Hilbert-Huang Transform Research Articles

Data Mining Applied to the Electrochemical Noise Technique in the Time/Frequency Domain for Stress Corrosion Cracking Recognition

In this paper, time/frequency domain data processing was proposed to analyse the EN signal recorded during stress corrosion cracking on precipitation-hardening martensitic stainless steel in a chloride environment. Continuous Wavelet Transform, albeit with some limitations, showed a suitable support in the discriminatory capacity among transient signals related to the different stress corrosion cracking mechanisms. In particular, the aim is to propose the analysis of electrochemical noise signals under stress corrosion cracking conditions in the time–frequency domain by using the Hilbert–Huang approach. The Hilbert–Huang Transform (performed by the Empirical Mode Decomposition approach) was finally proposed to carry out an identification of the corrosion mechanisms in comparison to conventional data processing methods. By using this approach, a detailed simultaneous decomposition of the original electrochemical noise data in the time and frequency domain was carried out. The method gave useful information about transitions among different corrosion mechanisms, allowing us to (i) identify a specific characteristic response for each corrosion damaging phenomenon induced by stress corrosion cracking, (ii) time each corrosion of the damaging phenomenon, and (iii) provide a topological description of the advancing SCC damaging stages. This characteristic evidences that the Hilbert–Huang Transform is a very powerful technique to potentially recognize and distinguish the different corrosion mechanisms occurring during stress corrosion cracking.

Investigation on the roller-pavement interaction and asphalt pavement compactness based on marginal spectrum of vibration signal energy

Compaction is a critical assurance for the quality and performance of asphalt pavement in terms of durability and serviceability. At present, there is a knowledge gap in the roller-pavement interaction in terms of energy variation during the process of asphalt pavement compaction. This paper aims to reveal the interaction and energy variation between the vibrating drum and pavement surface course during compaction process. Based on field tests, vibration signals of both the vibrating drum and pavement (i.e., the top, middle and bottom surface layers) were captured by acceleration sensors, and then the Hilbert marginal spectrum of the signals was obtained by the Hilbert-Huang Transform (HHT) for interpreting the signal features. Based on the marginal spectrum, the energy variation of the vibrating system (drum and pavement) during compaction was obtained. A predictive model of pavement compactness was further established according to the observed linear relationships between the pavement compactness and the energies of the vibrating system, and was then validated in the field application. The findings show that the energy-based approach adopted herein is able to not only characterize the compactness of asphalt pavement, but also reflect the uniformity of compaction. The developed relationships have a good potential as a useful tool for quality control in the field compaction practice.

Preliminary Result: Analysis of Dominant Frequency in Western Part of Java, Indonesia using Hilbert-Huang Transform-HVSR Method

The western part of Java is situated near various geological formations stemming from the collision between the Indo-Australian and Eurasian tectonic plates. These formations include the Java Trench, Sunda Strait, and several active onshore faults, rendering the area susceptible to seismic activity. The dynamic response of the soil to seismic shaking in this region warrants thorough investigation, particularly due to the prevalence of alluvium deposits in certain areas, which have the potential to amplify ground motion. In this research endeavor, seismic data recorded by 81 temporary seismic stations in West Java were utilized. The analysis employed the Hilbert-Huang Transform technique in conjunction with the Horizontal to Vertical Spectral Ratio (HVSR) method to derive the Horizontal-to-Vertical (H/V) spectral response curve for each measurement point. The implementation of the Hilbert-Huang Transform served the purpose of mitigating non-stationary transient noise commonly encountered in urban measurements, thereby enhancing the accuracy of the HVSR curve in portraying the dominant frequency characteristics of the measurement area. The findings of this study reveal that within the western part of Java, the dominant frequency values fall within the range of 0.9 to 7 Hz. Areas exhibiting lower dominant frequencies are indicative of a greater sediment thickness, predominantly observed in the northern region of the western part of Java, the Bandung Basin, some areas surrounding active volcanoes as well as various locales within the province of Banten.

Optimizing the performance of machine learning algorithms for the condition assessment of utility timber poles

ABSTRACT This study focuses on evaluating several machine learning algorithms for the condition assessment of utility timber poles. An efficient feature extraction technique combining Hilbert Huang transform (HHT) and wavelet packet transform (WPT) is adopted from the authors’ previous work and implemented to determine damage-sensitive features from vibration data related to five serviceable and eight unserviceable in-situ timber poles. Then, these features are pre-processed using correlation heat map analysis for feature selection. Principal component analysis (PCA) is adopted as the final step of pre-processing for reducing noise interference and enhancing classification accuracy. Afterwards, a feature matrix is formed, which is fed into the selected classifiers for pattern recognition. In addition, the information gain method is also implemented and compared against PCA to examine the effect of feature selection. Finally, selected classifiers are employed using those dominant features, and their performance is evaluated based on six parameters – accuracy, precision, recall, F1-score, confusion matrix and Receiver Operating Characteristic (ROC) curve. It was found that choosing the best feature set related to the health state helps to improve the performance of the pattern recognition algorithms to a great extent.

