Hilbert-Huang Transform Research Articles

Two-dimensional Hilbert-Huang transform-based thermographic data processing for non-destructive material defect detection

ABSTRACT Previous research has established the Hilbert-Huang transform (HHT) as a powerful tool for processing and analysing one-dimensional time series signals. Its extension into multi-dimensional Euclidean spaces further demonstrates its versatility. In this study, we leverage a two-dimensional (2D) HHT to enhance non-destructive testing, utilising active infrared thermographic data to improve the detection of material defects. The proposed methodology incorporates a 2D HHT, which synergises multidimensional ensemble empirical mode decomposition with the Riesz transform (RT). This combination is adept at uncovering both global (i.e. intrinsic mode functions) and local (i.e. phase angle and spatial frequency) information. In particular, RT is integrated with a Gaussian filter, which allows for a more thorough analysis of the inherent characteristics of defects through the monogenic signal produced by RT. The experimental application of this method on a mosaic sample, intentionally embedded with defects, has yielded promising results. The approach effectively distinguishes critical defect signals from the surroundings, leading to more accurate and clearer results.

Comparative analysis of time-frequency transform-based differential protection strategy for distributed generation integrated microgrid

This study presents a differential protection strategy for distributed generation-integrated power systems. It explores and compares two enhanced traditional signal processing methods: the Hilbert-Huang Transform (HHT) and the S-transform. The HHT has been improved by incorporating Variational Mode Decomposition (VMD), while the S-transform has been augmented with a Fourier component to create the Fast Fourier Discrete Orthonormal Stockwell Transform (FFDOST). VMD and FFDOST are applied to three-phase current signals from microgrid buses to calculate the Spectral Energy (SE). Fault detection is based on Differential Energy (DE), which measures the difference in SE between two specific faulty buses, with a tripping signal activated when DE surpasses a predetermined threshold. The effectiveness of this approach is rigorously tested and validated on a typical DG-integrated microgrid that includes synchronous generators and wind farms. A comprehensive set of case studies conducted on an IEC microgrid model examines various fault types (symmetrical and asymmetrical) across different operational modes (islanded and grid-connected) and configurations (radial and looped) under varying noise conditions. The performance of these two modified differential strategies is critically compared to determine the more effective method. Detailed sample-wise analysis and graphical presentations enrich the documentation of results. The VMD-based method outperforms the FFDOST approach, detecting faults 3 to 15 samples sooner and achieving quicker fault detection by approximately 0.05 milliseconds. Comparative analyses suggest that VMD is a faster, more secure, and highly reliable method for fault detection and mitigation, enhancing microgrids' operational security and reliability.

Comparative Study on PSD and HHT Techniques for Condition Assessment of Steel Truss Bridge Using Acceleration Data

Bridge structures deteriorate over time due to factors like corrosion, fatigue, aging of materials, and unexpected natural or accidental events. Consequently, the vibrations measured in these structures exhibit time-varying and non-stationary characteristics. Additionally, non-linearities are inherent in these structures due to material behavior, boundary condition changes, and joints or connections. Analysis of non-linear and non-stationary structural vibration data is necessary to extract information on the condition of the bridge. Most methods assessing bridge conditions from acceleration responses rely on the Power Spectral Density (PSD) which is based on the Fourier Transform. However, the accuracy of the Fourier transforms for non-linear and non-stationary signals limits its application potential. The Hilbert–Huang Transform (HHT) has emerged as an alternative for handling these non-stationary signals due to its time-frequency-energy representation. This study provides a comparative study of both techniques by utilizing the data obtained from continuously monitored Pamban Bridge. This steel truss bridge was fitted with accelerometers to record bidirectional acceleration time histories at twenty bottom node points on the bridge. This study examines the continuous variations in the frequency component by both methods for 136 days. A linear best-fit trendline is obtained for the frequency parameters at different sensor positions. The slope and intercept values of this linear best fit trendline is further studied. The HHT showcases various evolving dominant frequency components over time in contrast to the PSD representation. The frequency spectrum from the HHT displays less variation over time at each sensor position compared to the predominant peak value derived from the PSD of the acceleration signal. The spatial variability in the predominant frequency obtained from HHT is also less than the PSD. Therefore, the ability of HHT to discriminate damages needs further investigations.

