Degradation assessment of ball bearings utilizing curvilinear component analysis

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

Recently, ensemble empirical mode decomposition (EEMD) method has been developed for non-linear and non-stationary signal analysis. The method can work on nature signals (non-linear and nonstationary signals) and reduce the speckle noise. With the EEMD method, the signal is decomposed into several intrinsic mode functions (IMFs) and the frequencies of IMFs are arranged in decrease order (high to low) after the EEMD processing. The scaling mode of the EEMD method is similar to wavelet transform, but the signal resolutions in different frequency domains do not decrease by down-sampling. There are a large population and a developed economy in Weihe watershed, the disasters of droughts and floods caused by the autumn precipitation (here is precipitation in September and October) less or more than normal cause great loss and serious influence. In this paper, we propose the EEMD method to decompose the autumn precipitation series in the Weihe river basin during last 50 years into several IMFs, then extract the information including in the precipitation series and get the characteristics of multi-scales. The result shows that it is well response to the autumn precipitation series in the Weihe river basin and to the abrupt climate change in late 1970s and early 1980s of last century. The response appears earlier for high time scales than for low time scales In addition, the expression of the response for high time scales is the form of variability, but it is the amplitude of variability for low time scales.

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.

In this paper a modified ensemble empirical mode decomposition (EEMD) method is presented, which is named winning-EEMD (W-EEMD). Two aspects of the EEMD, the amplitude of added white noise and the number of intrinsic mode functions (IMFs), are discussed in this method. The signal-to-noise ratio (SNR) is used to measure the amplitude of added noise and the winning number of IMFs (which results most frequency) is used to unify the number of IMFs. By this method, the calculation speed of decomposition is improved, and the relative error between original data and sum of decompositions is reduced. In addition, the feasibility and effectiveness of this method are proved by the example of the oceanic internal solitary wave.

Transfer learning for bearing performance degradation assessment based on deep hierarchical features

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.

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.

In order to extract the vibration feature of remanufactured engines, the vibration signal is decomposed by ensemble empirical mode decomposition(EEMD), and this method is applied to study vibration mode of remanufactured engines. Based on the decomposition of vibration signal, correlation coefficient is introduced to study the correlation between IMF(Intrinsic Mode Function) components and original signal, and sensitive factors of IMF components are calculated using correlation coefficients. Hilbert transform is made with sensitive IMF components. The study results show that vibration feature of remanufactured engines is include in IMF components decomposed by EEMD, the vibration modes of remanufactured engines can be differentiated by Hilbert-Huang spectrum and marginal spectrum based on sensitive IMF components. According to vibration feature, the vibration state of remanufactured engines is divided into cylinder wall, cylinder cover and crankshaft vibration modes, which are important to improve the remanufacture level of engines.

Bearings are one of the most frequently used components in the rotatory machinery, so the performance degradation assessment of bearings plays an important role in the prognostics and health management of systems. Hidden Markov model (HMM) is a widely applied data-driven model used for bearing performance degradation assessment and has many successful applications. A normal HMM needs to be trained in advance, which has close relationship with the evaluation system. However, the trained HMM is quite influenced by many issues, such as the data integrity and the feature space. In this paper, an intelligent bearing performance degradation assessment method based on HMM and nuisance attribute projection (NAP) is proposed. The proposed method can combine the information from the experimental data and the real-time data effectively and assess the performance since the beginning of the monitoring. The effectiveness of the proposed method is verified through an accelerated life test of rolling element bearings.

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).

Frequency-modulation continuous-wave (FMCW) Laser radar (Ladar) signals may be polluted by noise, which reduces the recognition precision of the targets. This letter proposes an ensemble empirical modal decomposition (EEMD) denoising method with singular spectrum constraint for FMCW Ladar signals. In our approach, we apply EEMD to adaptively decompose the noisy FMCW Ladar signals into several intrinsic mode functions (IMFs) and decompose these IMFs into several singular value components by using the singular spectrum analysis. The singular values are then used to calculate the energy probability of each IMF, which serves as an indicator to detect the IMFs containing useful signals. The energy probability represents the coherence of the IMFs such that we could sort these IMFs into noisy and useful components according to their coherence differences. To suppress the residual noise that is interfered with the selected IMFs, we use a low-rank approximation to reconstruct the useful signals. Finally, the reconstructed IMFs are stacked together to obtain the denoised signals. Tests on synthetic and real data demonstrate that the proposed method, compared to the EEMD denoising method, could suppress more noise but filter out less useful signals in the FMCW Ladar signal denoising.

Summary This paper presents a random noise reduction method based on ensemble empirical mode decomposition (EEMD) and wavelet threshold filtering. Firstly, the frequency band range of effective signal and noise in the initial seismic data set are studied by the Fourier spectrum analysis method. Secondly, we make use of EEMD method on the initial seismic data set to obtain the intrinsic mode functions (IMFs) of each trace. Then, wavelet threshold noise reduction method is used on the high frequency IMFs of each trace to obtain the new de-noising high frequency IMFs. Finally, by adding the new high frequency IMFs on the low frequency IMFs and the trend item together we obtain the de-noising seismic data set. When applying our method on synthetic and field data sets we can get good results.

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.

Ensemble empirical mode decomposition (EEMD) has been widely used in fault diagnosis of planetary gearboxes. However, artificially selecting the amplitude of white Gaussian noise (WGN) which is the crucial parameter of EEMD probably produces subjective errors. To alleviate this drawback, a self-adaptive EEMD method based on particle swarm optimization (PSO-EEMD) is proposed. This method takes the uniform distribution characteristic of signal extreme points as the fitness function of PSO in order to self-adaptively determine the optimal amplitude of WGN, which can improve the self-adaptability and decomposition precision of EEMD. Furthermore, utilizing the advantages of PSO-EEMD in extracting weak characteristics from noisy signals, a new fault diagnosis method of planetary gearboxes based on PSO-EEMD and frequency demodulation analysis is put forward. Simulation analysis results show that the PSO-EEMD method can self-adaptively determine the optimal amplitude of GWN according to the original signal characteristics and obtain more accurate intrinsic mode functions (IMFs) than the traditional EEMD, which illustrate the effectiveness and superiority of the proposed method. The fault diagnosis case of a planetary gearbox shows that the proposed fault diagnosis method based on PSO-EEMD and frequency demodulation analysis can effectively extract the characteristic frequency from the sun gear with a crack fault.

Complex nonstationary and nonlinear signals can be adaptively analyzed by the Hilbert-Huang transform(HHT) through empirical mode decomposition(EMD) and the Hilbert transform to generate the Hilbert-Huang spectrum.The Hilbert-Huang spectrum is able to show the local characteristics of the signals and focus time-frequency information well,and therefore it is widely applied to analyzing vibration signals in the field of machinery fault diagnosis.EMD,however,sometimes cannot reveal the signal characteristics accurately because of the problem of mode confusion.Moreover,the extracted intrinsic mode functions(IMFs) have different sensitivity to faults.Some IMFs are sensitive and closely related to the faults but others are irrelevant.Thus it is necessary to enhance the fault diagnosis accuracy of the HHT based on all IMFs of EMD.Aiming at this problem,an improved HHT based on ensemble empirical mode decomposition(EEMD) and sensitive IMFs is proposed,in which EEMD is used to alleviate the problem of mode confusion,and the sensitivity evaluation algorithm to select sensitive IMFs and highlight potential fault characteristics.Thus,the fault diagnosis results obtained by the proposed method are more accurate than the HHT based on all IMFs of EMD.Both simulated signals and real signals of an early rub-impact fault verify the effectiveness of the improved HHT.