scholarly journals Multidimensional Iterative Filtering Method for the Decomposition of High–Dimensional Non–Stationary Signals

2017 ◽  
Vol 10 (2) ◽  
pp. 278-298 ◽  
Author(s):  
Antonio Cicone ◽  
Haomin Zhou
Keyword(s):  
Sufficient Conditions ◽  
Higher Dimensions ◽  
High Dimensional ◽  
Alternative Technique ◽  
Time Frequency ◽  
Filtering Method ◽  
Convergence Results ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Iterative Filtering

AbstractIterative Filtering (IF) is an alternative technique to the Empirical Mode Decomposition (EMD) algorithm for the decomposition of non–stationary and non–linear signals. Recently in [3] IF has been proved to be convergent for anyL2signal and its stability has been also demonstrated through examples. Furthermore in [3] the so called Fokker–Planck (FP) filters have been introduced. They are smooth at every point and have compact supports. Based on those results, in this paper we introduce the Multidimensional Iterative Filtering (MIF) technique for the decomposition and time–frequency analysis of non–stationary high–dimensional signals. We present the extension of FP filters to higher dimensions. We prove convergence results under general sufficient conditions on the filter shape. Finally we illustrate the promising performance of MIF algorithm, equipped with high–dimensional FP filters, when applied to the decomposition of two dimensional signals.

New insights and best practices for the succesful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms in the decomposition of nonlinear and nonstationary signals

2020 ◽  
Author(s):  
Antonio Cicone ◽  
Angela Stallone ◽  
Massimo Materassi ◽  
Haomin Zhou
Keyword(s):  
Empirical Mode Decomposition ◽  
Best Practice ◽  
Real Life ◽  
Original Signal ◽  
Open Problems ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Highly Nonlinear ◽  
Iterative Filtering

<p>Nonlinear and nonstationary signals are ubiquitous in real life. Their time–frequency analysis and features extraction can help in solving open problems in many fields of research. Two decades ago, the Empirical Mode Decomposition (EMD) algorithm was introduced to tackle highly nonlinear and nonstationary signals. It consists of a local and adaptive data–driven method which relaxes several limitations of the standard Fourier transform and the wavelet Transform techniques, yielding an accurate time-frequency representation of a signal. Over the years, several variants of the EMD algorithm have been proposed to improve the original technique, such as the Ensemble Empirical Mode Decomposition (EEMD) and the Iterative Filtering (IF).<br><br></p><p>The versatility of these techniques has opened the door to their application in many applied fields, like geophysics, physics, medicine, and finance. Although the EMD– and IF–based techniques are more suitable than traditional methods for the analysis of nonlinear and nonstationary data, they could easily be misused if their known limitations, together with the assumptions they rely on, are not carefully considered. Here we call attention to some of the pitfalls encountered when implementing these techniques. Specifically, there are three critical factors that are often neglected: boundary effects; presence of spikes in the original signal; signals containing a high degree of stochasticity. We show how an inappropriate implementation of the EMD and IF methods could return an artefact–prone decomposition of the original signal. We conclude with best practice guidelines for researchers who intend to use these techniques for their signal analysis.</p>

Identification of Power Quality Disturbances Based on EEMD and TEO

2013 ◽  
Vol 433-435 ◽  
pp. 469-476 ◽  
Author(s):  
Song Jun Wang ◽  
Qing Fen Liao ◽  
Di Chen Liu ◽  
Yu Tian Zhou ◽  
Bin Kun Xu ◽  
...  
Keyword(s):  
Power Quality ◽  
Empirical Mode Decomposition ◽  
Energy Operator ◽  
Ensemble Empirical Mode Decomposition ◽  
Good Time ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Power Quality Disturbance ◽  
Stationary Signals ◽  
Power Quality Disturbances

The empirical mode decomposition (EMD) is a good time-frequency analysis method, which can deal with nonlinear and non-stationary signals. Aiming at improving modal aliasing problem brought by the traditional EMD, white noise is introduced into the improved aided analysis algorithm namely ensemble empirical mode decomposition (EEMD), instantaneous amplitude and frequency can be obtained by using teager energy operator (TEO), which is adopted to identify the type of power quality disturbance. The anti-aliasing of EEMD and real-time detection of TEO are verified by the signal simulation in Matlab. Simulation and experimental results show that the proposed algorithm can detect and locate power quality disturbances accurately and quickly, with excellent detection effects.

