Vector Hilbert-Huang Transform signal processing based on scale filtering method

Low-complexity sinusoidal-assisted EMD (SAEMD) algorithms for solving mode-mixing problems in HHT

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.

Novel and efficient computation of Hilbert–Huang transform on surfaces

To investigate the nonstationary characteristics of strong typhoons, this paper considers the evolutionary spectral characteristics of strong typhoons based on the Hilbert-Huang transform (HHT). Discrete expressions are determined for the evolutionary spectral analysis based on the HHT. The study indicates that the classic empirical mode decomposition (EMD) method fails to extract all of the high-frequency fluctuations from wind velocity data, and the time-averaged power spectrum obtained directly using the HHT cannot provide the true wind velocity spectrum. The degrees of nonstationarity of different-order IMF components are analysed and a synthesized method of analysing the evolutionary spectrum and time-averaged power spectrum of a strong typhoon is proposed. To avoid the energy leakage problem that exists in HHT spectral analyses, the Gram-Schmidt method is used to orthogonalize the intrinsic mode function (IMF) components. The study indicates that when the orthogonalization is implemented in accordance with the sequence from high-order IMF components to low-order ones, the orthogonalized components retain the same good Hilbert property as that of the IMFs. The synthesized method proposed yields a time-averaged power spectrum that is consistent with the Fourier spectrum in value and can produce the energy distributions of a typhoon in the time and frequency domains simultaneously.

This paper presents an improved version of the Hilbert-Huang transform (HHT) for the modal evaluation of structural systems or signals. In this improved HHT, a well-designed bandpass filter is used as preprocessing to separate and determine each mode of the signal for solving the inherent modemixing problem in HHT (i.e., empirical mode decomposition, EMD, associated with the Hilbert transform). A screening process is then applied to remove undesired intrinsic mode functions (IMFs) derived from the EMD of the signal's mode. A "best" IMF is selected in each screening process that utilizes the orthogonalization coefficient between the signal's mode and its IMFs. Through mode-by-mode signal filtering, parameters such as the modal frequency can be evaluated accurately when compared to the theoretical value. Time history of the identified modal frequency is available. Numerical results prove the efficiency of the proposed approach, showing relative errors 1.40%, 2.06%, and 1.46%, respectively, for the test cases of a benchmark structure in the lab, a simulated time-varying structural system, and of a linear superimposed cosine waves.

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.

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.

The analysis and calculation are conducted in combination with a real example, the Lanzhou station in the upper reaches of the Yellow River and Lancun station in the Fenhe River, Hilbert-Huang Transform (HHT) and the empirical mode decomposition (EMD) method are used to analyze runoff time series in this paper. Firstly original series is step-by-step decomposed by means of EMD method, so the result is four intrinsic mode functions (IMF) and a residual component at the Lanzhou station, and is three intrinsic mode functions (IMF) and a residual component at the Lancun station. It is computed that natural annual runoff have the periodicity of 2.23 a, 5.57 a, 10.23a and 19.76a at the Lanzhou station, and 2.63 a, 6.67a and 25 a at the Lancun station. The physical cause is analyzed. The result provides scientific ground for planning and management water resource in the basin.

In distributed generation (DG) connected grid system, there is serious harmonic pollution caused by the wide use of inverter units and nonlinear loads. The traditional detection methods (such as Fast Fourier Transform and wavelet analysis) heavily depend on synchronous signal detection or basis functions selection, which don’t satisfy the requirements of the harmonic detection of the micro-grid environment. Therefore, a novel method combining discrete wavelet transform (DWT) with Hilbert–Huang transform (HHT) is proposed to detect and analyze the harmonic. The method uses multi resolution analysis of DWT to process the original signal. Then, a series of intrinsic mode function (IMF) components are obtained from the processed signal by using Empirical Mode Decomposition (EMD) algorithm. Thirdly, the fundamental component and harmonic are extracted from the IMF components. Finally, the frequency and amplitude of the signal are calculated by using the HHT. Simulation results demonstrate that the proposed algorithm has high precision and good real-time characteristics. Furthermore, the proposed algorithm satisfies the requirements of the harmonic detection of the DG connected grid system.

The Empirical Mode Decomposition (EMD) is a signal analysis method that separates multi-component signals into single oscillatory modes called intrinsic mode functions (IMFs). These IMFs can generally be associated to a physical meaning of the process from which the signal is obtained. When the phenomena of mode mixing occurs, as a result of the EMD sifting process, the IMFs may lose their physical meaning hindering the interpretation of the results of the analysis. Previous research presents a rigorous mathematical analysis that shows how EMD behaves in the case of a composite two-components signal, explaining the roots of the mode mixing problem. Also, the frequency-amplitude region within which a good separation is achieved with EMD is well identified and discussed. However, a solution that offers good IMF separation when components reside within the same octave is not yet available. In this paper, a method to separate spectral components that reside within the same octave, is presented. This method is based on reversing the conditions by which mode mixing occurs presented in the paper One or Two frequencies? The Empirical Mode Decomposition Answers, in [3]. Numerical experiments with signals containing spectral components within the same octave shows the effective separation of modes that EMD can perform after this principle is applied. This separation technique has potential application for identifying the cause of different oscillatory modes with spectral proximity present in the smart grid.

