PERFORMANCE EVALUATION OF ENSEMBLE EMPIRICAL MODE DECOMPOSITION

Various faults inevitably occur in mechanical systems and may result in unexpected failures. Hence, fault detection is critical to reduce unscheduled downtime and costly breakdowns. Empirical mode decomposition (EMD) is an adaptive time-frequency domain signal processing method, potentially suitable for nonstationary and/or nonlinear processes. However, the EMD method suffers from several problems such as mode mixing, defined as intrinsic mode functions (IMFs) with incorrect scales. In this paper, an ensemble noise-reconstructed EMD method is proposed to ameliorate the mode mixing problem and denoise IMFs for enhancing fault signatures. The proposed method defines the IMF components as an ensemble mean of EMD trials, where each trial is obtained by sifting signals that have been reconstructed using the estimated noise present in the measured signal. Unlike traditional denoising methods, the noise inherent in the input data is reconstructed and used to reduce the background noise. Furthermore, the reconstructed noise helps to project different scales of the signal onto their corresponding IMFs, instrumental in alleviating the mode mixing problem. Two critical issues concerned in the method, i.e., the noise estimation strategy and the number of EMD trials required for denoising are discussed. Furthermore, a comprehensive noise-assisted EMD method is proposed, which includes the proposed method and ensemble EMD (EEMD). Numerical simulations and experimental case studies on accelerometer data collected from an industrial shaving process are used to demonstrate and validate the proposed method. Results show that the proposed method can both detect impending faults and isolate multiple faults. Hence, the proposed method can act as a promising tool for mechanical fault detection.

Empirical mode decomposition (EMD) is a powerful tool for the non-stationary and nonlinear signal analysis and has attracted considerable attention recently. However, one of primary problems existing in the EMD is the mode mixing, which makes the physical meaning of decomposition results obscure. The ensemble EMD (EEMD) is presented to alleviate the shortcoming. The EEMD is a noise-added method and can extract the components with truly physical meaning from the signal. Firstly, a simulation signal is used to test the performance of the EEMD; compared with the EMD, the EEMD illustrates the superiority over the EMD. Then, the fault diagnosis method based on the EEMD is applied to diagnose the faults of the gearbox with multiple faults and successfully extracts the multiple faults information from the collected signal. The results show that the fault diagnosis method based on the EEMD is a promising method for the fault diagnosis of gearboxes.

Empirical mode decomposition (EMD) is a widely used adaptive signal processing method, which has shown some shortcomings in engineering practice, such as sifting stop criteria of intrinsic mode function (IMF), mode mixing and end effect. In this paper, an improved sifting stop criterion based on the valid data segment is proposed, and is compared with the traditional one. Results show that the new sifting stop criterion avoids the influence of end effects and improves the correctness of the EMD. In addition, a novel AEMD method combining the analysis mode decomposition (AMD) and EMD is developed to solve the mode-mixing problem, in which EMD is firstly applied to dispose the original signal, and then AMD is used to decompose these mixed modes. Then, these decomposed modes are reconstituted according to a certain principle. These reconstituted components showed mode mixing phenomena alleviated. Model comparison was conducted between the proposed method with the ensemble empirical mode decomposition (EEMD), which is the mainstream method improved based on EMD. Results indicated that the AEMD and EEMD can effectively restrain the mode mixing, but the AEMD has a shorter execution time than that of EEMD.

