Mode-by-mode evaluation of structural systems using a bandpass-HHT filtering approach

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.

Hilbert-Huang Transform (HHT) is a kind of signal analysis method suitable for non-stationary signal, and the combination of HHT and vector signal processing is called vector HHT, by which the instantaneous azimuth of the target can be estimated. In vector HHT signal processing method, the existence of intermittent signal and noise leads to mode mixing in the results of empirical mode decomposition (EMD). Mode mixing influences exact extraction of vibration mode, which causes that the signal which should be in the same order of intrinsic mode function (IMF) distributes in different IMFs. In vector HHT signal processing method, the two vibration speed components need to be multiplied by sound pressure respectively, so mode mixing will lead to great error in the estimation of azimuth of the target. To overcome the influence of mode mixing on vector HHT, this paper proposes a kind of vector HHT signal processing method based on scale filtering. The new method can effectively eliminate mode mixing resulting from intermittent signal and noise, and exact decomposition results can be achieved. The improved vector HHT method is used in processing acoustic vector signal, and the data obtained from a certain sea experiment in Dalian city is analyzed by the new method. The waterfall plot accurately shows the azimuth of the target ship, which proves the validity of the method.

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.

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

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.

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.

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.

Novel and efficient computation of Hilbert–Huang transform on surfaces

In this paper, we propose a novel ECG signal enhancement method based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) and Higher Order Statistics (HOS). In our scheme, the noisy ECG signal is first decomposed adaptively into oscillatory components called intrinsic mode functions (IMFs) by using Empirical Mode Decomposition (EMD) or its variants. Therefore, the obtained modes are separated into two groups of noisy signal modes and one group of useful signal modes, by using a novel criterion derived from the HOS namely the fourth order cumulant or kurtosis. After that, a modified shrinkage scheme based on Interval Thresholding technique is adaptively applied to each selected IMF from the noise-dominant groups in order to reduce the noise and to preserve the QRS complex. The overall filtered ECG signal is then reconstructed by combining the thresholded IMFs and the retained unprocessed lower frequency relevant IMFs. Various tests and simulations are investigated to evaluate the performance of our proposed approach in combination with the EMD, Ensemble EMD (EEMD) and CEEMDAN algorithms. The simulation results carried on MIT-BIH Arrhythmia database, show that CEEMDAN method gives better performance than the two other methods, and outperforms some state-of-the-art methods in terms of Signal to Noise Ratio (SNR) and Root Mean Square Error (RMSE).

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.

• 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.

Aerial Bundled Cables (ABCs) installed in coastal regions experience accelerated ageing due to rapid insulation degradation. Such damage causes unexpected and frequent cable failure. Sophisticated NDT methods are hence required for effective condition monitoring of ABCs. The corona discharge generated in vicinity of deteriorating ABCs is a consequence of damaged insulation. The discharge can be measured using super-heterodyned airborne ultrasonic listening. So measured corona discharge is intermittent and non-stationary, along the length of the ABC. Therefore, the usefulness of advanced adaptive techniques including Empirical Mode Decomposition (EMD), Ensemble EMD (EEMD) and Complementary Ensemble EMD (CEEMD) as Intrinsic Mode Functions (IMFs) extraction procedures is investigated for damage assessment of energized ABCs. Respective IMFs are used to compute Hilbert Huang Transform (HHT) spectrums. HHT spectrums are computed processing periodically acquired ultrasonic signals from different locations within the coastal region. All three IMF extraction techniques reveal a progressive shift in the signal energy spectrum towards lower frequency and, hence, are able to classify the health state of operational ABCs. The EMD, EEMD and CEEMD techniques are rated to be sequentially effective in damage quantification, with CEEMD being the most eloquent.

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.

Primal sketch performs an important role in early vision. In this paper, we propose a novel method to obtain the primal sketch of natural images by integrating empirical mode decomposition (EMD) techniques and image gradient. 2D EMD approach can decompose the image into a finite number of intrinsic mode functions (IMF), and each one represents the original image in a different scale, with the 1st IMF representing the finest scale. To enhance the information represented by the IMF, we multiply the 1st IMF by the image gradient. This enhanced IMF highlights intensity changes in the image. By linking all the maximal points in the enhanced IMF, we obtain a primal sketch of the original image. Compared with the existed primal sketch extraction methods, our method is fully driven by the image data, and it needs neither to choose filters nor to learn the image bases. The experiment results show that our method is fast and effective.