Operational status monitoring of smart grid and power communication network coupling and collaboration based on multi-head attention mechanism

Smart grid is an organic combination of traditional power grid and advanced digital communication technology, and power communication network plays a vital role in ensuring its steady operation. However, as the coupling correlation between the smart grid and the power communication network increases, the propagation of coupled network failures may constitute a great threat to the safe and stable operation of the power system. To address this phenomenon, based on the algorithm of the multi-head attention mechanism (MHA) and convolutional neural network (CNN), this paper proposes a framework that integrates the multi-head attention mechanism with the convolutional neural network (MHA-CNN) for the monitoring of the coupling network’s operation status. In the proposed algorithm, Hilbert–Huang transform (HHT) is used to extract the intrinsic features of the operational data, and MHA employs multi-subspace analysis and extracts the key feature information of the fault data to maximize the fault information extraction and help the system to discover the fault as soon as possible. Simulation results demonstrate that the proposed algorithm can effectively realize a better detection speed and higher detection probability compared with CNN and ResNet-50, and maintain certain robustness under poor transmission conditions, ensuring the steady operation of the coupled network.

Vasomotion heterogeneity and spectral characteristics in diabetic and hypertensive patients

Vasomotion refers to the spontaneous oscillation of blood vessels within a frequency range of 0.01 to 1.6 Hz. Various disease states, including hypertension and diabetes, have been associated with alterations in vasomotion at the finger, indicating potential impairment of skin microcirculation. Due to the non-linear nature of human vasculature, the modification of vasomotion may vary across different locations for different diseases. In this study, Laser Doppler Flowmetry was used to measure blood flow motion at acupoints LU8, LU5, SP6, and PC3 among 49 participants with or without diabetes and/or hypertension. Fast Fourier Transformation was used to analyze noise type while Hilbert-Huang Transformation and wavelet analysis were applied to assess Signal Noise Ratio (SNR) results. Statistical analysis revealed that different acupoints exhibit distinct spectral characteristics of vasomotion not only among healthy individuals but also among patients with diabetes and/or hypertension. The results showed strong heterogeneity of vasomotion among blood vessels, indicating that the vasomotion measured at a certain point may not reflect the real status of microcirculation.

Parameter Calibration of Wind Farm With Error Tracing Technique and Correlated Parameter Identification

With the increasing penetrations of wind power in power systems, periodical calibration of the large-scale Wind Farm (WF) model is crucial to maintaining high-quality model performance for stability investigations. However, the existing calibration methods mainly focus on correcting synchronous generators, not the more dynamical WF model. Challenges in tracing errors of inaccurate models and identifying the correlated parameters would further restrain the calibrating performance. To address such limitations, a novel parameter calibration approach for the WF model is developed explicitly in this article. With the development of a trajectory sensitivity based dominant parameters selection strategy, the parameters which significantly impact the model responses can be precisely located. Then, for discriminating the ill-conditioned parameters (deviating from their actual values), an improved error tracing method incorporating Hybrid Dynamic Simulation (HDS) and Hilbert-Huang Transform (HHT) is proposed. Lastly, to enhance the model performance, the ill-conditioned parameters are iteratively tuned by a well-designed multistage identification approach, with the consideration of parameter correlations. Additionally, theoretical proof of the error tracing technique is provided to guarantee the proposed method's validity mathematically. With realistic WF and a modified IEEE 39-bus system, the proposed method demonstrated its excellent performance in tracing and tuning inaccurate parameters.

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.

Robot Ground Media Classification Based on Hilbert–Huang Transform and Attention-Based Spatiotemporal Coupled Network

With the development of technology, mobile robots are increasingly deployed in real-world environments. To enable robots to work safely in a variety of terrain environments, we proposed a ground-type detection method based on the Hilbert–Huang transform (HHT) and attention-based spatiotemporal coupled network. Taking a dataset containing multiple sets of robot signals from a Kaggle competition as an example; we use the proposed method to classify the signals and thus achieve a terrain classification of the robot’s location. Firstly, the signal data were processed using the discrete wavelet transform for noise reduction, and all channels in the dataset were ranked by importance using the permutation importance method. Next, the instantaneous frequencies of the two most important channels were extracted using the HHT and added to the original dataset to expand the feature dimension. Then the features in the expanded dataset were extracted by the convolutional neural network, long short-term memory, and attention module. Afterward, the fully extracted features were passed into the fully connected layer for classification, and an average classification accuracy of 83.14% was obtained. The effectiveness of each part in our method was demonstrated using ablation experiments. Finally, we compared our method with some common methods in the field and found that our method obtained the highest classification accuracy, proving the superiority of the proposed method.