Vertical coherence of coherent structures during sand and dust storms: A multi-height synchronous observation study

An experiment was conducted on the Qingtu Lake Observation Array (QLOA) to measure wind and dust information at various wall-normal heights during the sand and dust storm (SDS) process. According to the indicators of the non-stationary features in the flow field, the SDS process can be divided into three stages: ascending, stabilizing, and descending. Based on this division, the Hilbert–Huang transform (HHT) is employed to extract dominant flow structures, which carries a significant portion of the turbulent kinetic energy. Moreover, the HHT spectrum of stream-wise velocity component reveals that the scales of the dominant structures are approximately hundreds of meters in the horizontal direction, and hence suggests the presence of large and very large-scale coherence during the SDS. The hypotheses of Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, 1976)] and Davenport [“The spectrum of horizontal gustiness near the ground in high winds,” Q. J. R. Meteorol. Soc. 87, 194–211 (1961)] are utilized to demonstrate the vertical coherence of turbulence, which suggests the wall-similarity and evolution of inner/outer interactions for coherent structures during the SDS. Finally, the coherence spectrum [γL2=exp(−2c1Δz/λx)] and the linear transfer kernel [|HL2|=exp(d1−d2Δz/λx)] are parameterized, where c1, d1, d2 are fitting parameters, Δz is wall-normal offset, and λx refers to streamwise wavelength, to illustrate the evolution of the interactions between near-wall and outer regions during the SDS, which highlights the strong connections during the stabilizing stage. In general, the present study analyzed horizontal and wall-normal structures for a comprehensive SDS process, and thus, these findings present abundant features of wall-attached eddies which further be used to improve/enrich existing near-wall models.

Adaptively multi-scale microstructure characterization of cancellous bone via photoacoustic signal decomposition

Osteoporosis is a systemic disease with a high incidence in the elderly and seriously affects the quality of life of patients. Photoacoustic (PA) technology, which combines the advantages of light and ultrasound, can provide information about the physiological structure and chemical information of biological tissues in a non-invasive and non-radiative way. Due to the complex structural characteristics of bone tissue, PA signals generated by bone tissue are non-stationary and nonlinear. However, conventional PA signal processing methods are not effective for non-stationary signal processing. In this study, an empirical mode decomposition (EMD)-based Hilbert-Huang transform (HHT) PA signal analysis method, called HHT PA signal analysis (HPSA), was developed to assess the microstructure information of bone tissue, which is closely related to bone health. The feasibility of the HPSA method in bone health assessment was proven by numerical simulation and experimental studies on animal samples with different bone volume/total volume (BV/TV) and bone mineral densities. First, based on adaptive EMD, the different modes correlated with multi-scale information were mined from the PA signal, the correlations between different intrinsic mode function (IMF) modes and BV/TVs were analyzed, and the optimal mode for more efficient PA time–frequency analysis was selected. Second, multi-wavelength HPSA was used to assess the changes in the chemical components of the bone tissue. The results demonstrate that the HPSA method can distinguish bones with different BV/TVs and microstructure conditions adaptively with high efficiency. They further emphasize the potential of PA techniques in characterizing biological tissues in bones for early and rapid detection of bone diseases.

Dynamic response and seismic vulnerability assessment of the near-fault steep slope

Existing field data demonstrates that structures situated near faults, such as slopes, dams, and bridges, are particularly vulnerable to damage. Near-fault ground motions exhibit marked disparities from their far-field counterparts, necessitating thorough investigation. This study conducts a comprehensive analysis of ground motion characteristics utilizing response spectra, Hilbert-Huang Transform (HHT), and marginal spectra to discern near-fault pulse-like ground motions (PLGMs), near-fault non-pulse-like ground motions (NPGMs), and far-fault ground motions (FFGMs). PLGMs distinguished by their heightened energy content, typically induce more pronounced amplification effects compared to NPGMs and FFGMs. Employing an efficacy criterion, optimal intensity measures (IMs) are identified and linked to dynamic response, referred to as engineering demand parameters (EDPs). Velocity-based IMs demonstrate substantial correlations across diverse ground motion types for both plastic volume ratio (PVR) and crest displacement (Dc). Lastly, probabilistic seismic demand models are leveraged to establish seismic vulnerability curves for steep slopes exposed to PLGMs and NPGMs. Notably, with Dc as the EDP, the exceedance probabilities associated with the three IMs under PLGMs generally surpass those under NPGMs. This underscores the propensity of PLGMs to trigger larger displacements in slopes, rendering them more prone to failure.

