Separation of closely spaced modes by combining complex envelope displacement analysis with method of generating intrinsic mode functions through filtering algorithm based on wavelet packet decomposition

Empirical Mode Decomposition (EMD) and Wavelet method have been widely used in the vibration signal analysis, mainly because of the powerful ability of blind modal separation. In the flutter test, modal identification and modal trajectories tracking online can help to ensure the test safety. However, traditional EMD method is only suitable for offline data batching, which limits its applications to the real-time or near real-time signal analysis. For this reason, according to the online processing requirements of flutter test under the turbulent excitation conditions, combining with wavelet spectrum analysis, an online EMD method based on a sliding window for structural modal identification and flutter boundary prediction (FBP) is proposed in this paper. The corresponding mathematical principles and implementation algorithms are given as well, which decompose the measured signal into the Intrinsic Mode Function (IMF) firstly, and then estimate the modal parameters by using the wavelet power spectrum method. The FBP result is typically obtained online during the test process by using curve fitting and extrapolation of the modal damping. The numerical simulations and test data from a low-speed wind tunnel flutter test are used to verify the effectiveness and engineering feasibility of the proposed method.

Envelope modified versions of the empirical mode decomposition (EMD) method such as the B‐spline interpolation‐based EMD (B‐EMD) method and cardinal spline interpolation‐based EMD (C‐EMD) method have been proposed recently for purpose of improving its effectiveness. To shed further light on their performance, the behaviours of these EMD‐type methods in the presence of white Gaussian noises are investigated in this study based on extensive numerical experiments. Similarly to the EMD method, it turns out that the envelope modified EMD methods also act as filter banks essentially. However, the spectra among the first several intrinsic mode functions of the B‐EMD method have fewer overlaps than those of the EMD and C‐EMD methods, which indicate that the B‐EMD method has a better ability to alleviate the mode mixing problem for signals with higher frequencies. On the other hand, the C‐EMD method is shown to perform better than the EMD and B‐EMD methods on separating tones with lower frequencies.

Focusing on feature extraction of non-stationary vibration signals in condition monitoring and fault diagnosis of gear pump, the fault diagnosis approach based on empirical mode decomposition method and kernel principal component analysis (KPCA) and support vector machines (SVM) is proposed. The improved empirical mode decomposition (EMD) method is used to decompose the mechanical equipment output signal into a number of intrinsic mode function (IMF) components and a residue component, and calculated ten dimensionless parameters of each IMF and residue component, then extract result from the original parameters by using KPCA, at last the kernel principal component is classified by inputting the new feature vector to SVM for training and recognizing. The simulation and experiment results show that the advanced method is effective in restraining end effect, and the analysis result of gear pump vibration signals in different conditions validate the method is effective.

The key to the fault diagnosis of rotating machinery is to extract the fault characteristics from the vibration signal of rotating machinery. Signal analysis and processing are the most commonly used methods for feature extraction. In this paper, a method combining the empirical mode decomposition (EMD) and spectral kurtosis is presented for fault detection of rotating machinery based on vibrational signal. According to the modulation characteristic of the rolling element bearing fault signal and the disadvantage of depending on the experience to select resonance high frequency band, an improved method integrating EMD with spectrum kurtosis for rolling bearing fault diagnosis is put forward. Firstly, the bearing fault signal is decomposed into a series of intrinsic mode function (IMF) through EMD method. Secondly, the false IMF components are eliminated through mutual information, kurtosis and cross-correlation, then the useful IMFs are selected to construct the fault signal. Finally, by designing the optimal band pass filter with the spectral kurtosis, it can be obtained that, the envelope demodulation spectrum of the filtered signal, and the fault feature of rolling bearing are extracted. The experimental result of the rolling bearing fault diagnosis shows that the proposed method can effectively extract the weak fault feature of rolling bearing, which is superior to envelope analysis.

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

Natural frequencies identification is important for dynamic analysis of subgrade for high-speed railway. The most commonly used method is analyzing the response spectrum feature undergoing ambient excitation directly without any processing. However, this method requires that the ambient excitation should be close to the white signal. If the ambient excitation includes some kinds of non-white signals, this method becomes hard to use. In this paper, based on empirical mode decomposition (EMD) method and random vibration theory, an improved identification method undergoing ambient excitation is proposed. First, the self-correlation function of an acceleration record is decomposed into several intrinsic mode functions (IMFs) via EMD method. Then natural frequencies are determined by Hilbert transform and basic modal analysis theory. The original acceleration records from the Wu-Guang Passenger Dedicated Railway are processed by the proposed method to identify natural frequencies of the subgrade. The identification results are compared with results from the field excitation tests and finite element analysis. Comparisons demonstrate that the proposed method is reliable to identify natural frequencies of subgrade for high-speed railway. The natural frequencies of the test subgrade are at low level.

