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 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.

FAST EMPIRICAL MODE DECOMPOSITIONS OF MULTIVARIATE DATA BASED ON ADAPTIVE SPLINE-WAVELETS AND A GENERALIZATION OF THE HILBERT–HUANG–TRANSFORMATION (HHT) TO ARBITRARY SPACE DIMENSIONS

2010 ◽  
Vol 02 (03) ◽  
pp. 337-358 ◽  
Author(s):  
ROLAND PABEL ◽  
ROBIN KOCH ◽  
GABRIELA JAGER ◽  
ANGELA KUNOTH
Keyword(s):  
Hilbert Transform ◽  
Multivariate Data ◽  
Intrinsic Mode Functions ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Local Means ◽  
Spline Wavelets ◽  
Mode Decomposition ◽  
Arbitrary Space ◽  
The Hilbert Transform

The Hilbert–Huang-Transform (HHT) has proven to be an appropriate multiscale analysis technique specifically for nonlinear and nonstationary time series on non-equidistant grids. It is empirically adapted to the data: first, an additive decomposition of the data (empirical mode decomposition, EMD) into certain multiscale components is computed, denoted as intrinsic mode functions. Second, to each of these components, the Hilbert transform is applied. The resulting Hilbert spectrum of the modes provides a localized time-frequency spectrum and instantaneous (time-dependent) frequencies. For the first step, the empirical decomposition of the data, a different method based on local means has been developed by Chen et al. (2006). In this paper, we extend their method to multivariate data sets in arbitrary space dimensions. We place special emphasis on deriving a method which is numerically fast also in higher dimensions. Our method works in a coarse-to-fine fashion and is based on adaptive (tensor-product) spline-wavelets. We provide some numerical comparisons to a method based on linear finite elements and one based on thin-plate-splines to demonstrate the performance of our method, both with respect to the quality of the approximation as well as the numerical efficiency. Second, for a generalization of the Hilbert transform to the multivariate case, we consider the Riesz transformation and an embedding into Clifford-algebra valued functions, from which instantaneous amplitudes, phases and orientations can be derived. We conclude with some numerical examples.

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).

Empirical Assay of the Use of the Hilbert-Huang Transform for the Spectral Analysis of Storm Waves

2008 ◽  
Author(s):  
Joaqui´n Ortega ◽  
George H. Smith
Keyword(s):  
Empirical Mode Decomposition ◽  
Hilbert Transform ◽  
Instantaneous Frequency ◽  
Sampling Rate ◽  
Stationary Time Series ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Storm Waves ◽  
Mode Decomposition ◽  
The Hilbert Transform

The Hilbert-Huang Transform (HHT) was proposed by Huang et al. [2] as a method for the analysis of non-linear, non-stationary time series. This procedure requires the decomposition of the signal into intrinsic mode functions using a method called empirical mode decomposition. These functions represent the essential oscillatory modes contained in the original signal. Their characteristics ensure that a meaningful instantaneous frequency is obtained through the application of the Hilbert Transform. The Hilbert Transform is applied to each intrinsic mode function and the amplitude and instantaneous frequency for every time-step is computed. The resulting representation of the energy in terms of time and frequency is defined as the Hilbert Spectrum. In previous work [7] using the HHT for the analysis of storm waves it has been observed that the number of IMFs needed for the decomposition and the amount of energy associated to different IMFs differ from what has been observed for the analysis of waves under ‘normal’ sea conditions by other authors. In this work we explore in detail the effect that the sampling rate has in the empirical mode decomposition and in the Hilbert Spectrum for storm waves. The results show that the amount of energy associated to different IMFs varies with the sampling rate and also that the number of IMFs needed for the empirical mode decomposition changes with record length.

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.

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.

Leak Detection in Gas Pipeline Using Hilbert-Huang Transform

2015 ◽  
Vol 815 ◽  
pp. 403-407 ◽  
Author(s):  
Nurul Fatiehah Adnan ◽  
Mohd Fairusham Ghazali ◽  
Makeen M. Amin ◽  
A.M.A. Hamat
Keyword(s):  
Detection Method ◽  
Leak Detection ◽  
Pipeline System ◽  
Simple Method ◽  
Hilbert Spectrum ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Leak Location ◽  
Mode Decomposition ◽  
Useful Signal

This paper proposes a leak detection method using acoustic. The Hamming chirp signal injected into the pipeline system and the estimation of the leak location from the delay time passing by the reflection in the pipeline if there is a leak. By using Hilbert-Huang Transform (HHT), it can give a useful signal to verify the leak. HHT transforms Empirical Mode Decomposition (EMD) and Hilbert Spectrum analysis to perform time-frequency analysis. The leak location can be detected by multiplying by the speed of sound. This simple method gives accurate leak location and easy to implement.

Feature Extraction of Machine Vibration Using Lifting Wavelet Denoising and EMD and its Application in Fault Diagnosis

2010 ◽  
Vol 152-153 ◽  
pp. 383-386
Author(s):  
Feng Li Wang ◽  
Shu Lin Duan ◽  
Hong Tao Gao
Keyword(s):  
Instantaneous Frequency ◽  
Random Noise ◽  
Vibration Signal ◽  
Original Data ◽  
Experimental Result ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Oil Whirl ◽  
Marginal Spectrum ◽  
Lifting Wavelet

In order to reduce the random noise influence on empirical mode decomposition (EMD), the original data is adaptively denoised by lifting wavelet transform to strain mode aliasing, avoid the pseudo mode functions and improve the quality in EMD. The method is employed to analyze the rotor oil whirl vibration signal. Obtaining intrinsic mode functions (IMFs), the instantaneous frequency and amplitude can be calculated by Hilbert transform. Hilbert marginal spectrum can exactly provide the energy distribution of the signal with the change of instantaneous frequency. Thus, the characteristics information of the rotor oil whirl vibration signal can be extracted effectively. Experimental result demonstrate the validity of the proposed method.

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.

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.

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