Performance Of Empirical Mode Decomposition Research Articles

Spline manipulations for empirical mode decomposition (EMD) on bounded intervals and beyond

Empirical mode decomposition (EMD), introduced by N.E. Huang et al. in 1998, is perhaps the most popular data-driven computational scheme for the decomposition of a non-stationary signal or time series f(t), with time-domain R:=(−∞,∞), into finitely many oscillatory components {f1(t),⋯,fK(t)}, called intrinsic mode functions (IMFs), and some “almost monotone” remainder r(t), called the trend of f(t). The core of EMD is the iterative “sifting process” applied to each function mk−1(t) to compute fk(t), for k=1,⋯,K, where m0(t):=f(t) and mk(t):=mk−1(t)−fk(t), with trend r(t):=mK(t). For the computation of each IMF, the sifting process depends on cubic spline interpolation of the local maxima and local minima for computing the upper and lower envelopes, respectively, and on subtracting the mean of the two envelopes from the result of the previous iterative step. Since it is not feasible to search for all local extrema in the entire time-domain (−∞,∞), implementation of the sifting process is commonly performed on some desired truncated bounded interval [a,b]. The main objective of this paper is to introduce and develop four “cubic spline manipulation engines”, called “quasi-interpolation (QI)”, “enhanced quasi-interpolation (EQI)”, “local interpolation (LI)”, and “improved global interpolation (IGI)” cubic spline manipulation engines, in order to significantly improve the performance of EMD on the truncated time-domains with minimal boundary artifacts, computational efficiency, accuracy, and consistency. Introduction and construction of the “fundamental quasi-interpolation” (FQI) splines as basis functions of the QI manipulation engine eliminates the need of matrix inversion for computing (global) cubic spline interpolation, since the local maximum values and local minimum values are used as coefficients of their FQI spline series representations, respectively. For the EQI spline manipulation engine, the FQI functions are formulated in terms of the same cubic B-spline basis for both the upper and lower envelopes; and for the LI spline manipulation engine, the “cubic spline blending” operation is applied to further modify the FQI splines to enable true cubic spline interpolation by “correcting the approximate interpolation error” of the EQI engine. As a consequence, the EQI and LI manipulation engines have the common property that in computing the means of the upper and lower envelopes, the only computation is averaging the B-spline coefficients, instead of computing the upper and lower envelopes separately. Furthermore, fast cubic spline pre-processing of the given f(t) is also introduced to assure numerical stability in the computation of the Hilbert transform of the first IMF f1(t) on the truncated time-domain. The theory, along with methods and explicit formulas, developed in this paper are intended for other applications beyond EMD.

Improving speech communication in the age of face masks: A study on EMD denoising method by subjective speech comparison

The widespread use of face masks during the COVID-19 pandemic has posed challenges to effective communication. This study investigates the application of the Empirical Mode Decomposition (EMD) denoising method to enhance the quality of acoustic signals affected by face masks. The EMD technique utilizes a Fast Fourier transform (FFT) of the intrinsic mode function to distinguish noise from the signal and improve the acoustic signal. The EMD-enhanced speech signal is compared to the acquired speech signal using Comparison Mean Opinion Scores (CMOS), and the spectral subtraction speech enhancement signal is also evaluated using CMOS. The results from various experimental conditions consistently demonstrate the superior performance of EMD denoising in producing enhanced signals. Specifically, the EMD method outperforms the spectral subtraction method in improving speech signal quality affected by face masks. These findings underscore the effectiveness of the EMD denoising method in improving the quality of speech signals impacted by face masks, highlighting its potential for enhancing communication in challenging acoustic environments.

Performance of Empirical Mode Decomposition for Frequency Identification in SSVEP Based BCI.

