Classical Empirical Mode Decomposition Research Articles

Segment empirical mode decomposition filtering method on distance correction signal for aerosol lidar

Aerosol lidar has been widely used in environmental monitoring. It is necessary to correct the distance before calculating the backscatter coefficient. However, the problem in this process is that the noise is greatly amplified, especially for long-distance signals. Based on previous theoretical research and signal characteristics, a segment empirical mode decomposition (EMD) filtering method that can denoise the distance correction signal is developed. Taking measured data of aerosol lidar as an example, the distance correction signal is divided into four segments, and each segment is decomposed by EMD. For low-height signals with low noise, the signal is reconstructed as comprehensively as possible. For high-height signals with high noise, most high-frequency signals are removed. This method is feasible because the aerosol concentration decreases with the increase in height. After segment EMD filtering, four segments of signals are recombined. Compared with the classical EMD, the segmented EMD filtering method not only retains the details of the low-height signal but also removes the high-height noise as much as possible. The segmented EMD filtering method is proven to be effective for aerosol lidar that conducts profile monitoring on the ground.

Bearing Fault Diagnosis Using Piecewise Aggregate Approximation and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise.

Complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) effectively separates the fault vibration signals of rolling bearings and improves the diagnosis of rolling bearing faults. However, CEEMDAN has high memory requirements and low computational efficiency. In each iteration of CEEMDAN, fault vibration signals are added with noises, both the vibration signals added with noises and the added noises are decomposed with classical empirical mode decomposition (EMD). This paper proposes a rolling bearing fault diagnosis method that combines piecewise aggregate approximation (PAA) with CEEMDAN. PAA enables CEEMDAN to decompose long signals and to achieve enhanced diagnosis. In particular, the method first yields the vibration envelope using bandpass filtering and demodulation, then compresses the envelope using PAA, and finally decomposes the compressed signal with CEEMDAN. Test data verification results show that the proposed method is more effective and more efficient than CEEMDAN.

A Hybrid Method for Structural Modal Parameter Identification Based on IEMD/ARMA: A Numerical Study and Experimental Model Validation

This article presents a hybrid method of structural modal parameter identification, based on improved empirical mode decomposition (EMD) and autoregressive and moving average (ARMA). Special attention is given to some implementation issues, such as the modal mixing, false modes, the judgment of the real intrinsic mode function (IMF) of classical EMD, and the difficulty of fixing the order of ARMA. To resolve the existing defects of EMD, an improved EMD (IEMD) that combines frequency band filtering and cluster analysis is proposed in this paper, where frequency band filtering divides the signal into several narrowband signals before the EMD process, and cluster analysis is used to determine the real IMFs. Euclidean distance is used to cluster the decomposition results, with no need to adjust any indexes or thresholds, and only by means of using the nearest distance to efficiently determine the real IMF. Moreover, IEMD is used as a pre-processing tool for ARMA, to resolve the difficulty of fixing its order. The capabilities of the proposed method were compared and assessed using a numerical simulation and an experimental model. The numerical simulation and experimental results showed that the improved method could resolve the modal mixing and false modal problems in the classical EMD process and could automatically identified the real IMFs, while the proposed IEMD was combined with ARMA to successfully identify the frequency and mode shape of the structure. Additionally, since each IMF is a single component signal, it is easy to determine the order of the ARMA model.

EEG analysis and classification based on cardinal spline empirical mode decomposition and synchrony features.

Dementia is a major cause of disability and dependency among older adults. Diagnosis is most effective at an early stage of the disease, as patients can start early treatment to delay progressive cognitive decline. While other diagnostic methods for dementia are available, electroencephalography (EEG) is noninvasive, more accessible, and less complicated than other biomarker measurements. Moreover, it may be orders of magnitude less expensive, thereby offering the possibility of low-cost mass screening. This paper presents a novel digital signal processing method called cardinal spline empirical mode decomposition (CS-EMD) for EEG processing. This new method uses a different signal envelope interpolation algorithm to separate EEG signals into constituent components, called intrinsic mode functions (IMFs), with better signal decomposition properties than classical empirical mode decomposition (EMD). The IMFs obtained from the new method are then used to compute longitudinal and transversal synchrony measures, which are explored as features for healthy and dementia classification using a support vector machine (SVM). The performance of the proposed method is studied on a publicly available EEG dataset. The results show that using multiple synchrony measures of both longitudinal and transversal EEG channels on five IMFs produces the best classification result of 90% accuracy, 96.67% specificity, 83.33% sensitivity, and 96.15% precision, outperforming the classical EMD method and various other approaches. This new, data-driven CS-EMD method shows good potential as a dementia screening tool. CS-EMD may also be applied in processing other nonlinear and nonstationary biosignals.