Dynamic response characteristics of shaking table model tests on the gabion reinforced retaining wall slope under seismic action

In the present study, a series of shaking table model tests were performed on a slope with a gabion reinforced retaining wall. Transfer functions were employed to compute the inherent frequencies of the slope. Furthermore, the investigation examined various aspects of the slope, including the peak acceleration amplification factor, incremental dynamic stresses, displacements, and tensile forces. Additionally, the study employed the Hilbert Huang transform (HHT) to analyze the slope's time-frequency characteristics and energy distribution. The findings of the study revealed that there is an inverse relationship between the amplitude of the input seismic wave and the natural frequency of the top of the gabion reinforced retaining wall slope. As the amplitude of the seismic wave increases, the natural frequency of the slope decreases. The amplification factors for peak acceleration were all found to be less than 1.9, suggesting a notable dissipation of seismic energy in comparison to typical slopes. The response of incremental dynamic stress was most pronounced in the middle section of the slope, followed by the top of the slope. The magnitude of the incremental displacement was found to be highest at layer 4, whereas the incremental tensile force exhibited its maximum value at layer 5. The dynamic response exhibited the least pronounced characteristics at the lower portion of the slope, demonstrating the most stable behavior. The peak frequencies observed in the Hilbert marginal spectrum displayed comparable characteristics to the natural frequencies.

An improved high-impedance fault identification scheme for distribution networks based on kernel extreme learning machine

In distribution networks, high-impedance faults (HIFs) occur frequently and have a harmful impact on the distribution network. However, fault detection and fault phase selection of HIFs are challenging due to weak fault characteristics. Therefore, this paper proposes an improved HIF identification scheme based on a kernel extreme learning machine (KELM) that can sensitively identify HIFs and select the fault phase by adaptively extracting the weak fault characteristics. First, a fault feature extraction strategy based on discrete wavelet decomposition (DWT) and the Hilbert–Huang transform (HHT) is proposed to obtain multiple features that describe the weak fault characteristics of HIFs. Second, an XGBoost-based fault feature selection scheme is proposed for screening with sensitive characterization of HIFs. Next, a sensitive and accurate HIF identification scheme based on the improved learning algorithm (KELM) is proposed to enable accurate and sensitive HIF detection and phase selection. Finally, numerical simulations based on PSCAD/EMTDC and MATLAB were carried out, which reveals the effectiveness and accuracy of the proposed HIF identification scheme. Compared with the traditional HIF identification scheme, the proposed method exhibits conciseness and correctness.

Hilbert–Huang Transformation-based subject-specific time–frequency-space pattern optimization for motor imagery electroencephalogram classification

The advancement of brain–computer interfaces (BCIs) has narrowed the gap between humans and computers, allowing intentional interaction by monitoring and translating brain signals in real time. Among BCI approaches, motor imagery electroencephalogram (MI-EEG) systems are popular due to their non-invasiveness, portability, and user-friendly operation without external stimuli. However, MI-EEG classification faces challenges from subject-specific variations in time, frequency, and spatial domains. To overcome this, the paper proposes a novel Hilbert–Huang transformation (HHT)-based method for subject-specific time–frequency-space pattern optimization in MI-EEG classification. The method utilizes a joint time–frequency pattern optimization module and a spatial pattern optimization module for EEG measurements. This efficient process identifies subject-specific dominant time–frequency components and extracts optimal spatial features. The optimized features are fed into a support vector machine (SVM) classifier, resulting in superior performance compared to standard baselines on three open-source datasets. The proposed method achieves 4.1% and 6.3% higher accuracy in 2-class and 4-class classification, respectively. Additionally, it demonstrates remarkable computational efficiency, requiring 70% less training time to achieve the optimal feature space. These improvements in classification accuracy and computational efficiency underscore the practical value of the proposed method for MI-BCI systems.