Empirical mode decomposition based conventional correlation (EMDCC) method is proposed to identify the frequency components in steady state visual evoked potentials (SSVEP) in electroencephalogram(EEG).The main aim of the proposed EMDCC method is to recognise narrow band frequency components that are present in SSVEP. The study is evaluated on two datasets. The first one is a 40 target benchmark dataset obtained from 35 subjects and the second is a 4 class Inhouse dataset collected from 10 healthy participants. The mean detection accuracy of the conventional correlation method is 85.64 % for the benchmark dataset and it is improved to 93.79 % in the proposed method. The mean detection accuracy of the conventional correlation method is 67.5 % for the Inhouse dataset and it is increased to 82.5 % in the proposed method. The mean detection accuracy of the proposed EMDCC method is also compared to time-weighting canonical correlation analysis (TWCCA) for the benchmark dataset. The mean detection accuracy of TWCCA is 91.04 %. Hence the results show better detection accuracies in the proposed EMDCC method than the simple conventional correlation method and also the existing TWCCA method.

A novel hybrid short-term electricity forecasting technique for residential loads using Empirical Mode Decomposition and Extreme Learning Machines

In recent years, the residential load forecasting problem has been gaining renewed interest due to the advent of Smart Meters and Data Analytics. A novel hybrid method based on Empirical Mode Decomposition (EMD) in tandem with Extreme Learning Machine (ELM) is proposed in this paper to improve the forecast accuracy of residential load signals derived from Smart Meter data. Three state-of-the-art machine learning methods, namely Artificial Neural Network (ANN), Support Vector Regression (SVR), and ELM, are selected for performance comparison. It is observed from the results that the proposed method is found effective in picking the peaks that are usually present in residential loads and hence improved the forecast accuracy. Further, the results show that the performance of EMD based models is improved when the test data is characterized by more peaks. Smart*, a public dataset containing residential load measurements, is used for evaluation.

Automatic Expansion of Voltage Signals Using Empirical Mode Decomposition for Voltage Sag Detection

Voltage sag is one of the most harmful power quality issues. In practical engineering, harmonic interference and noise interference problems will bring big challenges to the analysis of voltage signals. These disturbances can easily lead to a delay or even false detection of the voltage signal. To address this problem, adaptive processing and diagnosis methods of the voltage signal, such as the Empirical Mode Decomposition (EMD) and the Variational Mode Decomposition (VMD), have become a research hotspot. In order to overcome the interference of voltage harmonic and achieve rapid voltage sag detection, this paper first analyzes the performance of EMD and VMD in decomposing voltage sag signals. Then, a tailored EMD-based adaptive voltage signal expansion method for real-time voltage sag detection is proposed. The sampling voltage signal is automatically expanded using the real-time voltage signal to achieve the rapid detection of voltage sag under complex operational environments. Numerical results illustrate the effectiveness of the proposed method.

Enterprise financial management and trend prediction based on time series analytics and edge computing

In order to improve the prediction accuracy and reliability of long‐term financial trend, a financial time series prediction framework is proposed by combining empirical mode decomposition (EMD) and reduced support vector regression (SVR). Through the empirical mode decomposition, the framework can eliminate the disturbance caused by the multi band information of error sequence. The financial time series processed by EMD are used to train a reduced support vector regression model. Compared with classical support vector regression, the reduced support vector regression can discarded the samples, which would not become support vectors, to reduce the scale of problem. Therefore, the reduced support vector regression is much faster than support vector regression and is more suitable for edge computing. The experiments on benchmark dataset show that empirical mode decomposition plus reduced support vector regression can reach the close performance of empirical mode decomposition plus support vector regression, meanwhile running time only costs less than one fortieth of empirical mode decomposition plus support vector regression's.

Analysis of in-flight cabin vibration of a turboprop airplane by proposing a novel noise-tolerant signal decomposition method

