Hilbert-Huang Transform Method Research Articles

Analysis of the Burial Depth Pattern of Shallow Groundwater Based on Wavelet and Hilbert-Huang Transform Methods

Analysis of the Burial Depth Pattern of Shallow Groundwater Based on Wavelet and Hilbert-Huang Transform Methods

Recovery of High-energy Low-frequency Quasiperiodic Oscillations from Black Hole X-Ray Binary MAXI J1535–571 with a Hilbert–Huang Transform Method

We propose a method based on the Hilbert–Huang transform (HHT) to recover the high-energy waveform of low-frequency quasiperiodic oscillations (QPOs). Based on the method, we successfully obtain the modulation of the phase-folded light curve above 170 keV using the QPO phase reconstructed at lower energies in MAXI J1535–571 with Insight-HXMT observations. A comprehensive simulation study is conducted to demonstrate that such modulation indeed originates from the QPO. Thus, the highest energies turn out to significantly exceed the upper limit of ∼100 keV for QPOs reported previously using the Fourier method, marking the first opportunity to study QPO properties above 100 keV in this source. Detailed analyses of these high-energy QPO profiles reveal different QPO properties between the 30–100 and 100–200 keV energy ranges: the phase lag remains relatively stable, and the amplitude slightly increases below ∼100 keV, whereas above this threshold, soft phase lags and a decrease in amplitude are observed. Given the reports of a hard-tail detection in broad spectroscopy, we propose that the newly discovered QPO properties above 100 keV are dominated by the hard-tail component, possibly stemming from a relativistic jet. Our findings also indicate a strong correlation between the QPOs originating from the jet and corona, supporting the scenario of jet–corona coupling precession. We emphasize that our proposed HHT-based method can serve as an efficient manner in expanding the high-energy band for studying QPOs, thereby enhancing our understanding of their origin.

Investigating the Dynamic Relationship Between Greenhouse Gas Emissions and Gross Domestic Product in Türkiye

This study aims to investigate the causal relationship between Gross Domestic Product and greenhouse gas emissions in Türkiye from 1951 to 2018, using the Causal Decomposition Method that integrates Ensemble Empirical Mode Decomposition, Hilbert-Huang Transform, and Phase Coherence Methods. The primary focus is on identifying the key sectors contributing significantly to greenhouse gas emissions, particularly those connected to industrial production. The analysis reveals a one-way, short-term causal relationship from Gross Domestic Product to greenhouse gas emissions, spanning approximately 3 years. This finding suggests that changes in Gross Domestic Product have short-term effects on emissions, but not vice versa. Special emphasis is placed on the gases Cardon Dioxide, Methane and Nitrous Oxide, as they demonstrate a strong, consistent causal connection with Gross Domestic Product. The significance of this study lies in its utilization of the Ensemble Empirical Mode Decomposition approach to investigate this dynamic causality and address a notable gap in the existing literature. Empirical results indicate a complex yet observable association between Gross Domestic Product growth and greenhouse gas emissions in Türkiye, and that this relationship becomes more important, especially in the short and long term, with periodic fluctuations.

Time–Frequency–Energy Characteristics Analysis of Vibration Signals in Digital Electronic Detonators and Nonel Detonators Exploders Based on the HHT Method

The China Society of Explosives and Blasting required a larger than 20% annual increase in the national use of digital electronic detonators since 2018. So, this article conducted a large number of on-site tests and then used the Hilbert–Huang Transform method to analyze and compare the vibration signals of digital electronic and nonel detonators during the excavation process of minor cross-sectional rock roadways from the perspective of time, frequency, and energy. Then, through vibration energy analysis, identification of actual delay time, and formula derivation, it was proved that the delay time error of the detonator can control vibration wave random interference and reduce vibration. The analysis results showed that when using a segmented simultaneous blasting network for excavation in small-sectioned rock tunnels, nonel detonators may provide more excellent protection to structures than digital electronic detonators. In the same segment, the timing error of nonel detonators produces a vibration wave with a random superposition damping effect, resulting in an average vibration reduction of 19.4% per segment compared to digital electronic detonators. However, digital electronic detonators are superior to nonel detonators for the fragmentation effect on rock. The research conducted in this paper has the potential to facilitate a more rational and comprehensive promotion of digital electronic detonators in China.