Sea Clutter Suppression and Target Detection Algorithm of Marine Radar Image Sequence Based on Spatio-Temporal Domain Joint Filtering.

In marine radar target detection, sea clutter will cause a large number of missed alarms and false alarms, which will affect the accuracy of target detection. In order to suppress sea clutter effectively, a sea clutter suppression and target detection algorithm of marine radar image sequence based on spatio-temporal domain joint filtering is proposed in this paper. The proposed method is to add a sea clutter suppression link before detecting the target. Firstly, the marine radar image sequence is transformed into three-dimensional frequency wavenumber domain by three-dimensional fast Fourier transform (3D-FFT), and then the three-dimensional image spectrum is obtained. According to the fact that the sea clutter spectrum obtained from the image spectrum satisfies the dispersion relation of linear wave theory in the three-dimensional frequency wavenumber domain, a sea clutter model is established. Then, through the established sea clutter model, a spatio-temporal domain joint sea clutter suppressor is designed to filter the image spectrum. After that, the filtered image spectrum is transformed by three-dimensional inverse fast Fourier transform (3D-IFFT) to obtain the image sequence in which sea clutter is suppressed. Finally, target detection is carried out for sea clutter suppressed image sequence. The method is validated by using the real data of X-band marine radar. Compared with the classical Empirical mode decomposition (EMD) method, the improvement of signal-to-noise ratio (SNR) is more obvious, and SNR can be increased by 15.3 db at most. In addition, compared with target detection on original images directly, the proposed method has excellent detection rate and can increase detection rates by at least 8%.

Learnable Empirical Mode Decomposition based on Mathematical Morphology

Empirical mode decomposition (EMD) is a fully data driven method for multiscale decomposing signals into a set of components known as intrinsic mode functions. EMD is based on lower and upper envelopes of the signal in an iterated decomposition scheme. In this paper, we put forward a simple yet effective method to learn EMD from data by means of morphological operators. We propose an end-to-end framework by incorporating morphological EMD operators into deeply learned representations, trained using standard backpropagation principle and gradient descent-based optimization algorithms. Three generalizations of morphological EMD are proposed: a) by varying the family of structuring functions, b) by varying the pair of morphological operators used to calculate the envelopes, and c) the use of a convex sum of envelopes instead of the classical mean point used in classical EMD. We discuss in particular the invariances that are induced by the morphological EMD representation. Experimental results on supervised classification of hyperspectral images by 1D convolutional networks demonstrate the interest of our method.

Real-time chatter detection via iterative Vold-Kalman filter and energy entropy

Real-time chatter detection is important in improving the surface quality of workpieces in milling. Since the process from stable cutting to chatter is characterized by the progressive variation of the vibration energy distribution, entropy has been utilized to capture the decreasing randomness of vibration signals when chatter occurs. To make such an index more sensitive to transitions of the cutting state, the entropy can be computed based on signal components obtained through signal decomposition techniques. However, the classic empirical mode decomposition (EMD) is difficult to put into practice due to its weak robustness to noises. The up-to-date variational mode decomposition (VMD) has strict requirements on a priori information about the signal and thus is not applicable either. In this paper, a novel method named the iterative Vold-Kalman filter (I-VKF) is proposed under the framework of the greedy algorithm, where the Vold-Kalman filter (VKF), a classic order tracker for rotating machinery, is improved to recursively extract each signal component. In the meantime, a spectrum concentration index–based technique is developed for the estimation of the instantaneous chatter frequency to adaptively determine the filter parameter. Numerical examples demonstrate the superiority of the I-VKF over the original VKF, EMD, and VMD, especially in the presence of strong noises. Combined with the energy entropy of extracted components and an automatically calculated threshold, the proposed strategy greatly helps in timely chatter detection, which has been verified by dynamic simulation and experiments.

A method for detection of Mode-Mixing problem

Classical Empirical Mode Decomposition (EMD) is a data-driven method used to analyze non-linear and non-stationary time series data. Besides being an adaptable method by its nature, EMD assumes that every data consists of oscillations of the intrinsic mode functions (IMF). EMD also requires the condition that IMFs which represent the characteristic structures in the data should show only a unique sub-characteristic of the data. However, in some cases, depending on the way the sub-characteristics which make up a sophisticated data coexist, the IMFs are able to be not unique. This is called the mode-mixing problem. Although there are many studies and successful methods (such as EEMD, CEEMDAN) for eliminating the mode-mixing problem, a limited number of studies exist on determining the presence of the aforementioned problem. In this study, a method for the determination of the mode-mixing problem is proposed. In the suggested method, the Itakura–Saito distance, which is a measurement of the similarity of stationary signals and based on Fourier spectrums, is modified by applying Kaiser filter onto short-time signals. The performance of the method is tested via various applications with simulated and real data, and the results show successful detection of the mode-mixing if it exists in time series.

