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 Nonlinear Time-Varying Spectral Analysis: HHT and MODWPT

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Pei-Wei Shan ◽  
Ming Li
Keyword(s):  
Spectral Analysis ◽  
Nonlinear Systems ◽  
Discrete Wavelet ◽  
Time Varying ◽  
Nonstationary Processes ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Time Frequency Distribution

Time-frequency distribution has received a growing utilization for analysis and interpretation of nonlinear and nonstationary processes in a variety of fields. Among them, two methods, such as, the empirical mode decomposition (EMD) with Hilbert transform (HT) which is termed as the Hilbert-Huang Transform (HHT) and the Hilbert spectrum based on maximal overlap discrete wavelet package transform (MODWPT), are fairly noteworthy. Comparisons of HHT and MODWPT in analyzing several typical nonlinear systems and examinations of the effectiveness using these two methods are illustrated. This study demonstrates that HHT can provide comparatively more accurate identifications of nonlinear systems than MODWPT.

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 Assessment of Lift Passenger Comfort by the Hilbert–Huang Transform

2019 ◽  
Vol 8 (2) ◽  
pp. 373-380 ◽  
Author(s):  
Kamil Szydło ◽  
Piotr Wolszczak ◽  
Rafał Longwic ◽  
Grzegorz Litak ◽  
Mieczysław Dziubiński ◽  
...  
Keyword(s):  
Spectral Analysis ◽  
Human Body ◽  
Dominant Frequency ◽  
Health Condition ◽  
Passenger Comfort ◽  
Hilbert Huang Transform ◽  
Mode Decomposition ◽  
Resonance Frequencies ◽  
As Stress ◽  
The Hilbert Transform

Abstract Purpose The comfort of lift passengers has a significant effect on their general health condition as well as stress levels during travel. This study reports the results of vibration measurements taken during travel in a passenger lift. Methods Vibration signals were analyzed by the empirical mode decomposition method and the Hilbert transform. Results Selected modes from the Hilbert spectral analysis were compared with the resonance frequencies of human body organs (range 20–90 Hz) as well as with the resonance frequencies of lift components. Conclusion The use of Hilbert spectral analysis enables the isolation of individual signal components and the determination of the dominant frequency in the signal. This, in turn, allows for the isolation of raw vibration frequencies from the signal that are particularly significant for passenger comfort assessment (resonance frequencies of human body organs) and analysis of their occurrence.

scholarly journals The seismic signatures of the 2009 Shiaolin landslide in Taiwan

2011 ◽  
Vol 11 (5) ◽  
pp. 1559-1569 ◽  
Author(s):  
Z. Feng
Keyword(s):  
Surface Wave ◽  
Seismic Waves ◽  
Frequency Spectra ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Wave Velocities ◽  
Shear Wave Velocities ◽  
Mode Function ◽  
Mode Decomposition ◽  
Weak Surface

Abstract. The Shiaolin landslide occurred on 9 August 2009 after Typhoon Morakot struck Taiwan, claiming over 400 lives. The seismic signals produced by the landslide were recorded by broadband seismic stations in Taiwan. The time-frequency spectra for these signals were obtained by the Hilbert-Huang transform (HHT) and were analyzed to obtain the seismic characteristics of the landslide. Empirical mode decomposition (EMD) was applied to differentiate weak surface-wave signals from noise and to estimate the surface-wave velocities in the region. The surface-wave velocities were estimated using the fifth intrinsic mode function (IMF 5) obtained from the EMD. The spectra of the earthquake data were compared. The main frequency content of the seismic waves caused by the Shiaolin landslide were in the range of 0.5 to 1.5 Hz. This frequency range is smaller than the frequency ranges of other earthquakes. The spectral analysis of surface waves (SASW) method is suggested for characterizing the shear-wave velocities of the strata in the region.

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.

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 An Improvement in Representation of Audio Signal in Time-Frequency Plane using EMD-2TEMD Based Approach

2016 ◽  
Vol 44 ◽  
pp. 141-150
Author(s):  
Kazi Mahmudul Hassan ◽  
Md. Ekramul Hamid ◽  
Takayoshi Nakai
Keyword(s):  
Empirical Mode Decomposition ◽  
Source Separation ◽  
Audio Signal ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Separation Result ◽  
Mode Decomposition ◽  
Recent Approach ◽  
Non Stationary Signal

This study proposed an enhanced time-frequency representation of audio signal using EMD-2TEMD based approach. To analyze non-stationary signal like audio, timefrequency representation is an important aspect. In case of representing or analyzing such kind of signal in time-frequency-energy distribution, hilbert spectrum is a recent approach and popular way which has several advantages over other methods like STFT, WT etc. Hilbert-Huang Transform (HHT) is a prominent method consists of Empirical Mode Decomposition (EMD) and Hilbert Spectral Analysis (HSA). An enhanced method called Turning Tangent empirical mode decomposition (2T-EMD) has recently developed to overcome some limitations of classical EMD like cubic spline problems, sifting stopping condition etc. 2T-EMD based hilbert spectrum of audio signal encountered some issues due to the generation of too many IMFs in the process where EMD produces less. To mitigate those problems, a mutual implementation of 2T-EMD & classical EMD is proposed in this paper which enhances the representation of hilbert spectrum along with significant improvements in source separation result using Independent Subspace Analysis (ISA) based clustering in case of audio signals. This refinement of hilbert spectrum not only contributes to the future work of source separation problem but also many other applications in audio signal processing.

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.

scholarly journals Data Interpretation Technology of GPR Survey Based on Variational Mode Decomposition

2019 ◽  
Vol 9 (10) ◽  
pp. 2017 ◽  
Author(s):  
Juncai Xu ◽  
Bangjun Lei
Keyword(s):  
Instantaneous Frequency ◽  
Data Interpretation ◽  
Variational Mode Decomposition ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Synthetic Signal ◽  
Mode Decomposition ◽  
The Media ◽  
Ground Penetrating

Data interpretation is the crucial scientific component that influences the inspection accuracy of ground penetrating radar (GPR). Developing algorithms for interpreting GPR data is a research focus of increasing interest. The problem of algorithms for interpreting GPR data is unresolved. To this end, this study proposes a sophisticated algorithm for interpreting GPR data with the aim of improving the inspection resolution. The algorithm is formulated by integrating variational mode decomposition (VMD) and Hilbert–Huang transform techniques. With this method, the intrinsic mode function of the GPR data is first produced using the VMD of the data, followed by obtaining the instantaneous frequency by using the Hilbert–Huang transform to analyze the intrinsic mode functions. The instantaneous frequency data can be decomposed into three frequency attributes, including frequency division section, time-frequency section, and space frequency section, which constitute a platform to gain insight into the nature of the GPR data, such that the inspected media components can be examined. The effectiveness of the proposed method on a synthetic signal from a GPR forward model was studied, with the multi-resolution performance being tested. Inspecting the media of a highroad by analyzing the GPR data, with the abnormal characteristics being designated, validated the applicability of the proposed method.

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