Vibration in passenger cabins of turboprop airplanes is a serious challenge. One of the essential steps in studying the cabin vibrations is to determine the contributing sources of vibration. The vibration signals are highly nonstationary and noisy. Therefore, one may require a noise-tolerant signal processing method for decomposition of the signals. In this article, the wavelet-based empirical mode decomposition is introduced for the first time to improve the performance of the traditional empirical mode decomposition in dealing with noise. Unlike the traditional empirical mode decomposition that extracts the signal trend by averaging the upper and lower envelopes intersecting local maxima and minima of the signal, the wavelet-based empirical mode decomposition directly extracts the signal trend by applying the multilevel wavelet decomposition of the consecutive approximations within the sifting process. Numerical studies are undertaken to evaluate the effect of noise on the performance of the empirical mode decomposition and wavelet-based empirical mode decomposition. Also, comparisons are made between the methods at dissimilar noise powers based on the orthogonality, integral, and energy decomposition criteria. The results indicate that both methods generate similar results in the absence of noise. Considering the number of obtained intrinsic mode functions, decomposition quality criteria, and computational cost, however, the wavelet-based empirical mode decomposition outperforms the classic method at higher noise levels. In this article, the wavelet-based empirical mode decomposition is used for analysis of in-flight airplane cabin vibration. A 52-passenger turboprop aircraft is equipped with eight triaxial piezoelectric accelerometers, and several flight tests are performed to acquire in-flight vibration signals within the passenger cabin. The proposed wavelet-based empirical mode decomposition is applied to the experimental data. Then, the amplitudes and frequencies of the intrinsic mode functions are examined. Finally, the probable vibration sources are identified based on the intrinsic mode functions characteristics.

Detection of Consumer Preferences Using EEG Signals

In this study, a liking estimation system based on electroencephalogram (EEG) signals is developed for neuromarketing applications. The determination of the degree of appreciation of a product by consumers has become an important research topic using machine learning methods. Biological data is recorded while viewing product pictures or videos, then processed by signal processing methods. In this study, 32 channel EEG signals are recorded from subjects who watched two different car advertisement videos and the liking status is determined. After watching the advertisement videos, the participants were asked to vote for the rating of the different images (front view, dashboard, side view, rear view, taillight, logo and grille) of the products. The signals corresponding to these different video regions from the EEG recordings were segmented and analyzed by the Empirical Mode Decomposition (EMD) and Ensemble Empirical Mode Decomposition (EEMD). The statistical features were extracted from Intrinsic Mode Functions (IMF) and the liking status classifications were performed. The classification performance of EMD- and EEMD-based methods are 93.4% and 97.8% respectively on Brand1, and 93.5% and 97.4% respectively on Brand2. In addition, the classification accuracy on both brands combined are 85.1% and 85.7% respectively. The promising results obtained using Support Vector Machines (SVM) show that the proposed EEG-based method may be used in neuromarketing studies.

Complete Ensemble Empirical Mode Decomposition on FPGA for Condition Monitoring of Broken Bars in Induction Motors

Empirical mode decomposition (EMD)-based methods are powerful digital signal processing techniques because they do not need a priori information of the target signal due to their intrinsic adaptive behavior. Moreover, they can deal with non-linear and non-stationary signals. This paper presents the field programmable gate array (FPGA) implementation for the complete ensemble empirical mode decomposition (CEEMD) method, which is applied to the condition monitoring of an induction motor. The CEEMD method is chosen since it overcomes the performance of EMD and EEMD (ensemble empirical mode decomposition) methods. As a first application of the proposed FPGA-based system, the proposal is used as a processing technique for feature extraction in order to detect and classify broken rotor bar faults in induction motors. In order to obtain a complete online monitoring system, the feature extraction and classification modules are also implemented on the FPGA. Results show that an average effectiveness of 96% is obtained during the fault detection.

Partial ensemble approach to resolve the mode mixing of extreme-point weighted mode decomposition