Intrinsic time-scale decomposition: time–frequency–energy analysis and real-time filtering of non-stationary signals

2006 ◽  
Vol 463 (2078) ◽  
pp. 321-342 ◽  
Author(s):  
Mark G Frei ◽  
Ivan Osorio
Keyword(s):  
Real Time ◽  
Time Scale ◽  
Time Signal ◽  
Single Wave ◽  
Monotonic Trend ◽  
Time Frequency ◽  
Intrinsic Time ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Time Scale Decomposition

We introduce a new algorithm, the intrinsic time-scale decomposition (ITD), for efficient and precise time–frequency–energy (TFE) analysis of signals. The ITD method overcomes many of the limitations of both classical (e.g. Fourier transform or wavelet transform based) and more recent (empirical mode decomposition based) approaches to TFE analysis of signals that are nonlinear and/or non-stationary in nature. The ITD method decomposes a signal into (i) a sum of proper rotation components, for which instantaneous frequency and amplitude are well defined, and (ii) a monotonic trend. The decomposition preserves precise temporal information regarding signal critical points and riding waves, with a temporal resolution equal to the time-scale of extrema occurrence in the input signal. We also demonstrate how the ITD enables application of single-wave analysis and how this, in turn, leads to a powerful new class of real-time signal filters, which extract and utilize the inherent instantaneous amplitude and frequency/phase information in combination with other relevant morphological features.

Application of Hilbert-Huang Transform Method on Fault Diagnosis for Wind Turbine Rotor

2009 ◽  
Vol 413-414 ◽  
pp. 159-166
Author(s):  
Qian Huang ◽  
Dong Xiang Jiang ◽  
Liang You Hong
Keyword(s):  
Wind Turbine ◽  
Original Data ◽  
Turbine Rotor ◽  
Noticeable Effect ◽  
Transform Method ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Wind Turbine Rotor

Many signals of wind turbine faults are non-stationary and have highly complex time-frequency characteristics. Traditional time-frequency analysis method, such as Windowed Fourier Transform method, has no noticeable effect in handing non-stationary signals. Hilbert-Huang Transform (HHT) is a new signal processing method for analyzing the non-stationary mechanical signals. Based on Empirical Mode Decomposition (EMD), the Intrinsic Mode Function (IMF) in HHT can reflect the intrinsic physical characteristics of original data. Moreover, it is a good way to identify the faults involving a breakdown change. First, the principles and advantages of the HHT are presented in detail in this paper. Then, three typical faults of wind turbine rotor, such as rotor imbalance, aerodynamic asymmetry due to blade surface roughness and yaw misalignment are discussed by the HHT. Last, reasonable conclusions are drawn by the comparison between this method and the Wavelet Transform (WT) method with the help of simulation fault signals. The results show the effectiveness of HHT method for diagnosing those faults of wind turbine rotor.

Tracking the split: a non-linear iterative approach to the monitoring of recent SAA evolution

2021 ◽  
Author(s):  
Alexandra Parmentier ◽  
Antonio Cicone ◽  
Mirko Piersanti ◽  
Roberta Tozzi ◽  
Matteo Martucci ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Geographic Region ◽  
Low Earth Orbit ◽  
Radiation Hazard ◽  
Loss Cone ◽  
Mode Decomposition ◽  
Leo Satellites ◽  
Stationary Signals ◽  
Data Adaptive ◽  
Iterative Filtering

<p>Still today vaguely defined, the South Atlantic Anomaly (SAA) is the vast<br>geographic region where the Earth’s magnetic field is weakest relative to an<br>ideal Earth-centered dipole field, and the inner radiation belt comes closest<br>to the planet. Nonetheless it represents a major concern to the space science<br>community, since the local reduced magnetic intensity often results in satellite<br>outages and radiation hazard to humans, especially in geomagnetically disturbed<br>periods.<br>Since 1958, relentless investigation of the various morphological and dynamic<br>features of the SAA has been taking place, robustly relying on field, plasma and<br>particle measurements from Low-Earth-Orbit (LEO) satellites since the late<br>1970s.<br>New readings provided by magnetometers operating at LEO altitudes show that,<br>within the past decade, an apparent second center of minimum field intensity<br>has begun to be clearly resolved southwest of Africa, suggesting a possible rapid<br>splitting of the SAA into two cells. In addition to magnetic determinations, the<br>tracking of fluxes of sub-MeV electrons that are lost to the atmosphere when<br>drifting into the SAA due to its increased bounce loss cone, offers a specular<br>view of the same phenomenon. This multi-messenger approach from different<br>platforms is best suited to catch fine details of the splitting.<br>Directly stemming from the data-adaptive Empirical Mode Decomposition (EMD)<br>developed at NASA in the 1990s for the analysis of non-stationary signals, the<br>Fast Iterative Filtering (FIF) class of signal mode decompositions is recently<br>taking center stage due to enhanced rigorous formalization in terms of con-<br>vergence and stability. Multidimensional and Multivariate FIF (MMFIF) is a<br>brand-new extension that handles multidimensional and multichannel datasets.<br>The application of MMFIF techniques to magnetic-field and particle data from<br>an ensemble of LEO satellites has allowed us to best characterize the dynamic<br>evolution of the SAA lobes in the 2010s, and compare it to analogous data in<br>the literature from the previous decades.</p>