Application of the EEMD method for distinction and suppression of motion-induced noise in grounded electrical source airborne TEM system

Time-frequency analysis is of necessity for wrist pulse signal due to its complexity, among which, empirical mode decomposition (EMD) algorithm and its improved noise-assisted versions (such as ensemble EMD, noise-assisted multivariate EMD (NA-MEMD) and very recently median EMD) are deemed to be the most representative ones. In this study, we provide an in-depth evaluation of these well-established noise-assisted EMD algorithms in computational pulse analysis for the first time. In particular, we compare the performance of the different algorithms systematically and quantitatively based on objective quantitative criteria: number and central frequency of intrinsic mode function (IMF) components, total orthogonality index and mode mixing. Rather than using synthetic signals with visual inspection in most existing literature, the wrist pulse signals used in the evaluation are real recorded samples acquired from both healthy and patient subjects. Through extensive experiments, we found that: 1) Advanced EMD algorithm that has the best performance in other areas may not be the most suitable method for pulse signal analysis, which indicates its high dependence on the type of signal to be analyzed; 2) Adding noise can significantly improve algorithm performance, but tends to produce physiologically not relevant components, which however are usually neglected throughout the intelligent pulse diagnosis literature. Therefore, excluding redundant components and then extracting features is expected to improve performance further. Together, currently NA-MEMD achieves a better performance consistently, potential to become a powerful tool for computational pulse analysis, which in itself have not been applied in wrist pulse analysis before. We believe our works can bring up a new perspective to application of EMD-like algorithms in computational pulse analysis/diagnosis with effective information and guidance. Additionally, considering the similarity between physiological signals, especially such as photoplethysmogram/electrocardiogram, our research can be extended to wearable health monitoring technologies, including smart watches and fitness trackers, and their potential future applications, such as in heart rate estimation and evaluate various cardiovascular-related diseases. The present study underscored the necessity of evaluation noise-assisted EMDs or other adaptive decomposition algorithms based on real recorded signals with more objective measures. Especially, caution the possible redundant components that are introduced.

Application of the spectral analysis technique Ensemble Empirical Mode Decomposition (EEMD) to hydroclimatic time series produces an orthogonal set of decreasing frequency Intrinsic Mode Functions (IMFs) and a residual (or trend). As the EEMD algorithm is locally adaptive it is suitable for decomposing time series that appear non-stationary in terms of mean and variance: characteristics that are not uncommon in hydroclimatic series. EEMD utilises ensemble averaging to overcome the mode mixing problem observed in traditional Empirical Mode Decomposition (EMD). Here EEMD is briefly outlined and issues relating to the calculation of the Hilbert spectrum from EEMD output are discussed. EEMD is then applied to three climatic indices relevant to Australian hydroclimatic variability, namely the Southern Oscillation Index, Indian Ocean Dipole mode index and the Tasman Sea Index. Analysis of these indices reveals EEMD is capable of identifying physical process signals. For example, the known spectral structure of the SOI is identified by the EEMD algorithm. It was observed during analysis of the Indian Ocean Dipole mode index that EMD post processing may introduce end effects previously minimised by the EEMD ensemble average. These effects may inflate existing features, or potentially introduce low frequency artefacts, though this danger can be mitigated through careful examination of the complete Hilbert spectrum. EEMD and Hilbert spectrum analysis of hydroclimatic data provides insight into long-term trends, dominant frequencies and changes in energy with time for time series that are usually problematic to analyse with traditional spectral analysis techniques. The spectral fingerprints of the climatic indices assessed here are used in a companion paper that looks for those fingerprints within Australian precipitation and temperature data (Srikanthan et al., 2011).

A Hilbert–Huang transform (HHT) is a time–frequency technique and has been widely applied to analyzing vibration signals in the field of fault diagnosis of rotating machinery. It analyzes the vibration signals using intrinsic mode functions (IMFs) extracted using empirical mode decomposition (EMD). However, EMD sometimes cannot reveal the signal characteristics accurately because of the problem of mode mixing. Ensemble empirical mode decomposition (EEMD) was developed recently to alleviate this problem. The IMFs generated by EEMD have different sensitivity to faults. Some IMFs are sensitive and closely related to the faults but others are irrelevant. To enhance the accuracy of the HHT in fault diagnosis of rotating machinery, an improved HHT based on EEMD and sensitive IMFs is proposed in this paper. Simulated signals demonstrate the effectiveness of the improved HHT in diagnosing the faults of rotating machinery. Finally, the improved HHT is applied to diagnosing an early rub-impact fault of a heavy oil catalytic cracking machine set, and the application results prove that the improved HHT is superior to the HHT based on all IMFs of EMD.