Depth of anaesthesia (DoA) is an important measure for assessing the degree to which the central nervous system of a patient is depressed by a general anaesthetic agent, depending on the potency and concentration with which anaesthesia is administered during surgery. We can monitor the DoA by observing the patient’s electroencephalography (EEG) signals during the surgical procedure. Typically high frequency EEG signals indicates the patient is conscious, while low frequency signals mean the patient is in a general anaesthetic state. If the anaesthetist is able to observe the instantaneous frequency changes of the patient’s EEG signals during surgery this can help to better regulate and monitor DoA, reducing surgical and post-operative risks. This paper describes an approach towards the development of a 3D real-time visualization application which can show the instantaneous frequency and instantaneous amplitude of EEG simultaneously by using empirical mode decomposition (EMD) and the Hilbert–Huang transform (HHT). HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMFs). The Hilbert spectral analysis method is then used to obtain instantaneous frequency data. The HHT provides a new method of analyzing non-stationary and nonlinear time series data. We investigate this approach by analyzing EEG data collected from patients undergoing surgical procedures. The results show that the EEG differences between three distinct surgical stages computed by using sample entropy (SampEn) are consistent with the expected differences between these stages based on the bispectral index (BIS), which has been shown to be quantifiable measure of the effect of anaesthetics on the central nervous system. Also, the proposed filtering approach is more effective compared to the standard filtering method in filtering out signal noise resulting in more consistent results than those provided by the BIS. The proposed approach is therefore able to distinguish between key operational stages related to DoA, which is consistent with the clinical observations. SampEn can also be viewed as a useful index for evaluating and monitoring the DoA of a patient when used in combination with this approach.

• Introduces a novel method using Hilbert-Huang Transform (HHT) with LSTM networks for fault detection in DC microgrids. • Targets marine and satellite DC microgrids, addressing challenges with no zero-crossing points in traditional methods. • Demonstrates superior performance, outperforming SVM and Decision Tree techniques in fault detection time and accuracy. • Validates the method using MATLAB/Simulink, effectively detecting faults with resistance up to 1.3 ohms. • Ensures compliance with IEEE 8570 standards, enhancing reliability and applicability in real-world microgrid systems. Fault detection in DC microgrids is a major challenge because traditional protection methods like wavelet and Fourier transforms rely on zero-crossing points, which the DC signal lacks. This paper introduces a new approach combining the Hilbert-Huang Transform (HHT) and a long short-term memory (LSTM) neural network to improve fault detection and classification in DC microgrids. The proposed method first uses Empirical Mode Decomposition (EMD) to break down the fault current signal into multiple intrinsic mode function (IMFs). These IMFs capture important fault-related information at different frequency levels. Next, the Hilbert Transform is applied to these IMFs to obtain amplitude and frequency features over time. These features are used to create a set of numerical descriptors that summarize the fault characteristics. These extracted features are then fed into a two-layer LSTM neural network that can learn patterns in time-series data. The LSTM model is trained to classify the input into three categories: no fault, Pole-Ground (P-G) Fault, or Pole-Pole (P-P) Fault. Simulation tests were carried out using a MATLAB Simulink model of a 20kWatt DC microgrid under different fault conditions, noise levels, and load transients. Results show that the proposed HHT-LSTM model detects faults faster and more accurately than conventional techniques like Support Vector Machines (SVM) and Decision Trees (DT). It also meets the fault detection time requirements set by IEEE8570 and aligns with IEC standards. The model remains robust even under noisy conditions, making it reliable for real-time fault protection in marine, satellite, and an effective solution for enhancing fault detection in modern DC microgrids.

We present a new method for separation of the rhythms of the electroencephalogram (EEG) signal. The proposed method is based on the Hilbert-Huang transform (HHT). The HHT consists two steps namely empirical mode decomposition (EMD) and the Hilbert transform (HT). The EMD decomposes EEG signal into set of narrow-band intrinsic mode functions (IMFs), and the Hilbert transformation of these IMFs provide instantaneous frequency estimation of the IMFs. The instantaneous frequency estimation of IMFs have been used as a feature to identify the IMFs in order to separate rhythms of EEG signal. The central tendency measure (CTM) has been used to quantify the variability in second order difference (SOD) plots of rhythms of the EEG signal. The CTM parameter is very effective to discriminate epileptic seizure EEG signals from the seizure-free EEG signals. The experimental results show the effectiveness of the proposed method for epileptic seizure detection.

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.

Structural Health Monitoring (SHM) as a process in order to implement a damage detection strategy and assess the condition of structure plays a key role in structural reliability. In this paper, we aim to present a methodology for online detection of damages which may occur during a strong ground excitation. In this regard, Empirical Mode Decomposition (EMD) is superseded by Ensemble Empirical Mode Decomposition (EEMD) in the Hilbert Huang Transformation (HHT). Albeit analogous, EEMD brings about more appropriate Intrinsic Mode Functions (IMFs) than EMD. IMFs are employed to assess the first mode frequency and mode shape. Afterward, Artificial Neural Network (ANN) is applied to predict story acceleration based on previously measured values. Because ANN functions precisely, any congruency between predicted and measured acceleration indicates onset of damage. Then, another ANN method is applied to estimate the stiffness matrix. Though the first mode shape and frequency are calculated in advance, the process essentially requires an inverse problem to be solved in order to find stiffness matrix, which is done by ANN. This algorithm is implemented on moment-resisting steel frames, and the results show that the proposed methodology is reliable for online prediction of structural damage.