Experimental investigation of characteristics of tip leakage vortex cavitation-induced vibration of a pump

Cavitation and vibration are complicated and critical characteristics in pumps, which has a negative influence on the reliability and stability of nuclear power plant systems. In this paper, a synchronous experimental system including a high-speed camera and sensors is established to investigate the characteristics of blade tip leakage vortex (TLV) cavitation, cavitation-induced pressure fluctuation, and vibration. The results show that the formation of the TLV cavitation cloud significantly deteriorated the pump's performance, changed the pressure distribution, and increased the pressure fluctuation and vibration. Based on the Hilbert-Huang transformation (HHT) method, transient and non-stationary vibration signals are decomposed into Intrinsic Mode Functions (IMFs) by Empirical Mode Decomposition (EMD). The RMS values of first-order IMF in vibration signals increase rapidly as the TLV cavitation cloud develops. The properties extracted from the Hilbert marginal spectrum can be used to detect the pump's cavitation development stages.

Analysis of wave-induced vertical ship responses by Hilbert-Huang transform method

Time series of wave-induced ship responses are analysed by the Hilbert-Huang Transform (HHT) method. The results of the analysis of numerically simulated motions and loads on a chemical tanker in head waves are compared with the analysis of experimental data from laboratory model tests. The Empirical Mode Decomposition, which is a first part of HHT method is applied to the sea surface elevations of two sea states (high and low seas) and the wave-induced vertical motions and bending moments and the results are discussed. It is found that the decomposition of the experimental data into intrinsic components compares well with the decomposition of the numerically simulated ones for both high and low seas. The first two or three intrinsic mode functions carry the major part of the energy of both experimental and numerical simulated data. The time-frequency distribution of energy, called Hilbert spectrum, is calculated by the second part of HHT method. The Hilbert spectrum of the sea surface elevation is compared with Hilbert spectrum of wave-induced ship motions and moments in an attempt to study the time-frequency characteristics of ship response. The results of the present work provide confidence in the usage of numerical simulation data for the decomposition into intrinsic components of ship responses, avoiding the need for experimental data from laboratory model tests.

Prediksi Kunjungan Wisatawan Ke Indonesia Dengan Reduksi Noise Pada Mesin Pencari Menggunakan Metode Hilbert Huang Transform


 In many studies, Google Trends Data is efficient to analyze and estimate as explanatory variables, including tourism predictions. However, data retrieval and tourism are always plagued by noise. Without noise processing, the predictive ability of search engine data may be weak, even invalid. As a noise processing method, Hilbert-Huang Transform (HHT) can reduce or clean noise. Forecasting is the art and science of predicting future events. LSTM is able to overcome long-term dependence. This study tries to provide predictions of tourist visits by processing noise in search engines using the Hilbert-Huang Transform method. The forecasting architecture that is built is composed of 3 hidden LSTM layers with 100 units of neurons or nerves that function to process information, which in the LSTM layer also becomes the input layer. Prediction test results on a dataset of 156 rows, resulting in RMSE values in 2019 getting RMSE LSTM 129249 results, and RMSE HHT + LSTM 653058. so that the resulting RMSE is closer to remembering 0.

A brain-computer interface with gamification in the Metaverse

This study contributes to our understanding of the Metaverse by presenting a case study of the implementation of brain-computer interface supported game-based engagement in a Virtual Environment (VE). In VE, individuals can communicate with anyone, anywhere, anytime, without any limits. This situation will increase the barrier-free living standards of disabled people in a more accessible environment. A virtual world of well-being awaits these individuals, primarily through gamified applications thanks to Brain-Computer Interfaces. Virtual environments in the Metaverse can be infinitely large, but the user's movement in a virtual reality (VR) environment is constrained by the natural environment. Locomotion has become a popular motion interface as it allows for full exploration of VE. In this study, the teleport method from locomotion methods was used. To teleport, the user selects the intended location using brain signals before being instantly transported to that location. Brain signals are decomposed into alpha, beta, and gamma bands. The features of each band signal in Time, frequency, and time-frequency domains are extracted. In this proposed method, the highest performance of binary classification was obtained in the frequency domain and the Alpha band. Signals in the alpha band were tested in the domains Time, Frequency, and Time-Frequency. Teleport operations are faster with Time and more stable with the frequency domain. However, the Hilbert-Huang Transform (HHT) method used in the Time-Frequency domain could not respond adequately to real-time applications. All these analyses were experienced in the Erzurum Virtual Tour case study, which was prepared to promote cultural heritage with the gamification method.