Enhancement of adaptive mode decomposition via angular resampling for nonstationary signal analysis of rotating machinery: Principle and applications

Vibration signal analysis provides an effective approach for condition monitoring and fault diagnosis of rotating machines. Under time-varying conditions, vibration signals feature nonstationarity, consist of multiple frequency components, and usually have spectral overlaps. Adaptive mode decomposition methods can extract mono-components from a given multi-component signal to meet the requirement for estimating instantaneous frequency. Among them, the recently proposed methods, including empirical wavelet transform, variational mode decomposition and Fourier decomposition method, outperform the classic empirical mode decomposition in terms of rigorous mathematical formulation. Nevertheless, for multi-component signals with spectral overlaps, these three methods are subject to mode mixing and/or integrity issues, and fail to extract true mono-components, because they essentially separate mono-components based on spectral segmentation. In this paper, we propose a framework by exploiting the capability of angular resampling to address the mono-component overlapping issue. This methodology can separate true mono-components, thus facilitating accurate estimation of instantaneous frequency through Hilbert transform and generating perfect time–frequency representations (TFRs). Firstly, angular resampling is employed to make the constituent mono-components well separable in the frequency domain. Then, true mono-components are separated through adaptive mode decomposition. Next, informative mono-components are selected for further processing based on the prominent order information, and the selected mono-components are mapped into the time domain according to the relationship between the equal time and equal angle sampling. Finally, the instantaneous frequency and amplitude envelope of the recovered mono-components are calculated via Hilbert transform, and the TFR of raw signal is obtained by superposing the TFRs of all recovered mono-components. By doing so, the TFR achieves a fine time–frequency resolution and is free of both outer and inner interferences. The proposed methodology is demonstrated by simulated signal analysis, and further validated using the vibration data sets of three typical rotating machines (including a planetary gearbox in a wind turbine drivetrain, a civil aircraft engine and a hydraulic turbine rotor). The analysis results show its excellent capability to reveal the time-varying features of rotating machinery nonstationary signals.

A statistical approach to signal denoising based on data-driven multiscale representation

We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys superior mathematical and theoretical framework that makes it robust to noise and mode mixing. These desirable properties of VMD materialize in segregation of a major part of noise into a few final modes while majority of the signal content is distributed among the earlier ones. To exploit this representation for denoising purpose, we propose to estimate the distribution of noise from the predominantly noisy modes and then use it to detect and reject noise from the remaining modes. The proposed approach first selects the predominantly noisy modes using the CVM measure of statistical distance. Next, CVM statistic is used locally on the remaining modes to test how closely the modes fit the estimated noise distribution; the modes that yield closer fit to the noise distribution are rejected (set to zero). Extensive experiments demonstrate the superiority of the proposed method as compared to the state of the art in signal denoising and underscore its utility in practical applications where noise distribution is not known a priori.

A Method of HCN Gas Spectrum Denoising and Baseline Removal Used for FBG Interrogation

Hydrogen cyanide (HCN) gas based fiber Bragg grating (FBG) interrogation is a promising approach in thermal cycling environment. However, the HCN spectrum suffers from strong noise and baseline wander induced by the interrogation system, which limits the measurement stability and reliability. In this paper, we propose an integrated method for spectral denoising and baseline removal to improve the interrogation performance. The method combines the classical empirical mode decomposition (EMD) with the recently developed convolution window (CW) filtering. After the HCN spectrum is decomposed by EMD, the noise and baseline components are extracted from the intrinsic mode functions via a “multiband” filtering approach. Verification experiments are performed using HCN gas cells with different absorption spectra. The results show that the proposed method is able to remove both noise and baseline with minimum signal distortion. Compared with other methods, the optimal interrogation stability with 25 Torr HCN gas cell is improved from ±1.43 pm to ±0.87 pm. For the 100 Torr HCN gas cell, the optimal interrogation stability is improved from ±1.75 pm to ±0.99 pm. In addition, the proposed method also improves the reliability of the interrogation system in the case of large light attenuation.

