Hilbert-Huang Transform Spectrum Research Articles

Characterizing Rockbursts and Analysis on Hilbert-Huang Transform Spectrum of Microseismic Events, Shuangjiangkou Hydropower Station, Based on Microseismic Monitoring

The Shuangjiangkou hydropower station in China has complex geological conditions with high in situ stress. During the tunnel excavation, rockbursts occurred frequently, which seriously affected construction progress. Microseismic (MS) monitoring technology was used to explore rock MS activities to predict rockbursts. The MS monitoring system can capture a large number of MS signals. Based on Hilbert–Huang transform (HHT) instantaneous frequency analysis technology, using MATLAB software (R2022a) to write a program to convert the MS waveform, the frequency and energy characteristics of MS signals at a certain time can be obtained. By analyzing the frequency and energy characteristics of every event, the microseism active areas can be determined, and then rockbursts can be predicted scientifically. This paper selected two different construction sites, which were the main powerhouse and the access tunnel in the main powerhouse, as the research background. Introducing HHT instantaneous time–frequency analysis technology conducted MS event dynamic analysis and predicted rockbursts. The HHT spectrum scientifically and comprehensively displayed MS signal frequency characteristics at a certain time and reflected the change laws of signal instantaneous energy and local abrupt change information. The results indicated that some parameter anomalies in the event spectrum can predict rockbursts. For complex tunnel construction conditions, the HHT time–frequency analysis technology can realize a new idea of using a single-channel signal to predict rockbursts, which was very meaningful.

Multi-view features fusion for birdsong classification

As important members of the ecosystem, birds are good monitors of the ecological environment. Bird recognition, especially birdsong recognition, has attracted more and more attention in the field of artificial intelligence. At present, traditional machine learning and deep learning are widely used in birdsong recognition. Deep learning can not only classify and recognize the spectrums of birdsong, but also be used as a feature extractor. Machine learning is often used to classify and recognize the extracted birdsong handcrafted feature parameters. As the data samples of the classifier, the feature of birdsong directly determines the performance of the classifier. Multi-view features from different methods of feature extraction can obtain more perfect information of birdsong. Therefore, aiming at enriching the representational capacity of single feature and getting a better way to combine features, this paper proposes a birdsong classification model based multi-view features, which combines the deep features extracted by convolutional neural network (CNN) and handcrafted features. Firstly, four kinds of handcrafted features are extracted. Those are wavelet transform (WT) spectrum, Hilbert-Huang transform (HHT) spectrum, short-time Fourier transform (STFT) spectrum and Mel-frequency cepstral coefficients (MFCC). Then CNN is used to extract the deep features from WT, HHT and STFT spectrum, and the minimal-redundancy-maximal-relevance (mRMR) to select optimal features. Finally, three classification models (random forest, support vector machine and multi-layer perceptron) are built with the deep features and handcrafted features, and the probability of classification results of the two types of features are fused as the new features to recognize birdsong. Taking sixteen species of birds as research objects, the experimental results show that the three classifiers obtain the accuracy of 95.49%, 96.25% and 96.16% respectively for the features of the proposed method, which are better than the seven single features and three fused features involved in the experiment. This proposed method effectively combines the deep features and handcrafted features from the perspectives of signal. The fused features can more comprehensively express the information of the bird audio itself, and have higher classification accuracy and lower dimension, which can effectively improve the performance of bird audio classification.

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.