Empirical mode decomposition (EMD) is an effective tool for breaking down components (modes) of a nonlinear and non-stationary signal. Recently, a newly adaptive signal decomposition method, namely extreme-point weighted mode decomposition (EWMD), was put forward to improve the performance of EMD, in particular, to resolve the over- or undershooting issue associated with the large amplitude variations. However, similar to EMD, EWMD also suffers the mode mixing problem caused by intermittence or noisy signals. In this paper, inspired by complementary ensemble EMD (CEEMD), a noise-assisted data analysis method called partial ensemble extreme-point weighted mode decomposition (PEEWMD) is proposed to eliminate the mode mixing problem and enhance the performance of EWMD. In the proposed PEEWMD method, firstly white noises in pairs are added to the targeted signal and then the noisy signals are decomposed using the EWMD method to obtain the intrinsic mode functions (IMFs) in the first several stages. Secondly, permutation entropy is employed to detect the components that cause mode mixing. The residual signal is obtained after the identified components are separated from the original signal. Lastly, the residual signal is fully decomposed by using the EWMD method. The proposed PEEWMD method is compared with original EWMD, ensemble EWMD (EEWMD) and CEEMD using simulated signals. The results demonstrate that PEEWMD can effectively restrain the mode mixing issue and generates IMFs with much better performance. Based on that the PEEWMD and envelope power spectrum based fault diagnosis method was proposed and applied to the rubbing fault identification of rotor system and the fault diagnosis of rolling bearing with inner race. The result indicates that the proposed method of fault diagnosis gets much better effect than EMD and EWMD.

Extraction of Fault Features of Machinery Based on Fourier Decomposition Method

Separations of close-frequency signal components are important for accurate diagnosis of machinery faults. Conventional methods for processing vibration signals of defective machinery can be divided into adaptive methods and parametric methods. Empirical mode decomposition (EMD), an adaptive method, suffers from a bottleneck of performance in adaptively separating close-frequency signal components. Parametric methods, such as ensemble EMD (EEMD) and variational mode decomposition (VMD), face difficulties in parameter setting. As a result, these conventional methods demonstrate limited capabilities to extract fault features from machinery vibration signals. To overcome these deficiencies, this paper proposes a novel method for extraction of fault features of machinery based on Fourier decomposition method (FDM). Firstly, this paper demonstrates adaptive narrow-band filtering properties of FDM both in low frequency and in high frequency by examining Gaussian white noise. Afterwards, this paper numerally proves that FDM can transcend the bottleneck of performance of EMD in adaptively separating close-frequency signal components. Furthermore, the proposed method is compared with the method based on EMD, EEMD or VMD by investigating a turbine gearbox vibration signal. The results show that the proposed method outperforms the others in feature extraction of machinery vibration signals.

A Generalized Framework of Adaptive Mode Decomposition

As an effective tool for nonlinear and non-stationary signal separation method, empirical mode decomposition (EMD) has attracted a lot of attention of many scholars and has been successfully applied to many engineering areas. Since the kernel of EMD is to define a baseline and then implement the sift process, it is important to select an appropriate baseline to improve the performance of EMD for an accurate decomposition. However, it is difficult to choose the most suitable method for dealing with a given arbitrary signal. Besides, the baseline constructed through the existing methods generally does not equal the expected one. To address these problems, we propose a new generalized framework for adaptive mode decomposition (GF-AMD) based on EMD, in which the optimal baseline is firstly chosen from different ones and a weighted factor is introduced to adjust the baseline for getting the optimal one. Then the optimal baseline is implemented to the sift process of EMD. Two simulation signals are used to verify the effectiveness and superiority to EMD. Finally, the proposed GF-AMD method is applied to the vibration signal analysis of faulty rotary machinery by comparing with EMD method and the analysis results indicate its effect and superiority.

Improving the performance of empirical mode decomposition via Tsallis entropy: Application to Alzheimer EEG analysis.

Alzheimer is a degenerative disorder that attacks neurons, resulting in loss of memory, thinking, language skills, and behavioral changes. Computer-aided detection methods can uncover crucial information recorded by electroencephalograms. A systematic literature search presents the wavelet transform as a frequently used technique in Alzheimer's detection. However, it requires a defined basis function considered a significant problem. In this work, the concept of empirical mode decomposition is introduced as an alternative to process Alzheimer signals. The performance of empirical mode decomposition heavily relies on a parameter called threshold. In our previous works, we found that the existing thresholding techniques were not able to highlight relevant information. The use of Tsallis entropy as a thresholder is evaluated through the combination of empirical mode decomposition and neural networks. Thanks to the extraction of better features that boost the classification accuracy, the proposed approach outperforms the state-of-the-art in terms of peak signal to noise ratio and root mean square error. Hence, our methodology is more likely to succeed than methods based on other landmarks such as Bayes, Normal and Visu shrink. We finally report an accuracy rate of 80%, while the aforementioned techniques only yield performances of 65%, 60% and 40%, respectively.

