~2018 in this study, which is a powerful method developed for the time-frequency analysis of nonlinear, nonstationary time series. This method can not only analyze the spatial locality and temporal locality of signals but also decompose the multiple-dimensional time series into several Intrinsic Mode Functions (IMFs). By the set of IMFs, the meaningful instantaneous frequency and the trend of the signals can be observed. Considering stochastic and deterministic influences, to enhance the accuracy this study also reconstruct IMFs into two components, stochastic and deterministic, by the coefficient of auto-correlation.</p><p>In this study, the influences of temperature and precipitation on the drought events will be discussed. Furthermore, to decrease the significant impact of drought events, this study also attempts to forecast the occurrences of drought events in the short-term via the Artificial Neural Network technique. And, based on the CMIP5 model, this study also investigates the trend and variability of drought events and warming in different climatic scenarios.</p><p> </p><p>Keywords: Multi-dimensional Ensemble Empirical Mode Decomposition (MEEMD), Intrinsic Mode Function(IMF), Drought</p>

The Application of Improved HHT to Harmonic Analysis and Fault Detection of Power System

2011 ◽  
Vol 354-355 ◽  
pp. 1406-1411
Author(s):  
Wen Hua Han ◽  
Hai Xia Ren ◽  
Xu Chen ◽  
Xiao Juan Tao
Keyword(s):  
Fault Detection ◽  
Power System ◽  
Harmonic Analysis ◽  
Harmonic Signal ◽  
Ensemble Empirical Mode Decomposition ◽  
Frequency Domain Analysis ◽  
Analysis Method ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition

Hilbert-Huang transform (HHT) is a new time-frequency-domain analysis method, which is suitable for non-stationary and nonlinear signals. In this paper, endpoint continuation and ensemble empirical mode decomposition (EEMD) decomposition method are introduced to improve the HHT, which solve the endpoint winger and modal aliasing problem. The improved HHT (IHHT) is used for analyzing the harmonic signal and detecting the fault signal of power system. Simulation results show that IHHT is feasible and effective for harmonic analysis and fault detection.

Applications of variational mode decomposition in seismic time-frequency analysis

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. V365-V378 ◽  
Author(s):  
Wei Liu ◽  
Siyuan Cao ◽  
Yangkang Chen
Keyword(s):  
Empirical Mode Decomposition ◽  
Frequency Analysis ◽  
Synthetic Data ◽  
Ensemble Empirical Mode Decomposition ◽  
Variational Mode Decomposition ◽  
Intrinsic Mode Functions ◽  
Decomposition Approach ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Mode Decomposition

We have introduced a novel time-frequency decomposition approach for analyzing seismic data. This method is inspired by the newly developed variational mode decomposition (VMD). The principle of VMD is to look for an ensemble of modes with their respective center frequencies, such that the modes collectively reproduce the input signal and each mode is smooth after demodulation into baseband. The advantage of VMD is that there is no residual noise in the modes and it can further decrease redundant modes compared with the complete ensemble empirical mode decomposition (CEEMD) and improved CEEMD (ICEEMD). Moreover, VMD is an adaptive signal decomposition technique, which can nonrecursively decompose a multicomponent signal into several quasi-orthogonal intrinsic mode functions. This new tool, in contrast to empirical mode decomposition (EMD) and its variations, such as EEMD, CEEMD, and ICEEMD, is based on a solid mathematical foundation and can obtain a time-frequency representation that is less sensitive to noise. Two tests on synthetic data showed the effectiveness of our VMD-based time-frequency analysis method. Application on field data showed the potential of the proposed approach in highlighting geologic characteristics and stratigraphic information effectively. All the performances of the VMD-based approach were compared with those from the CEEMD- and ICEEMD-based approaches.

scholarly journals On Holo-Hilbert spectral analysis: a full informational spectral representation for nonlinear and non-stationary data

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150206 ◽  
Author(s):  
Norden E. Huang ◽  
Kun Hu ◽  
Albert C. C. Yang ◽  
Hsing-Chih Chang ◽  
Deng Jia ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
A Priori ◽  
Integral Transforms ◽  
Density Variation ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Wave Nonlinearity ◽  
Frequency Modulations ◽  
Multiplicative Processes

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert–Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time–frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and non-stationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

scholarly journals ANALYSIS OF TEMPORAL VARIATIONS IN TURBIDITY FOR A COASTAL AREA USING THE HILBERT-HUANG-TRANSFORM

2011 ◽  
Vol 1 (32) ◽  
pp. 25
Author(s):  
Shigeru Kato ◽  
Magnus Larson ◽  
Takumi Okabe ◽  
Shin-ichi Aoki
Keyword(s):  
Instantaneous Frequency ◽  
River Mouth ◽  
Original Data ◽  
Temporal Variations ◽  
Intrinsic Mode Functions ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
The Hilbert Transform