Research on Vibration Saltation of the Transformer Core Caused by DC Bias of Based on Empirical Mode Decomposition

This paper presents a time–frequency analysis of the vibration of transformer under direct current (DC) bias through Hilbert–Huang transform (HHT). First, the empirical mode decomposition (EMD) process, which is the key in HHT, was introduced. The results of EMD, namely, intrinsic mode functions (IMFs), were calculated and summed by Hilbert transform (HT) to obtain time-dependent series in a 2D time–frequency domain. Next, the theory of DC bias for the transformer was analyzed. In consideration of the DC bias effect and in combination with the existing transformer vibration-related mechanism, the electromagnetic force equations of the transformer core were deduced. Lastly, a test system of vibration measurement for the transformer was set up. Three direction (x, y, and z axes) components of core vibration were measured. Decomposition of EMD and HHT spectra showed that vibration strength increased, and odd harmonics were produced with DC bias. This method illustrates the most obvious vibration distortion in the z-axis direction when the transformer is DC biased. Among them, the distortion of IMF3 has increased by more than 5 times. However, the distortion in the x-axis and y-axis directions also exists, but it is not obvious. Especially, 50 Hz component appeared in z-direction, 50 Hz component increased twofold in y-direction, and 150 Hz component increased threefold in z-direction. Results indicated that HHT can not only provide the occurrence time of DC bias but can also obtain the signal change components of the transformer vibration. Thus, HHT is a viable signal processing tool for transformer health monitoring.

End-to-End Noisy Speech Recognition Using Fourier and Hilbert Spectrum Features

Despite the progress of deep neural networks over the last decade, the state-of-the-art speech recognizers in noisy environment conditions are still far from reaching satisfactory performance. Methods to improve noise robustness usually include adding components to the recognition system that often need optimization. For this reason, data augmentation of the input features derived from the Short-Time Fourier Transform (STFT) has become a popular approach. However, for many speech processing tasks, there is an evidence that the combination of STFT-based and Hilbert–Huang transform (HHT)-based features improves the overall performance. The Hilbert spectrum can be obtained using adaptive mode decomposition (AMD) techniques, which are noise-robust and suitable for non-linear and non-stationary signal analysis. In this study, we developed a DeepSpeech2-based recognition system by adding a combination of STFT and HHT spectrum-based features. We propose several ways to combine those features at different levels of the neural network. All evaluations were performed using the WSJ and CHiME-4 databases. Experimental results show that combining STFT and HHT spectra leads to a 5–7% relative improvement in noisy speech recognition.

Chatter identification in turning process based on vibration analysis using Hilbert-Huang transform

In machining process, the increasing cutting depth is aimed to accelerate machining operations in a short time. However, the increasing cutting depth can cause chatter vibration at any time. Chatter can accelerate tool wear and lead to poor machined surface. This paper studied the application of Hilbert-Huang transform (HHT) to analyse chatter caused by the increasing cutting depth during operation. Chatter vibration is typical of non-stationary and non-linear vibration signals, therefore it should be analysed by appropriate signal processing; HHT. In this research, initially “hammering tests” were conducted to observe dynamic modal parameters of cutting system; modal mass, damping ratio, and stiffness. Then stability lobe chart was generated based on those dynamic modal parameters to determine cutting parameters. Second, turning tests were conducted and then vibrations obtained in turning tests were analysed using HHT for chatter detection. The results were then compared by conventional signal processing; short-time Fourier (STFT) transforms. The results show that the empirical mode decomposition (EMD) of HHT process separated complex vibrations into simple components and isolated chatter from the others. The chatter was isolated in the first IMF. Therefore, chatter can be identified by EMD process. In the spectrum analysis, HHT spectra showed its superiority over STFT spectra. HHT spectra provided high time resolution and high frequency resolution both rather than STFT spectra that provided blurry and blocked spectra. The implication is that HHT can be applied to monitor the machining process.

Spectral Analysis of Electricity Demand Using Hilbert–Huang Transform

The large amount of sensors in modern electrical networks poses a serious challenge in the data processing side. For many years, spectral analysis has been one of the most used approaches to extract physically meaningful information from a sea of data. Fourier Transform (FT) and Wavelet Transform (WT) are by far the most employed tools in this analysis. In this paper we explore the alternative use of Hilbert–Huang Transform (HHT) for electricity demand spectral representation. A sequence of hourly consumptions, spanning 40 months of electrical demand in Spain, has been used as dataset. First, by Empirical Mode Decomposition (EMD), the sequence has been time-represented as an ensemble of 13 Intrinsic Mode Functions (IMFs). Later on, by applying Hilbert Transform (HT) to every IMF, an HHT spectrum has been obtained. Results show smoother spectra with more defined shapes and an excellent frequency resolution. EMD also fosters a deeper analysis of abnormal electricity demand at different timescales. Additionally, EMD permits information compression, which becomes very significant for lossless sequence representation. A 35% reduction has been obtained for the electricity demand sequence. On the negative side, HHT demands more computer resources than conventional spectral analysis techniques.