Comprehensive degree of nonlinearity in the dynamic response of high-speed Maglev train

The aim of this study is to propose a method for evaluating the comprehensive degree of nonlinearity in the dynamic response of high-speed maglev train system through mathematical modeling and numerical simulation. A model of a typical high-speed maglev vehicle is established based on the principles of maglev vehicle dynamics, and control models for the suspension magnet and the guide magnet are developed using principles from the electromagnetism and automatic control theory. The vibration responses of the vehicle system, including acceleration and electromagnetic forces are calculated using a fast numerical integration method. This calculation is performed for various control parameters and track harmonic excitations. The Hilbert-Huang transform (HHT) is adopted to decompose the response signal and derive the local mean frequency (amplitude) and instantaneous frequency (amplitude) of the response, based on which the Degree of Nonlinearity (DN) of the vibration response of a single component is obtained by calculating the deviation between the instantaneous frequency and the mean frequency. The Comprehensive Degree of Nonlinearity (CDN) of the vibration response in the maglev train system is proposed and defined by incorporating the DNs of the vertical and lateral vibrations of the carbody, bogie, suspension magnet and guide magnet, and by quantitatively evaluating them. The effects of the electromagnet control parameters and harmonic irregularities (wavelength and amplitude) of the track on the DN of each component and the CDN of the entire vehicle system are analyzed in detail. The analysis results show that the DN and CDN can demonstrate the extent of instability in the vehicle system and can be applied for safety warning on maglev vehicles.

Detekcija klimatskih kolebanja Hilbert-Huangovom metodom na podacima stoljetnog opservatorija Zagreb-Grič, Hrvatska

Advanced statistical methods are applied on long-term data sets from Zagreb-Grič centennial observatory in Croatia to address recent climate change and variabilities; annual averages are used. Hilbert-Huang transform (HHT), consisting of empirical mode decomposition (EMD) and Hilbert spectral analysis (HSA), is an empirically based data-analysis method for extracting periodic components embedded within generally nonlinear and non-stationary data. The EMD splits the original series into a so-called intrinsic mode functions (IMFs). First, using the EMD algorithm, intrinsic mode functions (IMFs) are obtained. The analysis of low frequency IMFs indicates significant influence of the North-Atlantic Oscillation on the air temperature, cloudiness and precipitation series in the part of northern Croatia. For the considered climatic elements, the analysis revealed mild deviations in natural fluctuations of the analyzed signal for the last 30 to 40 years, which are most likely caused by anthropogenic activities. Next, HSA is applied to each IMF obtained for the series of annual averages of sea level air pressure. In order to validate this approach and the results, an associated Hilbert spectrum (HS) is compared with the continuous wavelet analysis, i.e., this is another corresponding checkup. The comparison shows significantly improved time and frequency resolution in favor of HS. Moreover, HS provides a unique capability of displaying intra-wave frequency modulation, i.e., changes in frequency that occur within one cycle of oscillation.