Comparison on Turnovers of Agricultural Products Futures Based on Hilbert-Huang Transform

2014 ◽  
Vol 989-994 ◽  
pp. 2713-2718
Author(s):  
Qing Bin Han ◽  
Hai Li Shi
Keyword(s):  
Empirical Mode Decomposition ◽  
Frequency Analysis ◽  
Agricultural Products ◽  
Analysis Approach ◽  
Commodity Exchange ◽  
Time Frequency Analysis ◽  
Hilbert Huang Transform ◽  
Time Frequency ◽  
Mode Decomposition ◽  
Stationary Signals

In order to distinguish the different patterns and evolving trends on turnovers of agricultural products futures between Zhengzhou Commodity Exchange (Z-CE) and Dalian Commodity Exchange (D-CE), a novel time-frequency analysis approach, i.e. Hilbert-Huang transform (HHT), is investigated in this paper. Firstly, Hilbert-Huang transform is briefly introduced. Secondly, two different non-stationary signals of turnover of agricultural products futures from 2009 to 2013 coming from Z-CE and D-CE are described in Empirical Mode Decomposition (EMD). With these results, the two signals are distinctly different from each other. It is proved that the technique of HHT is effective for the purpose of distinction of turnover of agricultural products futures in commodity exchanges.

Multivariate empirical mode decomposition

2009 ◽  
Vol 466 (2117) ◽  
pp. 1291-1302 ◽  
Author(s):  
N. Rehman ◽  
D. P. Mandic
Keyword(s):  
Empirical Mode Decomposition ◽  
Human Motion ◽  
Time Frequency ◽  
Quasi Monte Carlo ◽  
Multivariate Empirical Mode Decomposition ◽  
Low Discrepancy Sequences ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Local Mean ◽  
Multivariate Signals

Despite empirical mode decomposition (EMD) becoming a de facto standard for time-frequency analysis of nonlinear and non-stationary signals, its multivariate extensions are only emerging; yet, they are a prerequisite for direct multichannel data analysis. An important step in this direction is the computation of the local mean, as the concept of local extrema is not well defined for multivariate signals. To this end, we propose to use real-valued projections along multiple directions on hyperspheres ( n -spheres) in order to calculate the envelopes and the local mean of multivariate signals, leading to multivariate extension of EMD. To generate a suitable set of direction vectors, unit hyperspheres ( n -spheres) are sampled based on both uniform angular sampling methods and quasi-Monte Carlo-based low-discrepancy sequences. The potential of the proposed algorithm to find common oscillatory modes within multivariate data is demonstrated by simulations performed on both hexavariate synthetic and real-world human motion signals.

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.

scholarly journals Multivariate empirical mode decomposition–based structural damage localization using limited sensors

2021 ◽  
pp. 107754632110069
Author(s):  
Sandeep Sony ◽  
Ayan Sadhu
Keyword(s):  
Empirical Mode Decomposition ◽  
Structural Damage ◽  
Cost Effective ◽  
Threshold Value ◽  
Damage Localization ◽  
Time Frequency ◽  
Multivariate Empirical Mode Decomposition ◽  
Percentage Difference ◽  
Mode Decomposition

In this article, multivariate empirical mode decomposition is proposed for damage localization in structures using limited measurements. Multivariate empirical mode decomposition is first used to decompose the acceleration responses into their mono-component modal responses. The major contributing modal responses are then used to evaluate the modal energy for the respective modes. A damage localization feature is proposed by calculating the percentage difference in the modal energies of damaged and undamaged structures, followed by the determination of the threshold value of the feature. The feature of the specific sensor location exceeding the threshold value is finally used to identify the location of structural damage. The proposed method is validated using a suite of numerical and full-scale studies. The validation is further explored using various limited measurement cases for evaluating the feasibility of using a fewer number of sensors to enable cost-effective structural health monitoring. The results show the capability of the proposed method in identifying as minimal as 2% change in global modal parameters of structures, outperforming the existing time–frequency methods to delineate such minor global damage.

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