Optimal Intrinsic Mode Function Based Detection of Motor Bearing Damages

This paper proposes a model which uses the greedy algorithm to select the optimal intrinsic mode functions (IMFs) of the empirical mode decomposition (EMD), namely the greedy empirical mode decomposition (GEMD) model. The optimal IMFs can more sufficiently represent the characteristics of damage bearings since the proposed GEMD model effectively selects some IMFs not affected by noise. To validate the superiority of the proposed GEMD model, various damage types of motor bearings were shaped by electrical discharge machining (EDM) in this experiment. The measured motor current signals of various types were decomposed to IMFs by using EMD. Then the optimal IMFs can be obtained by using the proposed GEMD model. The results show that the Hilbert–Huang transform (HHT) spectrums when using the optimal IMFs become easier in the detection system than when using all IMFs. Simultaneously, the detection accuracy of motor bearing damages is increased by using the features extracted from the lower complexity HHT spectrum. The average detection accuracy can be also improved from 69.5% to 74.6% by using the features extracted from the GEMD-HHT spectrum even in a noise interference 10dB

Recognition of Damage Modes and Hilbert–Huang Transform Analyses of 3D Braided Composites

The identification and classification of acoustic emission (AE) based failure modes are complex due to the fact that AE waves are generally released simultaneously from all AE-emitting damage sources. To fully understand the occurrence of damage and the damage evolution law of 3D braided composites, the tensile response characteristics and failure mechanisms of such composites were revealed by experiments, followed by frequency domain analyses. The results indicated good correlation between the number of AE events and the evolution of damage in 3D braided composites. After an AE signal was decomposed by the Hilbert–Huang transform (HHT) method, it might extract and separate all damage modes included in this AE signal. Additionally, the frequency saltation in the HHT spectra implied changes in the failure mode of the 3D braided composites. This study provides an effective new method for the analysis of the tensile fracture mechanism in 3D braided composites.

Profiling cellular morphodynamics by spatiotemporal spectrum decomposition.

Cellular morphology and associated morphodynamics are widely used for qualitative and quantitative assessments of cell state. Here we implement a framework to profile cellular morphodynamics based on an adaptive decomposition of local cell boundary motion into instantaneous frequency spectra defined by the Hilbert-Huang transform (HHT). Our approach revealed that spontaneously migrating cells with approximately homogeneous molecular makeup show remarkably consistent instantaneous frequency distributions, though they have markedly heterogeneous mobility. Distinctions in cell edge motion between these cells are captured predominantly by differences in the magnitude of the frequencies. We found that acute photo-inhibition of Vav2 guanine exchange factor, an activator of the Rho family of signaling proteins coordinating cell motility, produces significant shifts in the frequency distribution, but does not affect frequency magnitude. We therefore concluded that the frequency spectrum encodes the wiring of the molecular circuitry that regulates cell boundary movements, whereas the magnitude captures the activation level of the circuitry. We also used HHT spectra as multi-scale spatiotemporal features in statistical region merging to identify subcellular regions of distinct motion behavior. In line with our conclusion that different HHT spectra relate to different signaling regimes, we found that subcellular regions with different morphodynamics indeed exhibit distinct Rac1 activities. This algorithm thus can serve as an accurate and sensitive classifier of cellular morphodynamics to pinpoint spatial and temporal boundaries between signaling regimes.