An adaptive frequency-based C/N0-constrained multipath extraction and mitigation method for GNSS pseudorange measurements

Abstract The multipath effect poses an inevitable challenge for Global Navigation Satellite System (GNSS) receivers, particularly pronounced in smart devices, which are nevertheless the most common means through which the general public accesses GNSS positioning. Therefore, we propose a novel adaptive method for extracting multipath errors, which fully exploits the multipath frequency characteristics, multipath repeatability, and the correlation between multipath errors and carrier-to-noise ratio (C/N0). This approach aims to enhance the susceptibility of smart devices to multipath influences. Specifically, this method uses the code minus carrier method to calculate the noisy multipath error, exploits the correlation between C/N0 and multipath to constrain the frequency range, employs the ensemble empirical mode decomposition method to decompose the error signal, and utilizes the Hilbert–Huang transform method to obtain the frequency information of the signal component. In multipath repeatability, the proposed method can effectively improve the correlation of multipath signals by up to 0.79. By applying the extraction method, the positioning performance of smart devices can be improved by 13.9%. Therefore, the proposed method extracts multipath error more accurately and is highly usable in low-cost devices.

Analysis of application of entropy methods of vibration diagnostic signal processing to assess technical condition of pipelines

The purpose of this article is to review the existing reliability problems of pipeline systems of power complexes. The article considers the existing statistical and logistics systems, which allow to process diagnostic information when assessing the technical condition of pipelines. Modern diagnostic methods are mainly based on the use of vibration, sound, and ultrasonic sensors. The presence of a defect in a pipeline is determined by analysis of the amplitude of a diagnostic signal. Higher efficiency in detecting defects was shown by probability-statistical methods of signal analysis, which are based on chaos theory. One such method is entropy analysis. Analysis of modern signal processing methods has shown that methods based on chaos theory are the most effective. The possibility of using entropy indices as sensitive diagnostic signs is considered. Comparative analysis of signal processing was carried out using entropy methods (Shannon entropy, Kolmogorov entropy) and using known statistical and logistic methods (Fourier Transform, Wavelet Transform, Hilbert-Huang Transform). The analysis results showed that entropy indicators respond to a change in signal structure caused by the presence of a defect in the pipeline or Entropy analysis is a promising method of processing diagnostic signals when assessing the technical condition of pipelines.

Towards Analysis of Multivariate Time Series Using Topological Data Analysis

Topological data analysis (TDA) has proven to be a potent approach for extracting intricate topological structures from complex and high-dimensional data. In this paper, we propose a TDA-based processing pipeline for analyzing multi-channel scalp EEG data. The pipeline starts with extracting both frequency and temporal information from the signals via the Hilbert–Huang Transform. The sequences of instantaneous frequency and instantaneous amplitude across all electrode channels are treated as approximations of curves in the high-dimensional space. TDA features, which represent the local topological structure of the curves, are further extracted and used in the classification models. Three sets of scalp EEG data, including one collected in a lab and two Brain–computer Interface (BCI) competition data, were used to validate the proposed methods, and compare with other state-of-art TDA methods. The proposed TDA-based approach shows superior performance and outperform the winner of the BCI competition. Besides BCI, the proposed method can also be applied to spatial and temporal data in other domains such as computer vision, remote sensing, and medical imaging.

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

Electromyography signal based hand gesture classification system using Hilbert Huang transform and deep neural networks

This research aims to provide the groundwork for smartly categorizing hand movements for use with prosthetic hands. The hand motions are classified using surface electromyography (sEMG) data. In reaction to a predetermined sequence of fibre activation, every single one of our muscles contracts. They could be useful in developing control protocols for bio-control systems, such human-computer interaction and upper limb prostheses. When focusing on hand gestures, data gloves and vision-based approaches are often used. The data glove technique requires tedious and unnatural user engagement, whereas the vision-based solution requires significantly more expensive sensors. This research offered a Deep Neural Network (DNN) automated hand gesticulation recognition system based on electromyography to circumvent these restrictions. This work primarily aims to augment the concert of the hand gesture recognition system via the use of an artificial classifier. To advance the recognition system's classification accuracy, this study explains how to build models of neural networks and how to use signal processing methods. By locating the Hilbert Huang Transform (HHT), one may get the essential properties of the signal. When training a DNN classifier, these characteristics are sent into it. The investigational results reveal that the suggested technique accomplishes a better categorization rate (98.5 % vs. the alternatives).