An improved empirical mode decomposition method using second generation wavelets interpolation

Empirical mode decomposition (EMD) may generate undesirable intrinsic mode functions (IMFs) under low sampling rate, which can significantly affect the results of decomposition. In this paper, an improved EMD method using second generation wavelets interpolation is presented which can eliminate undesirable IMFs and reduce the scale mixing effectively under low sampling rate. Firstly, the original signal under low sampling rate is reconstructed by inverse process of second generation wavelets lifting algorithm. Secondly, the location algorithm of extrema using second generation wavelets is given to obtain the accurate position of extrema. Finally, five examples are demonstrated to justify the effectiveness. Numerical simulation and experimental results are attained to show the effectiveness of the proposed method in eliminating undesirable IMFs and reducing the scale mixing, thereby making the proposed improved EMD a promising method for improving the performance of EMD under low sampling rate.

Improvement of Decomposing Results of Empirical Mode Decomposition and its Variations for Sea-level Records Analysis

ABSTRACT Lee, H.S., 2018. Improvement of decomposing results of empirical mode decomposition and its variations for sea-level records analysis. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 526–530. Coconut Creek (Florida), ISSN 0749-0208. The performance of empirical mode decomposition (EMD) and its variations such as ensemble EMD (EEMD), complete EEMD with adaptive noise (CEEMDAN) and improved CEEMDAN (impCEEMDAN) are tested using artificial signal tests. In the artificial signal test, intrinsic mode functions (IMFs) are obtained using EMD, EEMD, CEEMDAN, and impCEEMDAN and then compared to prescribed oscillations in an artificial a priori known signal. In all cases, extra and redundant modes are found due to residual noises. Furthermore, the low frequency modes are generally distorted. To overcome this problem a novel approach for reconstructing IMFs is p...

Complex Variational Mode Decomposition for Slop-Preserving Denoising

We have introduced a new decomposition method for seismic data, termed complex variational mode decomposition (VMD), and we have also designed a new filtering technique for random noise attenuation in seismic data by applying the VMD on constant-frequency slices in the frequency–offset ( $f$ – $x$ ) domain. The motivation behind this paper is to overcome the potential low performance of empirical mode decomposition (EMD) for energy preservation of the steeply dipping events when used for noise attenuation, and low resolution when used for signal decomposition. The VMD is proposed to decompose a signal into an ensemble of band-limited modes. For seismic data consisting of linear events, the constant-frequency slices of its $f$ – $x$ spectrum are exactly band-limited. The noise attenuation algorithm is summarized as follows. First, the Fourier transform is applied on the time axis of the 2-D seismic data. Next, the VMD is applied on each frequency slice of the $f$ – $x$ spectrum and the decomposed modes are combined to obtain the filtered frequency slice. Finally, an inverse Fourier transform is applied on the frequency axis of the $f$ – $x$ spectrum to obtain the denoised result. The resulting VMD-based noise attenuation method is equivalent to applying a Wiener filter on each decomposed mode, which is achieved during the decomposition progress. We also applied 2-D VMD on 3-D seismic data for denoising. Numerical results show that the proposed VMD-based method achieves a higher denoising quality than both the $f$ – $x$ deconvolution method and the EMD-based denoising method, especially for preserving the steep slopes.

Features Of Sleep Apnea Recognition And Analysis

abstract Sleep apnea is a growing sleep disorder issue and estimate to affect 7% of the adult population in Malaysia. In this study, the electrical activity of the brain is studied using Electroencephalogram (EEG). The data obtained was then decomposed using three methods; Empirical Mode Decomposition (EMD), Bivariate EMD and finally Ensemble EMD. The Index of Orthogonatility (IO) was obtained which shows EMD performed the most poorly, EEMD the best and Bivariate in between. The performance of EMD greatly improves when the number of samples was greatly decreased and very high peaks and more complex parts of the signal were excluded in the analysis. Segmentation was also conducted and the segmentation error revealed when an Event Related Potential (ERP) has happened which is when apnea occurred.