Feature extraction for gas metal arc welding based on EMD and time–frequency entropy

Hilbert–Huang transform (HHT) and time–frequency entropy were used to estimate the stability of short-circuiting gas metal arc welding (GMAW). First, the current signals were divided by empirical mode decomposition (EMD) into several intrinsic mode functions (IMFs). Then the IMFs were converted by Hilbert transform to Hilbert–Huang spectrum which describes the instantaneous time–frequency distribution of welding current signals. Since the uniformity of energy amplitude distribution with time–frequency reflects the stability, we introduced time–frequency entropy to quantify the energy distribution with time–frequency range in the HHT spectrum. We found HHT can effectively depict the amplitude with time and frequency distribution of welding current signals, and the welding was more stable when the time–frequency entropy was larger. Thus, this is a new way to assess and quantify the stability of short-circuiting GMAW.

Morphodynamic Profiling of Cell Protrusion Based on Spatiotemporal Spectrum Decomposition and Unsupervised Clustering

Cellular morphogenesis is governed and regulated by complex interactions between the cytoskeleton and molecular pathways. Due to their central roles in the differentiation, embryogenesis and homeostasis process, cell morphology and morphodynamics are often used for qualitative and quantitative assessments of cell state. Here, we propose a framework to quantitatively profile cellular morphodynamics based on an adaptive spectrum decomposition method. This method decomposes the motion of cell boundary into analytical instantaneous frequency spectrum through Hilbert-Huang transform (HHT). Subsequently, we computed for each decomposed signal the distribution of instantaneous frequency and amplitude, from which we compiled the HHT spectrum. For spontaneously protrusive Cos7 cells, the instantaneous magnitudes of protrusion were found to greatly vary across different cells with nearly identical genetic and molecular backgrounds, whereas the frequency spectra were remarkably consistent. Meanwhile we examined Cos7 cells in which the Vav2 Guanine Exchange Factor (GEF) activity was acutely perturbed by optogenetic tools, and found significant shifts in the frequency distribution for specific signals. We thus concluded that edge motion velocity is an arbitrary parameter of cell morphogenesis whereas the frequency spectrum encodes the molecular state of regulation. The features extracted from the HHT spectrum could be used as a classifier to group subcellular regions into numerous characteristic sectors with specific molecular states through Statistical Region Merging (SRM) based clustering. Finally, we monitored the Rac1 activity downstream of Vav2 expressed in Cos7 cells and found that those clustering sectors distinguished by morphodynamic parameters indeed reflect regions with different local signaling. Thus, cell morphodynamic behavior can be used to detect different modes of operations or perturbations in cellular signaling.

The chatter identification in end milling based on combining EMD and WPD

On-line detection of chatter in the cutting process can identify the chatter in time or before the chatter happens, so the initiative to change the cutting parameters can be taken to avoid chatter and improve the surface quality. At present, time-frequency analysis technology is performed to extract the time-frequency features of chatter by scholars. With respect to the modal aliasing problem in the process of empirical mode decomposition (EMD), the chatter identification method of combining EMD and wavelet packets decomposition (WPD) is proposed to eliminate the influence of modal aliasing. To fully extract the main features of signal, the intrinsic mode functions (IMFs) changing consistent with power spectrum or amplitude-frequency are selected for signal reconstruction. Then, WPD is used in the reconstructed signal. The two times reconstruction of signal is based on wavelet packet node with the maximum energy. The distribution of frequency and energy in the time domain is presented by Hilbert Huang Transform (HHT) spectrum, and the mean value and standard deviation of the HHT spectrum are extracted as the feature vectors. The chatter features can be extracted from the original simulation signal by this method. Three groups of experiments with different cutting depth which are on behalf of the three cutting conditions (stable cutting, slight chatter, and severe chatter) were carried out. More cutting tests were carried out under the same cutting condition. Experimental results show that this method can be used to effectively identify the chatter features in milling process.