Experimental and numerical investigations on the influence of center-hung scoreboard on dynamic characteristics of suspend-dome structure

The LED display, i.e., the center-hung scoreboard, nowadays has become an indispensable display device in large stadiums, and some of which with weight is more than 30t. To investigate the influence of center-hung scoreboard load on the dynamic characteristics of the suspend-dome structure, a 1:20 dynamically scaled model of the Lanzhou Olympic Sports Complex was designed, considering different lifting-lowering heights of the center-hung scoreboard by changing the sling length. Shaking table dynamic characteristics experiment was conducted by using the white noise excitation method for the suspend-dome structure with the sling lengths of 200 mm, 400 mm, and 600 mm individually. The change rule of dynamic characteristic parameters such as natural frequencies and damping ratios was concluded by the Hilbert-Huang Transformation method for modal identification and the transfer function method for checking. With the increase of sling length, the natural frequencies of the center-hung scoreboard become smaller, and the damping ratios become more extensive. Compared with the results of the scaled model without a center-hung scoreboard, the high-order natural frequencies and damping ratios of the overall structure with the center-hung scoreboard are significantly increased, and the coupling effect between the center-hung scoreboard and the structure should not be ignored in the dynamic analysis. The test values were compared with the simulation results of Abaqus as well. It is shown that the test values of the scaled model are essentially consistent with the simulation results, which indicates that the test points are reasonably arranged, the test method is correct, and the finite element modeling method is accurate. The effects of sling stiffness and sling length on the dynamic characteristics of the suspend-dome structure were studied by Abaqus software. The results show that the sling stiffness hardly affect the dynamic characteristics of the overall model. When the sling length is less than 300 mm, the lifting-lowering of the center-hung scoreboard influences the distribution of the natural frequency and the vibration mode of the overall structure. In this range, the lifting-lowering of the center-hung scoreboard should be focused on actual engineering.

Hand gesture classification using time–frequency images and transfer learning based on CNN

Hand gesture-based systems are one of the most effective technological advances and continue to develop with improvements in the field of human–computer interaction. Surface electromyography (sEMG) is utilized as a popular input data for gesture classification with elevated accuracy and advanced control capability. This paper presents a comparative hand gesture classification approach using time–frequency (TF) images of the spontaneous sEMG signals and the transfer learning method. 4-channel sEMG signals are collected from 30 subjects performing 7 specific hand gestures. After the required pre-processing, segmentation, and windowing steps, three TF analysis methods, namely Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Hilbert-Huang Transform (HHT), are applied to EMG signals to obtain TF images. Spectrograms from STFT, scalograms from CWT, and Hilbert-Huang spectra (HHS) from HHT obtained from multi-channel sEMG data are separately fused. TF images are then utilized to extract distinct features using seven state-of-the-art, pre-trained Convolutional Neural Network (CNN) architectures and classify seven hand gestures. Two different robust cross-validation strategies are conducted to evaluate the proposed method; stratified k-fold cross-validation (SKCV) and leave-one-subject-out cross-validation (LOOCV). We also investigate the effect of window size and the combination of Intrinsic Mode Functions (IMFs) on classification performance. The results demonstrated that the HHT utilizing IMFs obtained by Empirical Mode Decomposition (EMD) provided improved TF resolution and better results than STFT and CWT in the classification of sEMG signals. Finally, the best average accuracies (93.75% for SKCV) and (94.41% for LOOCV) are obtained by the HHT method with the pre-trained ResNet-50 model.