Signal is a non-linear and non- stationary signal, the empirical mode decomposition (EMD) can decompose the signal into several intrinsic mode functions(IMF), the IMF can reflect the characteristic in frequency changing of logging data along depth, IMF curves of different steps might reveal cycle characteristics of different scale, which are in correspondence with geological cycles o different scales, so that different scale sequences might be detected clearly from IMF curves. Empirical mode decomposition method is used to demarcat stratigraphic sequence and stratigraphic correlation in this paper ,the result show that EMD method can better show the internal vibration of logging signal and reflect the characteristics of the stratigraphic sequence ,and EMD method can provide technical support for stratigraphic correlation.

Comparative study of spectral properties of temperature and CO2 fluxes measured by eddy covariance method at Yucheng (36 57'E, 28 m.a.s.1., in the North China Plain) and at Lhasa (29 41'N, 91 20' E, 3688 m.a.s.1., on the Tibetan Plateau) is described using the empirical mode decomposition (EMD) method. The main results are: (1) The intrinsic oscillation modes or intrinsic mode functions (IMFs) were extracted from data of temperature (T) and CO2 fluxes (F) measured at Yucheng (T1 and F1) and Lhasa (T2 and F2). (2) Hilbert transform was applied to these IMF compontents, then the Hilbert-Huang spectra and the marginal spectra of these data were obtained. (3) Comparison of temperature and CO2 fluxes in North China Plain and on Tibetan Plain illustrated that the characteristic frequencies corresponding to T1, F1, T2 and F2 are 0.05 Hz, 0.03 Hz, 0.014Hz and 0.005Hz, respectively. * Supported by the National Program on Key Basic Research Projects (Grant No. G1999-11708) and National Natural Science Foundation of China (Grant No. 40320081) Keywords: empirical mode decomposition (EMD)intrinsic mode function (IMF)fluxHilbert transformwheatTibet Notes * Supported by the National Program on Key Basic Research Projects (Grant No. G1999-11708) and National Natural Science Foundation of China (Grant No. 40320081)

Similarity analysis of DNA sequences based on the EMD method

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 order to obtain a more accurate topographic model, a noise filtering step must be performed before the unwrapping of phase. In this article, a filter for suppressing speckle in SAR interferogram is proposed. The filter is based on the empirical mode decomposition (EMD) method which can separate the information to parts with different scale, when the parts related to the speckle is subtracted from the original interferogram, the speckle noise is reduced. The result is compared to that of two other methods and shows that EMD method is powerful to interferogram speckle noise reduction, as well as it can preserve fine details in the interferogram that are directly related to the ground topography and maintain phase values distribution.

A filtering method based on empirical mode decomposition (EMD) for coulostatically-induced transients (CITs) was presented. The effect of EMD filtering was evaluated from different simulation systems. To boost the applicable solution for EMD filtering and reduce the subjectivity of filtering, discussions of the simulating noises were mainly focused on white noise, high frequency noise, 50 Hz noise from commercial power and blend of above-mentioned noises. To illustrate the most importance of EMD filtering for the goodness of fit of CIS, one real corrosion system involving multi-time constant was simultaneously investigated by electrochemical impedance spectrum (EIS) and coulostatically-induced spectrum (CIS). The results reported here demonstrate that EMD de-noising is applicable for CITs. The proposed method shows good performance of de-noising and is an alternative de-noising method for the CITs analysis. CIS with EMD filtering are in good agreement with EIS. For practical application of EMD, removal of the first two items of intrinsic mode function (IMF) and 50 Hz element in forth IMF will be generally satisfactory for CIS analysis.

Using filter bank property to simplify the calculations of Empirical Mode Decomposition

The electrical energy supply relies on the satisfactory operation of insulators. The ultrasound recorded from insulators in different conditions has a time series output, which can be used to classify faulty insulators. The random convolutional kernel transform (Rocket) algorithms use convolutional filters to extract various features from the time series data. This paper proposes a combination of Rocket algorithms, machine learning classifiers, and empirical mode decomposition (EMD) methods, such as complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), empirical wavelet transform (EWT), and variational mode decomposition (VMD). The results show that the EMD methods, combined with MiniRocket, significantly improve the accuracy of logistic regression in insulator fault diagnosis. The proposed strategy achieves an accuracy of 0.992 using CEEMDAN, 0.995 with EWT, and 0.980 with VMD. These results highlight the potential of incorporating EMD methods in insulator failure detection models to enhance the safety and dependability of power systems.