Time-frequency analysis of DC bias vibration of transformer core on the basis of Hilbert–Huang transform

<p>This paper presents a time–frequency analysis of the vibration of transformer under direct current (DC) bias through Hilbert–Huang transform (HHT). First, the theory of DC bias for the transformer was analyzed. Next, the empirical mode decomposition (EMD) process, which is the key in HHT, was introduced. The results of EMD, namely, intrinsic mode functions (IMFs), were calculated and summed by Hilbert transform(HT) to obtain time-dependent series in a 2D time–frequency domain. Lastly, a test system of vibration measurement for the transformer was set up. Three direction (x, y, and z axes) components of core vibration were measured. Decomposition of EMD and HHT spectra showed that vibration strength increased, and odd harmonics were produced with DC bias. Results indicated that HHT is a viable signal processing tool for transformer health monitoring.</p>

Time–frequency interpretation of multi-frequency signal from rotating machinery using an improved Hilbert–Huang transform

The Hilbert–Huang transform (HHT) has proven to be a promising tool for the analysis of non-stationary signals commonly occurred in industrial machines. However, in practice, multi-frequency intrinsic mode functions (IMFs) and pseudo IMFs are likely generated and lead to grossly erroneous or even completely meaningless instantaneous frequencies, which raise difficulties in interpreting signal features by the HHT spectrum. To enhance the time–frequency resolution of the traditional HHT, an improved HHT is proposed in this study. By constructing a bank of partially overlapping bandpass filters, a series of filtered signals are obtained at first. Then a subset of filtered signals, each associated with certain energy-dominated components, are selected based on the maximal-spectral kurtosis–minimal-redundancy criterion and the information-related coefficient, and further decomposed by empirical mode decomposition to extract sets of IMFs. Furthermore, IMF selection scheme is applied to select the relevant IMFs on which the HHT spectrum is constructed. The novelty of this method is that the HHT spectrum is just constructed with the relevant, almost monochromatic IMFs rather than with the IMFs possibly with multiple frequency components or with pseudo components. The results on the simulated data, test rig data, and industrial gearbox data show that the proposed method is superior to the traditional HHT in feature extraction and can produce a more accurate time–frequency distribution for the inspected signal.

A case study of damage detection in four-bays steel structures using the HHT approach

This study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert-Huang transform (HHT) method. Two damage detection indices are proposed: the ratio of bandwidth (RB), and the ratio of effective stiffness (RES). The nonlinear four bays multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA earthquake data (Japan 311, Chi-Chi 921) are used as the excitations. Next, the damage detection indices obtained using the HHT and the fast Fourier transform (FFT) methods are evaluated based on the acceleration responses of the structures to earthquakes. Simulation results indicate that, the column of the 1st floor is the first yielding position and the RB value is changed when the RES<90% in all cases. Moreover, the RB value of the 1st floor changes more sensitive than those from the top floor. In addition, when the structural response is nonlinear (i.e., RES<100%), the RB and the RES curves indicate the incremental change in the HHT spectra. However, the same phenomenon can be found from FFT spectra only when the stiffness reduction is large enough. Therefore, the RB estimated from the smoothed HHT spectra is an effective and sensitive index for detecting structural damage.

An Approach to Monitoring of Gearbox Based on HHT Spectrum

Hilbert-Huang Transform (HHT) Spectrum is analyzed, and is compared with Wigner-Ville distribution(WVD). And it is proposed a method that is “band pass filtering --signal purification and reconstruction --HHT spectrum analyses” method to carry on the state recognition and fault diagnosis of the mechanical equipment. The compared signals include: the signals of harmonic, amplitude modulation and frequency modulation, and the mixed signals that are composed of these single signal, then it is pointed out: HHT Spectrum have higher frequency resolution than WVD, and it has overcome the latter influence of cross-term interference. At last, real signals of fault gear are analyzed by this method, and it is indicated that the method can offer a new and effective method for fault diagnosis and condition monitoring.