Turbidity data obtained by field observations off the Tenryu River mouth were analyzed using the Hilbert-Huang Transform (HHT) in order to investigate the characteristic variations in time and in the frequency domain. The Empirical Mode Decomposition (EMD) decomposed the original data into only eight intrinsic mode functions (IMFs) and a residue in the first step of the HHT. In the second step, the Hilbert transform was applied to the IMFs to calculate the Hilbert spectrum, which is the time-frequency distribution of the instantaneous frequency and energy. The changes in instantaneous frequencies showed correspondence to high turbidity events in the Hilbert spectrum. The investigation of instantaneous frequency variations can be used to understand transitions in the state of the turbidity. The comparison between the Fourier spectrum and the Hilbert spectrum integrated in time showed that the Hilbert spectrum makes it possible to detect and quantify the cycle of locally repeated events.

scholarly journals Fault Diagnosis of Rolling Bearing based on an Improved Denoising Technique using Complete Ensemble Empirical Mode Decomposition and Adaptive Thresholding Method

2021 ◽  
Author(s):  
Prashant Kumar Sahu ◽  
Rajiv Nandan Rai
Keyword(s):  
Empirical Mode Decomposition ◽  
Signal Reconstruction ◽  
Low Frequency ◽  
Rolling Bearing ◽  
Ensemble Empirical Mode Decomposition ◽  
Adaptive Thresholding ◽  
Intrinsic Mode Functions ◽  
Vibration Signals ◽  
Mode Decomposition ◽  
Envelope Spectrum

Abstract The vibration signals for rotating machines are generally polluted by excessive noise and can lose the fault information at the early development phase. In this paper, an improved denoising technique is proposed for early faults diagnosis of rolling bearing based on the complete ensemble empirical mode decomposition (CEEMD) and adaptive thresholding (ATD) method. Firstly, the bearing vibration signals are decomposed into a set of various intrinsic mode functions (IMFs) using CEEMD algorithm. The IMFs grouping and selection are formed based upon the correlation coefficient value. The noise-predominant IMFs are subjected to adaptive thresholding for denoising and then added to the low-frequency IMFs for signal reconstruction. The effectiveness of the proposed method denoised signals are measured based on kurtosis value and the envelope spectrum analysis. The presented method results on experimental datasets illustrate that the proposed approach is an effective denoising technique for early fault detection in the rolling bearing.

scholarly journals Analysis in the frequency domain of multicomponent oscillatory modes of the human electroencephalogram extracted with multivariate empirical mode decomposition

2020 ◽  
Author(s):  
Eduardo Arrufat-Pié ◽  
Mario Estévez-Báez ◽  
José Mario Estévez-Carreras ◽  
Calixto Machado Curbelo ◽  
Gerry Leisman ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Empirical Mode Decomposition ◽  
A Priori ◽  
Quantitative Eeg ◽  
Frequency Resolution ◽  
Intrinsic Mode Functions ◽  
Multivariate Empirical Mode Decomposition ◽  
Healthy Humans ◽  
Mode Decomposition ◽  
Mixing Problem

AbstractConsidering the properties of the empirical mode decomposition to extract from a signal its natural oscillatory components known as intrinsic mode functions (IMFs), the spectral analysis of these IMFs could provide a novel alternative for the quantitative EEG analysis without a priori establish more or less arbitrary band limits. This approach has begun to be used in the last years for studies of EEG records of patients included in database repositories or including a low number of individuals or of limited EEG leads, but a detailed study in healthy humans has not yet been reported. Therefore, in this study the aims were to explore and describe the main spectral indices of the IMFs of the EEG in healthy humans using a method based on the FFT and another on the Hilbert-Huang transform (HHT). The EEG of 34 healthy volunteers was recorded and decomposed using a recently developed multivariate empirical mode decomposition algorithm. Extracted IMFs were submitted to spectral analysis with, and the results were compared with an ANOVA test. The first six decomposed IMFs from the EEG showed frequency values in the range of the classical bands of the EEG (1.5 to 56 Hz). Both methods showed in general similar results for mean weighted frequencies and estimations of power spectral density, although the HHT is recommended because of its better frequency resolution. It was shown the presence of the mode-mixing problem producing a slight overlapping of spectral frequencies mainly between the IMF3 and IMF4 modes.

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