Hilbert spectrum analysis method of blast vibration signal based on HHT instantaneous phase optimization

Compared with wavelet analysis method of signal data, HHT (Hilbert-Huang Transform) method is widely used for the local signal data analysis in the time–frequency domain associated with adaptable capacity, which has been recognized as one of the most efficient method to address the non-stationary signals. In this study, Matlab software was used as the calculation code and field millisecond delay blasting data was collected as the research objects, the Hilbert time–frequency spectrum, marginal spectrum, instantaneous energy spectrum and Hilbert energy spectrum scatter were obtained for the signal IMF components under the standard instfreq.m function (as shown in Section 3.3) frequency modulation with the identified bandwidth of 1 Hz. The reasons of negative frequency for digital signals were discussed based on the theoretical analysis and the digitial signals were then summarized as two types of negative frequency according to the instantaneous phase characteristics. The field collected blasting vibration signals were used to illustrate the features of the negative frequency points such as large number, correlated relation between the signal amplitude extent and frequency band, and non-negligible of the total vibration energy. In addition, a theoretical equation was proposed for the instantaneous phase optimization function based on the HHT method, and a triple identification approach of millisecond time was proposed based on instantaneous phase optimization method. The process of Hilbert spectrum analysis based on HHT instantaneous phase optimization was implemented using Matlab, which was used to analyze Hilbert spectrum characteristics. Further, a theoretical comparison and analysis between the standard instfreq.m time–frequency modulation and the proposed phase optimized HHT spectrum were performed, and the results shows that the optimized HHT spectrum analysis improves the accuracy of time–frequency spectrum and Hilbert spectrum calculation, besides, the frequency domain recognition width is about 2∙r times of that from the standard solution. Finally, the phase optimization was used to analyze the amplitude spectrum, instantaneous velocity energy spectrum and 3D time–frequency seismic velocity energy spectrum features, application of HHT-based instantaneous phase optimization method is given for the accurate recognition application of multi-segment detonation millisecond time in underground blasting.

Study of Resonance Helical Magnetic Field (RHF) Effect In IR-T1 Tokamak Plasma Using Hilbert-Huang Transform

In the IR-T1 Tokamak the effect of a resonance helical magnetic field (RHF) on plasma confienment are presented using Hilbert-Huang Transform method.Mirnov coil data analyzed by Hilbert-Huang Transform (HHT) and decomposed to the main intrinsic mode functions(imfs) and their instantanous frequencies (IFs). We find that, HHT method can extract MHD activities with different amplitudes in the different times. Then, the IFs of these modes can be calculated by Hilbert Transform (HT). As a comparison of WT and HHT analysis the Hilbert spectrum has much better frequency definition. Amplitude modulation of Mironov oscillations in IR-T1 tokamak plasma generate intra-wave frequency modulation, In the Hilbert spectrum analysis this effect is small compared to the STFT and WT spectrums. In our study, Magnetic islands with frequency around 40 kHz can be seen in wavlet Transform(WT) and HHT results in ohmic and RHF discharges. The HHT results after application of l=2/n=1 resonant field show that, the amplitude of m=2 poloidal MHD mode are amplified and then suppressed for a few milliseconds after amplification. Similarly, the amplitude of the m=3 MHD mode are amplified and then strongly suppressed by the start of the l=3/n=1 resonant field.

Research on electromagnetic radiation (EMR) waveform characteristics of coal failure process using Hilbert-Huang transform (HHT)

Electromagnetic radiation (EMR) waveforms contain rich information on coal fracture law, which is of great value to the refined study of their characteristics. In this paper, the Hilbert-Huang transform (HHT) method is used to analyze and process EMR waveform of coal failure process. The results show that HHT method can adapt well to the nonstationary and nonlinear characteristics of EMR waveform. It adaptively decomposes EMR waveforms by empirical mode decomposition (EMD), extracts the intrinsic mode function (IMF) characteristics of EMR waveforms, and obtains the law of instantaneous energy changes of EMR waveforms. At the same time, EMR waveform energy is quantitatively expressed on the three-dimensional Hilbert energy spectrum (time–frequency-energy distribution), and the refined features of EMR waveform signal are effectively extracted. The instantaneous energy of EMR and the three-dimensional Hilbert energy spectrum processed by HHT method more easily describe the fracture law of coal body. Compared with conventional characteristic parameters, such as EMR amplitude and dominant frequency, the identification degree of the precursor characteristics of coal body instability is greatly improved. Among the short-term Fourier transform (STFT), wavelet transform (WT) and HHT nonstationary signal processing methods, HHT method has an improved adaptability and superiority and can reveal the characteristics of coal deformation and failure more carefully and accurately, which provides a new means for better using and improving EMR method to monitor coal instability and failure.