Applications of Hilbert-Huang transform to structural damage detection

This study investigates the feasibility of detecting structural damage using the HHT method. A damage detection index, the ratio of bandwidth (RB) is proposed. This index is highly correlated or approximately equal to the change of equivalent damping ratio for an intact structure incurring damage from strong ground motions. Based on an analysis of shaking table test data from benchmark models subjected to adjusted Kobe and El Centro earthquakes, the damage detection index is evaluated using the Hilbert-Huang Transform (HHT) and the Fast Fourier Transform (FFT) methods, respectively. Results indicate that, when the response of the structure is in the elastic region, the RB value only slightly changes in both the HHT and the FFT spectra. Additionally, RB values estimated from the HHT spectra vs. the PGA values change incrementally when the structure response is nonlinear i.e., member yielding occurs, but not in the RB curve from the FFT spectra. Moreover, the RB value of the top floor changes more than those from the other floors. Furthermore, structural damage is detected only when using the acceleration response data from the top floor. Therefore, the ratio of bandwidth RB estimated from the smoothed HHT spectra is an effective and sensitive damage index for detecting structural damage. Results of this study also demonstrate that the HHT is a powerful method in analyzing the nonlinear responses of steel structures to strong ground motions.

Detecting the sensitivity of structural damage based on the Hilbert‐Huang transform approach

PurposeThis study aims to investigate the relationship between structural damage and sensitivity indices using the Hilbert‐Huang transform (HHT) method.Design/methodology/approachThe relationship between structural damage and the sensitivity indices is obtained by using the HHT method. Three sensitivity indices are proposed: the ratio of rotation (RR), the ratio of shifting value (SV) and the ratio of bandwidth (RB). The nonlinear single degree of freedom and multiple degree of freedom models with various predominant frequencies are constructed using the SAP2000 program. Adjusted PGA El Centro and Chi‐Chi (TCU068) earthquake data are used as the excitations. Next, the sensitivity indices obtained using the HHT and the fast Fourier transform (FFT) methods are evaluated separately based on the acceleration responses of the roof structures to earthquakes.FindingsSimulation results indicate that, when RR &lt; 1, the structural response is in the elastic region, and neither the RB nor SV in the HHT and FFT spectra change. When the structural response is nonlinear, i.e. RR1, a positive trend of change occurs in RB and RR, while in the HHT spectra, SV increases with an increasing RR. Moreover, the FFT spectra reveal that SV changes only when the RR is sufficiently large. No steady relationship between the RB and the RR can be found.Originality/valueThe paper demonstrates the effectiveness of the HHT method.

A comparison study of improved Hilbert–Huang transform and wavelet transform: Application to fault diagnosis for rolling bearing

For rolling bearing fault detection, it is expected that a desired time–frequency analysis method should have good computation efficiency, and have good resolution in both time domain and frequency domain. As the best available time–frequency method so far, the wavelet transform still cannot fulfill the rolling bearing fault detection task very well since it has some inevitable deficiencies. The recent popular time–frequency analysis method, Hilbert–Huang transform (HHT), has good computation efficiency and does not involve the concept of the frequency resolution and the time resolution. So the HHT seems to have potential to become a perfect tool for rolling bearing fault detection. However, in practical applications, the HHT also suffers from some unsolved deficiencies. To ameliorate these deficiencies, by seeking help from the wavelet packet transform (WPT) and a simple but effective method for intrinsic mode function (IMF) selection, an improved HHT is put forward in this studying. Several numerical study cases will be used to validate the capabilities of the improved HHT. Finally, the improved HHT's performance in rolling bearing fault detection is compared with that of the wavelet based scalogram through experimental case studies. The comparison results have shown that (1) the improved HHT has better resolution both in time domain and in frequency domain than the scalogram; (2) the improved HHT has better computing efficiency than scalogram; (3) the HHT spectrum also has one unresolved and maybe inevitable deficiency—ripple phenomenon in its estimated frequency, which would mislead our analysis.