Investigation of the dynamic response of h-type anti-slide pile based on shaking table test

The h-type anti-slide piles (hTPs) are extensively utilized in slope stabilization projects, yet their response to seismic activities remains inadequately understood. This study investigated the dynamic response of hTPs with circular cross-sections (hTCPs) through a shaking table test, focusing on seismic events along Jiuzhaigou-Mianyang highway slopes (ZK142 + 124 to ZK142 + 274). Time-frequency analysis using Fast Fourier Transform (FFT) and Hilbert-Huang Transform (HHT) was conducted. The peak acceleration and its direction, dynamic earth pressure and its sharing ratio, and moment were characterized, and the variations of pile displacement and the seismic damage on different parts of hTCPs were analyzed under varying loading conditions. Results reveal a distinct pressure distribution and damage characteristics between the long and short piles in hTCPs. A positive correlation between peak accelerations and loading conditions was observed in both long and short piles, with peak amplification occurring only at the top of long piles. Long piles exhibited diverse acceleration directions under different loading conditions, contrasting with the infrequent occurrence in short piles. The peak dynamic earth pressure distribution varied between the front and back side of pile bodies, with opposite overall trends between the long and short piles. The sharing ratio displayed an increasing followed by decreasing trend in long piles, but an opposite trend in short piles, with the turn point occurring at a loading condition of 0.3 g. These differences were significantly influenced by El Centro waves within a low frequency band (13.34 Hz–16.18 Hz), as a single large peak HHT energy spectrum was observed in long piles, but multiple and destructive low-frequency energy spectra in short piles. The results suggest an independent dynamic response occurred in the long and short piles of hTCPs during shaking table test, providing insights for their field engineering application in seismic active regions.

Seismic mitigation analysis of base-isolated structure with sliding magnetic bearings considering local-site conditions

Base-isolation systems applied in building structures and infrastructures often suffer from damage even failure during strong earthquakes. The adaptability of isolators to local sites is a main concern for the robust design of base-isolation systems. In this study, seismic mitigation analysis of base-isolated structure with newly-developed sliding hydro-magnetic bearing (HMB) and sliding implant-magnetic bearing (IMB) considering local-site conditions is carried out. Extension of modeling of sliding magnetic bearings is first conducted based on the data of shaking-table tests of a reduced-scale base-isolated structure. To assess the instantaneous frequency for quantifying sliding magnetic bearings’ resisting force, the Hilbert–Huang transform (HHT) is applied. The influences of local-site conditions upon mitigation performance of the sliding magnetic bearings are then addressed, including far-field and near-field, ground motions with and without velocity pulses, and hard-soil and soft-soil. For comparison purposes, the seismic mitigation analysis of the base-isolated structure attached with lead rubber bearing (LRB) and curved surface slider (CSS) is carried out as well. Numerical results show that the sliding magnetic bearings outperform the state-of-the-art seismic isolators in both seismic mitigation and deformation constraint, and the IMB has excellent applicability for engineering since its perfect adaptability to local sites. However, the LRB cannot achieve the desired seismic mitigation under near-field pulse-like ground motions.

Fault detection and classification scheme for power islands with inverter interfaced distributed generators

The low fault current contribution from inverter-interfaced distributed generators (IIDGs) and bidirectional flow of current in the power networks introduces protection challenges when islanded. The existing fault detection scheme based on the transient monitoring function (TMF) fails under such scenarios. A new decentralised machine learning (ML) based fault detection and classification scheme is proposed in this paper using terminal voltage information of IIDG (vo−abc). TMF of vo−abc, along with the zero sequence component of vo−abc, is utilised for training and testing of ensemble bagged trees ML algorithm. The proposed scheme is implemented inside each IIDG, and hence, it does not require communication. It is validated on a modified CIGRE test benchmark microgrid for all shunt faults at various locations with different loading, fault resistances, and inception angles. The accuracy of detection and classification of fault (DCF) during fault cases with unbalanced loads, noise, harmonic loads, and no-fault scenarios such as load and DG switching proves the effectiveness of the proposed method with varying scenarios. The performance of the proposed scheme is found to be superior when compared with the existing threshold based TMF and Hilbert–Huang transform (HHT) based techniques considering accuracy, dependability, security, and response time.