Short Term Wind Power Prediction Based on Improved Kriging Interpolation, Empirical Mode Decomposition, and Closed-Loop Forecasting Engine

The growing trend of wind generation in power systems and its uncertain nature have recently highlighted the importance of wind power prediction. In this paper a new wind power prediction approach is proposed which includes an improved version of Kriging Interpolation Method (KIM), Empirical Mode Decomposition (EMD), an information-theoretic feature selection method, and a closed-loop forecasting engine. In the proposed approach, EMD decomposes volatile wind power time series into more smooth and well-behaved components. To enhance the performance of EMD, Improved KIM (IKIM) is used instead of Cubic Spline (CS) fitting in it. The proposed IKIM includes the von Karman covariance model whose settings are optimized based on error variance minimization using an evolutionary algorithm. Each component obtained by this EMD decomposition is separately predicted by a closed-loop neural network-based forecasting engine whose inputs are determined by an information-theoretic feature selection method. Wind power prediction results are obtained by combining all individual forecasts of these components. The proposed wind power forecast approach is tested on the real-world wind farms in Spain and Alberta, Canada. The results obtained from the proposed approach are extensively compared with the results of many other wind power prediction methods.

Denoising of Raman spectroscopy for biological samples based on empirical mode decomposition

Raman spectroscopy of biological samples presents undesirable noise and fluorescence generated by the biomolecular excitation. The reduction of these types of noise is a fundamental task to obtain the valuable information of the sample under analysis. This paper proposes the application of the empirical mode decomposition (EMD) for noise elimination. EMD is a parameter-free and adaptive signal processing method useful for the analysis of nonstationary signals. EMD performance was compared with the commonly used Vancouver algorithm (VRA) through artificial data (Teflon), synthetic (Vitamin E and paracetamol) and biological (Mouse brain and human nails) Raman spectra. The correlation coefficient ([Formula: see text]) was used as performance measure. Results on synthetic data showed a better performance of EMD ([Formula: see text]) at high noise levels compared with VRA ([Formula: see text]). The methods with simulated fluorescence added to artificial material exhibited a similar shape of fluorescence in both cases ([Formula: see text] for VRA and [Formula: see text] for EMD). For synthetic data, Raman spectra of vitamin E were used and the results showed a good performance comparing both methods ([Formula: see text] for EMD and [Formula: see text] for VRA). Finally, in biological data, EMD and VRA displayed a similar behavior ([Formula: see text] for EMD and [Formula: see text] for VRA), but with the advantage that EMD maintains small amplitude Raman peaks. The results suggest that EMD could be an effective method for denoising biological Raman spectra, EMD is able to retain information and correctly eliminates the fluorescence without parameter tuning.

An effective secondary decomposition approach for wind power forecasting using extreme learning machine trained by crisscross optimization

Large-scale integration of wind energy into electric grid is restricted by its inherent intermittence and volatility. So the increased utilization of wind power necessitates its accurate prediction. The contribution of this study is to develop a new hybrid forecasting model for the short-term wind power prediction by using a secondary hybrid decomposition approach. In the data pre-processing phase, the empirical mode decomposition is used to decompose the original time series into several intrinsic mode functions (IMFs). A unique feature is that the generated IMF1 continues to be decomposed into appropriate and detailed components by applying wavelet packet decomposition. In the training phase, all the transformed sub-series are forecasted with extreme learning machine trained by our recently developed crisscross optimization algorithm (CSO). The final predicted values are obtained from aggregation. The results show that: (a) The performance of empirical mode decomposition can be significantly improved with its IMF1 decomposed by wavelet packet decomposition. (b) The CSO algorithm has satisfactory performance in addressing the premature convergence problem when applied to optimize extreme learning machine. (c) The proposed approach has great advantage over other previous hybrid models in terms of prediction accuracy.