Time-Frequency Characteristics of Fluctuating Pressure on the Bottom of the Stilling Basin with Step-Down Floor Based on Hilbert–Huang Transform

Fluctuating pressure is an important feature of the bottom of a stilling basin with step-down floor. To analyze the frequency domain characteristics and energy distribution of this fluctuating pressure, the Hilbert–Huang transform (HHT) method is used. First, empirical mode decomposition is performed on the pressure fluctuation signal to obtain a number of intrinsic mode functions (IMFs), and then the Hilbert transformation is performed on each IMF to obtain the Hilbert spectrum and marginal spectrum for characterizing the pressure fluctuation signal. The results show that the fluctuating pressure signal of the stilling basin with step-down floor has obvious characteristics of low frequency and large amplitude. The dominant frequencies of the head and tail of the stilling basin are very prominent, and most of the energy is concentrated below 5.0 Hz; with the increase in the relative position of the measuring point, the energy distribution in stilling basin with step-down floor changes from high-frequency component to low-frequency component. The fluctuating pressure signal of the stilling basin with step-down floor has random amplitude modulation and frequency modulation. The marginal spectrum obtained by the HHT method can obtain the local characteristics of the signal more accurately and is more suitable for processing nonlinear and nonstationary signals.

Transient-Based Leak Detection and Monitoring of Water Pipes Using Complementary Ensemble Empirical Mode Decomposition (CEEMD) Method

Transient signal occurs when there is sudden change of pressure inside the pipeline especially due to pressure surge or opening and closing valve. Decomposition method applied in this study to analyze the transient signal and remove noise that contaminate the signal. In this paper, an adaptive decomposition algorithm that is Complementary Ensemble Empirical Mode Decomposition (CEEMD) proposed in order to overcome the problem occur in Hilbert-Huang Transform (HHT) method. This method takes over the Empirical Mode Decomposition (EMD) method that purpose as pre-processing method in HHT. This improvement made to overcome mode mixing and reconstruction error that lies in EMD method. CEEMD method used to extract the IMF’s component of a contaminated signal to remove undesirable noise signal. Instantaneous analysis using Hilbert Transform (HT) apply for selected IMF to locate the feature’s position along the pipeline. The result prove that proposed decomposition method show success with the percentage of error between measured and analysed distance only below that 4% for all features extracted.

Vibration Response of Brick Concrete Buliding under Shaft Blasting

During the blasting construction, the problem of building vibration caused by blasting cannot be ignored. Therefore, this paper uses the measured blasting seismic wave of a shaft in Qingdao Metro as the input parameter to conduct numerical simulation to research the influence of blasting vibration of shaft on brick concrete bulidings. The results show that The Z-direction vibration velocity has obvious local amplification on the roof, and the amplification factor is 1.4-1.9 relative to the top floor. The magnification factor on the backward side is smaller than the magnification factor on the frontward side, and the elevation magnification effect gradually weakens as the elevation difference increases. HHT (Hilbert-Huang Transform) method is used to analyze blasting seismic wave signals, when the blasting seismic wave propagates from the first floor of the brick concrete buliding to the roof, the energy is reduced by about 67%-80%. The frequency band of 0-30 Hz is the main range of blasting energy distribution in brick concrete buildings, and attention should be paid to resonance phenomenon.

Using CNN and HHT to Predict Blood Pressure Level Based on Photoplethysmography and Its Derivatives.