Emotion feature extraction is the key to speech emotional recognition. And ensemble empirical mode decomposition(EEMD) is a newly developed method aimed at eliminating emotion mode mixing present in the original empirical mode decomposition(EMD). To evaluate the performance of this new method, this paper investigates the effect of a parameters pertinent to EEMD: speech emotional envelope. Firstly, a speaker emotional envelope features extraction based on EEMD is proposed in the paper. Using the piecewise power function in speech emotional envelope has a better effect in emotional identification. At the same time, the proposed technique has been utilized for classification of fo ur kinds of emotional(angry, happy, sad and neutral) speech signals. Emotional intrinsic mode functions(IMFe) are obtained by empirical mode decomposition on emotional speech signals, the fast fourier transform(FFT) of each intrinsic mode function is extracte d as the emotional feature coefficient which is used in speaker emotional identification applying by vector quantization. MATLAB is used to ca lculate the characteristic of emotional speech signals using empirical mode decomposition (EEMD). We obtain an emotional envelope by transforming the IMFe of emotional speech signals, and obtain a new method of emotion recognition according to different emotional envelop feature vectors. The results indicate the proposed method works well in speaker emotional identification.

Satellite Image Time Series (SITS) have recently been of great interest due to the emerging remote sensing capabilities for Earth observation. Trend and seasonal components are two crucial elements of SITS. In this paper, a novel framework of SITS decomposition based on Ensemble Empirical Mode Decomposition (EEMD) is proposed. EEMD is achieved by sifting an ensemble of adaptive orthogonal components called Intrinsic Mode Functions (IMFs). EEMD is noise-assisted and overcomes the drawback of mode mixing in conventional Empirical Mode Decomposition (EMD). Inspired by these advantages, the aim of this work is to employ EEMD to decompose SITS into IMFs and to choose relevant IMFs for the separation of seasonal and trend components. In a series of simulations, IMFs extracted by EEMD achieved a clear representation with physical meaning. The experimental results of 16-day compositions of Moderate Resolution Imaging Spectroradiometer (MODIS), Normalized Difference Vegetation Index (NDVI), and Global Environment Monitoring Index (GEMI) time series with disturbance illustrated the effectiveness and stability of the proposed approach to monitoring tasks, such as applications for the detection of abrupt changes.

The acquisition of ballistocardiogram (BCG) signals during sleeping always presents all kinds of high-frequency noise, which causes the problem to extract effective signals. This article proposes a new method to extract heartbeat and respiration signals by combining the whale optimization algorithm (WOA) and variational mode decomposition (VMD). Firstly, the sample entropy and energy difference ratio are used as the fitness function of WOA to optimize the penalty factor in the variational mode decomposition a and the number of decomposition layers K;Then the original signal was decomposed into multiple modal components (IMF) by optimized VMD; Finally, respiration and heartbeat signals were reconstructed, and their frequencies got calculated. Compared with the experimental results of empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD), the average respiratory rate error obtained by this algorithm is 0.097 and 0.013 lower than EMD and EEMD respectively, and the average heart rate error is 0.03 and 0.006 lower than EMD and EEMD respectively, it is proved that the algorithm can extract breath and heartbeat signals more effectively and accurately.

The importance of load forecasting has provided valuable information for power grid analysis since the early 2000's. It has been established that no specific load forecasting model can be generalized for all demand types. This study aims to fill the gaps among the plethora of existing mathematical forecasting methods, specifically using the Naive Bayes Theorem. Naive Bayes, by itself, has an issue when dealing with large amounts of input which is the reason it has not been used in load forecasting. The integration of Naive Bayes along with the Ensemble method and Empirical Mode Decomposition provided our Hybridized Naive Bayes Algorithm with adequate improvement in its accuracy given the large amount of input data. The results were justified using key performance indicators MAE, MAPE and MSE. We obtained an average of 34.35 for MSE, 60.72MW for MAE and 4.41% for its MAPE. Although the hybridized Naive Bayes presented in this study is not ready for industrial use, it is very promising due to its mathematical prediction model and even more improvement is highly feasible.