A Data Augmentation Scheme for Geometric Deep Learning in Personalized Brain–Computer Interfaces

Electroencephalography signals inherently deviate from the notion of regular spatial sampling, as they reflect the coordinated action from multiple distributed overlapping cortical networks. Hence, the observed brain dynamics are influenced both by the topology of the sensor array and the underlying functional connectivity. Neural engineers are currently exploiting the advances in the domain of graph signal processing in an attempt to create robust and reliable brain decoding systems. In this direction, Geometric Deep Learning is a highly promising concept for combining the benefits of graph signal processing and deep learning towards revolutionising Brain-Computer Interfaces (BCIs). However, its exploitation has been hindered by its data-demanding character. As a remedy, we propose here a novel data augmentation approach that combines the multiplex network modelling of multichannel signal with a graph variant of the classical Empirical Mode Decomposition (EMD), and which proves to be a strong asset when combined with Graph Convolutional Neural Networks (GCNNs). As our graph-EMD algorithm makes no assumptions with respect to linearity and stationarity, it appears as an appealing solution towards analysing brain signals without artificially imposing regularities in either temporal or spatial domain. Our experimental results indicate that the proposed scheme for data augmentation leads to substantial improvement when it is combined with GCNNs. Using recordings from two distinct BCI applications and comparing against a state-of-the-art augmentation method, we illustrate the benefits from its use. By making it available to BCI community, we hope to further foster the application of geometric deep learning in the field.

Realising the decomposition of a multi‐frequency signal under the coloured noise background by the adaptive stochastic resonance in the non‐linear system with periodic potential

The authors investigate a multi-frequency signal which is decomposed failure by the traditional empirical mode decomposition (EMD) method. Moreover, the multi-frequency signal submerged in the coloured noise increases the difficulty in signal decomposition. As a result, this noisy signal is decomposed unsuccessfully by the cooperation of the adaptive stochastic resonance (SR) in the classic bistable system and EMD. Then, a method combined adaptive SR in the periodic potential system and EMD is put forward to realise the decomposition. Meanwhile, the random particle swarm optimisation algorithm is applied to reach the optimal situation when signal-to-noise ratio attains the maximum value. Different simulation results verify the effectiveness of the proposed method. The proposed method might be useful in dealing with signal processing problems.

Fractional empirical mode decomposition energy entropy based on segmentation and its application to the electrocardiograph signal

The generalized fractional entropy is a powerful tool for allowing an high sensitivity to the signal evolution, which is available to depict the dynamics of complex systems. Besides, empirical mode decomposition (EMD) energy entropy has received largely extensive attention, such as the field of roller bearing fault diagnosis. In this paper, we change the perspective of research and propose an improved EMD energy entropy built on the theory of the generalized fractional entropy, that is, fractional EMD energy entropy. Furthermore, we also combine the proposed method with new multi-scale algorithm based on the segmentation ideas. In order to show the advantages of this particular method for detecting the complexity of systems, several simulated time series and electrocardiograph (ECG) signal experiments are chosen to examine the performance of them. Through experiments, we find that the new fractional EMD energy entropy shows a better characteristic in the complexity analysis of dynamical systems compared with the classical EMD energy entropy. Moreover, the results reveal that tuning the fractional order allows a higher sensitivity to the series fluctuation. In addition, when the experiment bonds with the multi-scale algorithm based on segmentation, we can obtain more abundant complexity properties of time series through fractional EMD energy entropy. Also, it can effectively discriminate the differences in the complexity of different time series, whereas the original method does not have such good advantages. Especially when applied to ECG signals, this new method can be more effective to distinguish between healthy people and patients with heart disease, which is a valuable advantage. Beyond all that, results of the test on surrogate data generated by randomizing series also further strengthen our summing-up.

Fault Feature Extraction of Single-Channel Signal from Gearbox Based on EEMD and CICA

Background: Single-channel observed signal analysis based on independent component analysis (ICA) model belongs to the extremely underdetermined blind source separation (BBS) problem. Method: In order to extract the fault feature hidden in the single-channel measured signal from multi-stage gearbox, a joint approach of fault feature extraction based on ensemble empirical mode decomposition (EEMD) and constrained independent component analysis (CICA) is proposed. The single-channel vibration fault signal is decomposed into several intrinsic mode functions (IMFs) by EEMD, which can overcome the shortcomings of classical empirical mode decomposition (EMD). By computing the kurtosis and correlation coefficients of each IMF, we can select some suitable IMFs to construct a newly observed vector combined with the original signal, which meets the requirement of CICA algorithm. Finally, the suitable reference signal including faulty gear meshing frequency is generated, and the desired gear low frequency slight feature is extracted by CICA combined with envelope analysis. Conclusion: Through the experiment analysis of fault feature extraction with a missing tooth on the low speed gear pairs, the effectiveness and applicability of the proposed method are verified. Keywords: Gearbox, single-channel measured signal, ensemble empirical mode decomposition (EEMD), constrained independent component analysis (CICA), fault feature extraction, FFT spectrum.