Comparison of impulse noise energy distribution from two generations of parachute gun

The rocket ejection seat is an advanced life-saving device for fighter pilots. However, it can also produce damaging impulse noise during ejection, which could compromise the pilot’s hearing health, and the manufacturer must assess the noise damage. This study uses Variational Mode Decomposition (VMD) and Hilbert-Huang transform (HHT) to analyze energy-instantaneous distribution over time and frequency-instantaneous and energy contribution of different modes of impulse noise generated by the parachute gun in two generations of rocket ejection seats. The results demonstrate considerable disparities in the energy distribution of impulse noise generated by the parachute gun in the new generation seat compared to the old generation seat. The new generation seat has higher overall energy, more concentrated action time, and a higher energy contribution in the 1-10 kHz frequency range. These findings provide valuable data for the design of the new generation of noise protection equipment for pilots.

Classification of ECG Signals Based on Hilbert-Huang Transform and 1D Convolution Neural Network

Classification of ECG Signals Based on Hilbert-Huang Transform and 1D Convolution Neural Network

Power Signal Analysis for Early Fault Detection in Brushless DC Motor Drivers Based on the Hilbert–Huang Transform

Brushless DC machines have demonstrated significant advantages in electrical engineering by eliminating commutators and brushes. Every year, these machines increase their presence in transportation applications. In this sense, early fault identification in these systems, specifically in the electronic speed controllers, is relevant for correct device operation. In this context, the techniques reported in the literature for fault identification based on the Hilbert–Huang transform have shown efficiency in electrical systems. This manuscript proposes a novel technique for early fault identification in electronic speed controllers based on the Hilbert–Huang transform algorithm. Initially, currents from the device are captured with non-invasive sensors in a time window during motor operation. Subsequently, the signals are processed to obtain pertinent information about amplitudes and frequencies using the Hilbert–Huang transform, focusing on fundamental components. Then, estimated parameters are evaluated by computing the error between signals. The existing electrical norms of a balanced system are used to identify a healthy or damaged driver. Through amplitude and frequency error analysis between three-phase signals, early faults caused by system imbalances such as current increasing, torque reduction, and speed reduction are detected. The proposed technique is implemented through data acquisition devices at different voltage conditions and then physical signals are evaluated offline through several simulations in the Matlab environment. The method’s robustness against signal variations is highlighted, as each intrinsic mode function serves as a component representation of the signal and instantaneous frequency computation provides resilience against these variations. Two study cases are conducted in different conditions to validate this technique. The experimental results demonstrate the effectiveness of the proposed method in identifying early faults in brushless DC motor drivers. This study provides data from each power line within the electronic speed controller to detect early faults and extend different approaches, contributing to addressing early failures in speed controllers while expanding beyond the conventional focus on motor failure analysis.

Research on Speech Denoising Algorithm for Equipment Trains in Fully Mechanized Mining Working Faces based on CEEMDAN High and Low Frequency Filtering

This paper proposes a high and low frequency filtering denoising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN). CEEMDAN to address the issue of noise in speech signals obtained in the environment of fully mechanized mining face equipment trains. This algorithm first decomposes speech signals into multiple Intrinsic Mode Functions (IMFs) in different frequency domains through CEEMDAN, then uses Hilbert-Huang Transform (HHT) to obtain the instantaneous frequency and amplitude of IMFs, calculates the Euclidean distance between IMFs, normalizes it to obtain the average distance between IMFs, and divides the IMFs components into high and low frequency categories based on the average distance. Next, Optimally Modified Log Spectral Amplitude (OMLSA) algorithm and Kalman filtering algorithm are used for the high-frequency and low-frequency IMF components, respectively. Finally, the processed IMF components are reconstructed to obtain a denoised signal. After comparative experiments, the noise reduction algorithm proposed in this paper significantly improves the Signal to Noise Ratio (SNR), Peak Signal to Noise Ratio (PSNR), Mean Square Error (RMSE), and Mean Absolute Distance (MAE) of speech signals obtained in the environment of fully mechanized mining face equipment trains compared to other commonly used noise reduction algorithms.