Ensemble empirical mode decomposition (EEMD) is a noise-assisted adaptive data analysis method to solve the problem of mode mixing caused by empirical mode decomposition (EMD). It is shown that the decomposition error tends to zero, as ensemble number increases to infinity in EEMD. In this paper, a novel EEMD-based ridge regression model (REEMD) is proposed, which solves the problem of mode mixing and achieves less decomposition error compared with the EEMD. When the ensemble number is small, the weights of outliers are constraint to zero to reduce the decomposition error in REEMD and the result of REEMD is asymptotic to that of EEMD, as the ensemble number increases. The proposed REEMD is suitable for tissue clutter rejection in color flow imaging system. Simulation shows that reasonable flow-frequency estimations can be achieved by REEMD and the estimation error limits to zero, as the flow frequency increases.

Because of the improvement of optical remote sensing instrument, hyperspectral images now collect information of the ground with hundreds of wavelengths. This spectral information can be used to identify different materials, since each material should have its unique absorption spectrum. Traditionally the spectra was discriminated by measuring either the spectral distance or angle between two spectra directly. However, the remote spectra usually contain noises and interferences from other sources, and even the same material has various spectra. In this case, the conventional measurements may not have the capability enough to tolerate the distortions and to identify each material. In this study, the Ensemble Empirical Mode Decomposition (EEMD) is adopted to measure the similarity between the spectra and discriminate materials. EEMD not only can decompose the spectrum into several components as original Empirical Mode Decomposition (EMD), but also compensating the noises and interferences in the signal as an improved version. Although EEMD is a time-consuming process, its structure is suitable for parallel computing. In this paper we propose a graphic-processing-unit (GPU)-based EEMD on a cluster. Experimental results showed that it can extract the spectral features more effectively than common spectral similarity measures, and it has better ability in characterizing spectral properties. It also demonstrated that the proposed GPU-based high-throughput EEMD achieved a significant 60.62x speedup compared to its CPU-based single-threaded counterpart written in C language.

Electroencephalograph (EEG) is brain activity measurement technique that it is widely used by placing electrode on the scalp. The EEG recording signals are vulnerably contaminated by noise. Thus, it can lead to misperception in analyzing EEG signals. One of the noise that has major influence on the recorded EEG signals is ocular artifacts (OAs). In this paper, a new method to remove OAs automatically is proposed by combining between Complete Ensemble Empirical Mode Decomposition (CEEMD) and Independent Component Analysis (ICA). CEEMD-ICA-OD removes OAs based on the concentration of noise that is calculated by calculating entropy for every CEEMD decomposition. Every selected decomposition of CEEMD will be used as input to the ICA method. Then, ICA will decompose selected CEEMD decomposition into independent components (ICs). Then, Chauvenet Criterion (CC) as Outlier Detection (OD) method is used to detect OAs pattern. Every detected OAs pattern will be eliminated by zeroing process on OAs pattern so that the EEG signal information remains secure. The proposed method were compared with Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD) and Complete EEMD (CEEMD) with zeroing ICA combination for every comparison method. The performance measure of the proposed method and the benchmark method is calculated by using Root Mean Square Error (RMSE) and Signal to Noise Ratio (SNR) to show the performance quality in eliminating OAs. The experiment results show that the proposed method is successfully removing OAs better than the other methods with RMSE value and SNR value are 0.2491 and -0.3449, respectively.

A comparative study between Empirical Wavelet Transforms and Empirical Mode Decomposition Methods: Application to bearing defect diagnosis