Ultra-Short-Term Multistep Wind Power Prediction Based on Improved EMD and Reconstruction Method Using Run-Length Analysis

With larger scale wind farm being connected to the power grid, the high-precision wind power prediction has become an important means which can ensure the safe operation of power system. The large fluctuations or abnormal data which exist in the local wind power sequences may lead to the phenomenon of over-iterative decomposition of the classical empirical mode decomposition (EMD). In response to this defect, first, the raw wind power sequences are decomposed using improved EMD with introducing the weight function and modifying the mean judgment condition in the classical EMD. Then, the reconstruction strategy based on run-test analysis is proposed based on the fluctuation characteristics of the decomposed components. Finally, the ultra-short-term prediction of the high-frequency item, the middle-frequency item, the low-frequency item, and the trend item in the reconstruction sequences are performed according to different prediction methods. The wind power data of three wind farms in northeast China were selected for forecasting analysis. The analysis shows that compared with other classical prediction methods, this method can effectively improve the prediction accuracy and verify the effectiveness of the proposed method.

Feature extraction of power transformer vibration signals based on empirical wavelet transform and multiscale entropy

To achieve an effective feature extraction for power transformer vibration signals, the authors propose a method for signal feature extraction based on empirical wavelet transform (EWT) and multiscale entropy (MSE). First, transformer vibration signals are decomposed into several empirical wavelet functions (EWFs) with the method of EWT. Then, the frequency characteristics of signals are demonstrated in the time-frequency representation by applying a Hilbert transform to each EWF component. Finally, in order to quantify the extracted features, the MSEs of components being highly correlated with the original signals are calculated to construct the eigenvectors of transformer vibration signals. Several experiments are presented showing the effectiveness of this method compared with the classic empirical mode decomposition method.

An optimized time varying filtering based empirical mode decomposition method with grey wolf optimizer for machinery fault diagnosis

A time varying filtering based empirical mode decomposition (EMD) (TVF-EMD) method was proposed recently to solve the mode mixing problem of EMD method. Compared with the classical EMD, TVF-EMD was proven to improve the frequency separation performance and be robust to noise interference. However, the decomposition parameters (i.e., bandwidth threshold and B-spline order) significantly affect the decomposition results of this method. In original TVF-EMD method, the parameter values are assigned in advance, which makes it difficult to achieve satisfactory analysis results. To solve this problem, this paper develops an optimized TVF-EMD method based on grey wolf optimizer (GWO) algorithm for fault diagnosis of rotating machinery. Firstly, a measurement index termed weighted kurtosis index is constructed by using kurtosis index and correlation coefficient. Subsequently, the optimal TVF-EMD parameters that match with the input signal can be obtained by GWO algorithm using the maximum weighted kurtosis index as objective function. Finally, fault features can be extracted by analyzing the sensitive intrinsic mode function (IMF) owning the maximum weighted kurtosis index. Simulations and comparisons highlight the performance of TVF-EMD method for signal decomposition, and meanwhile verify the fact that bandwidth threshold and B-spline order are critical to the decomposition results. Two case studies on rotating machinery fault diagnosis demonstrate the effectiveness and advantages of the proposed method.

The application of EMD-based methods for diagnosis of winding faults in a transformer using transient and steady state currents

The application of signal processing techniques is a fundamental step for fault diagnostic methodologies. The application of empirical mode decomposition (EMD)-based methods such as classic EMD, ensemble EMD (EEMD), and complete EEMD (CEEMD) is presented in this work for the analysis of inrush current signals. This analysis leads to the detection of short-circuited turns in transformers. Results show that CEEMD provides the best performance, as it readily extracts the information related to the fault, requiring of acceptable computational resources. Actual inrush current signals of a transformer with short-circuited turns are also considered. The number of short-circuited turns ranges from 5 to 40. Useful indices, such as the Shannon Entropy, Energy, and root-mean-square value, are obtained from the information provided by the CEEMD approach. These indices are analyzed for both the transient state and the steady state of the current signals, providing the proper quantification of the fault severity.

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

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.