According to the WTO, there were 1.13 billion hypertension patients worldwide in 2015. The WTO encouraged people to check the blood pressure regularly because a large amount of patients do not have any symptoms. However, traditional cuff measurement results are not enough to represent the patient′s blood pressure status over a period of time. Therefore, there is an urgent need for portable, easy to operate, continuous measurement, and low-cost blood pressure measuring devices. In this paper, we adopted the convolutional neural network (CNN), based on the Hilbert–Huang Transform (HHT) method, to predict blood pressure (BP) risk level using photoplethysmography (PPG). Considering that the PPG′s first and second derivative signals are related to atherosclerosis and vascular elasticity, we created a dataset called PPG+; the images of PPG+ carry information on PPG and its derivatives. We built three classification experiments by collecting 582 data records (the length of each record is 10 s) from the Medical Information Mart for Intensive Care (MIMIC) database: NT (normotension) vs. HT (hypertension), NT vs. PHT (prehypertension), and (NT + PHT) vs. HT; the F1 scores of the PPG + experiments using AlexNet were 98.90%, 85.80%, and 93.54%, respectively. We found that, first, the dataset established by the HHT method performed well in the BP grade prediction experiment. Second, because the Hilbert spectra of the PPG are simple and periodic, AlexNet, which has only 8 layers, got better results. More layers instead increased the cost and difficulty of training.

Hilbert-Huang transform of infrasound for tsunami early warning systems

When an earthquake occurs tectonically and volcanically, it is preceded by the emergence of sound wave propagation that cannot be heard by the human ear because it has a low frequency, called infrasound. These infrasound waves are difficult to detect because they are much weaker than earthquake waves and other natural sound waves in nature. The Hilbert-Huang transform method (HHT) is proposed, which in principle decomposes a wave into several simpler sinusoidal harmonic waves so as to separate the low-frequency infrasound waves from the other waves. Once separated, the envelope frequency can be determined which represents the frequency of the earthquake occurrence, then the amplitude represents the predicted earthquake strength, and the wave propagation phase that represents the location of the earthquake source. From the comparison of secondary data, it was obtained that HHT was able to obtain all three information faster than the data from seismographs so that it had the potential to increase the evacuation time which in turn reduced the potential for greater casualties and losses.

Application of the Automatic Segmented Hilbert Huang Transform Method for the Evaluation of the Single-Event Characteristics of Voltage Sags in Power Systems

Depending on the type of the electrical network, the source of the voltage sag (or dip), and the settings of the protective devices, the magnitude, duration, and phase of the voltage sag (or dip) during an event may behave differently. Because of the nonstationary characteristics of the voltage sag, the conventional fast Fourier transform (FFT) and Hilbert Huang transform (HHT) methods show ambiguities at the starting and at the recovery points of the voltage sag waveform. This can lead to errors in the calculation of the single-event characteristics (SEC) of the voltage sag. This article investigates the application of a novel automatic segmented HHT (SHHT) method for evaluating the SEC of the voltage sag caused by different types of symmetrical and unsymmetrical faults in both transmission and distribution networks. It also investigates the influence of several factors on the three important parameters of the voltage sag-the magnitude, the phase angle, and the point-on-wave (POW) of the voltage sag waveform. These factors include the types of fault, the location of the fault, and the X/R ratio of the lines before and after the fault, the transformer and load connections, and the POW of the sag initiation. The simulation results and tests with real data validate the effectiveness of the SHHT method in the evaluation of the SEC of the voltage sag when compared with those obtained using the traditional FFT and the analytical method.

Seismic behavior of MSCSS based on story drift and failure path

Abstract The Mega-Sub Controlled Structure System (MSCSS) is a new type of seismic structural system. This research aims to find weak members in the structure and better describe the failure state. To achieve this, we enhanced the story drift ratio indicator by combining it with the structural failure path and proposed a new comprehensive indicator that can more accurately describe the seismic behavior of the structure. The new concept of seismic behavior is proposed. The seismic waves used in the analysis in this article are generated by the Hilbert-Huang transformation method. The failure path of the structure under random seismic waves is calculated by the weighted rank-sum ratio method. The comprehensive indicator is checked on the MSCSS with or without lead-rubber bearings and traditional Mega-Sub structure. The calculation results show that the story drift ratio alone cannot fully reflect the damage of structures in earthquakes. The new indicator combined with the failure path can describe the seismic behavior of the MSCSS more comprehensively and can better assist the seismic design and optimization of structures.