Research on power fluctuation strategy of hybrid energy storage to suppress wind-photovoltaic hybrid power system

In this paper, an adaptive hybrid energy storage power optimal allocation strategy is proposed. The strategy aims to suppress the fluctuation of grid-connected power under different operation conditions and improve the operation reliability of a high proportion of renewable energy connected to the grid. Firstly, an online control strategy of grid-connected power fluctuation rate based on model predictive control (MPC) is established. This strategy can realize the grid-connected target power dynamic generation of wind-photovoltaic-energy storage (Wind-PV-ES) hybrid power system and the optimal allocation of energy storage (ES) output power. Secondly, an adaptive hybrid ES power allocation strategy based on the variational mode decomposition (VMD), Hilbert-Huang transform (HHT) and filtering algorithm is constructed to realize adaptive adjustment and optimal allocation of hybrid ES output power. Finally, the hybrid ES capacity configuration is verified by simulation analysis and theoretical calculation. The simulation results show that the proposed hybrid ES output power optimal allocation strategy has certain engineering practical value to suppress the grid-connected power fluctuation.

Frequency Characteristics of High Strain Rate Compressions of Cf-MWCNTs/SiC Composites

The incorporation of ductile reinforcements into ceramics helps restrain crack deflection, which can enhance ceramics’ toughness and overcome the matrix’s brittleness. In this paper, we produced a ceramic composite reinforced by carbon fibers coated by multi-wall carbon nanotubes (shortened by Cf-MWCNT/SiC composites) for enhanced impact resistance at a high strain rate that commonly occurs in composite materials used in astronautics, marine, and other engineering fields. The fabrication process involves growing multi-wall carbon nanotubes (MWCNTs) on a carbon fiber woven fabric (Cf) to create the fibril/fabric hybrid reinforcement. It is then impregnated by polymer solution (precursor of the ceramics), forming composites after the pyrolysis process, known as the liquid polymer infiltration and pyrolysis (PIP) technique. To assess the impact resistance of the Cf-MWCNT/SiC under high-strain rate compressions, the split Hopkinson pressure bar (SHPB) technique is employed. Since the failure behavior of the Cf-MWCNT/SiC composites in the absence of the ductile phase is not well understood, the study employs the Hilbert–Huang transform (HHT) to analyze the stress–time curves obtained from the SHPB experiments. By applying the HHT, we obtained the frequency–time spectrum and the marginal Hilbert spectrum of the stress signals. These analyses reveal the frequency characteristics of the Cf-MWCNT/SiC composite and provide insights into the relationship between transformed signal frequency and fracture behavior. By understanding the dynamic fracture behavior and frequency response of the Cf-MWCNT/SiC, it becomes possible to enhance its impact resistance and tailor its performance for specific protective requirements. Therefore, the findings of this study can guide the future design and optimization of Cf-MWCNT/SiC structures for various protective applications, such as body armor, civil structures, and protections for vehicles and aircraft.

Non-Contact Impact Source Localization in Composite Symmetry Panels Based on A0 Mode of Lamb Waves

Traditional methods for detecting damage in engineering structures often use offline static damage detection. To enable the real-time and precise identification of dynamic damage while maintaining symmetry in engineering structures, this study primarily concentrates on isotropic plate structures widely employed in engineering. Moreover, fiberglass board composite plates were opted as a specific research object. By utilizing the weak S0 mode signals generated by low-frequency ultrasonic Lamb waves, the non-stationary A0 wave signals in the composite symmetry plate structure are collected using the non-contact SLDV (Scanning Laser Doppler Vibrometer) technique. The frequency characteristic parameters in the vibration signals are obtained through HHT (Hilbert–Huang Transform) analysis, followed by filtering and noise reduction. Finally, the circular trajectory intersection method is employed to accurately locate dynamic damage sources in plate structures with different material properties, thereby validating the positioning effect of contact sensors in detecting impacts caused by random impulses.

Saltwater intrusion in the Po River Delta (Italy) during drought conditions: Analyzing its spatio-temporal evolution and potential impact on agriculture

Saltwater intrusion along rivers is a complex process controlled by multiple factors and thus fluctuates with a highly nonlinear nature and time-varying characteristics. It is challenging to monitor saltwater intrusion. The objective of this study was to clarify the spatial-temporal variation of saltwater intrusion and its potential impact on agriculture in the Po River Delta (Italy). 2006 was the most severe year of saltwater intrusion in the period we considered. 2022 was even worse, but the data are still under processing. In this study, the Hilbert-Huang transform (HHT) and rescaled range (R/S) were used to identify the multi-time scales and change trends of the salinity and discharge in 2006. After that, the time-dependent intrinsic correlation (TDIC) was used to depict intrinsic relationships between salinity and discharge at different time scales. The results showed that discharge and salinity exhibited behaviours of positive long-range correlation during different periods. The temporal series of salinity and discharge was decomposed into six intrinsic mode functions (IMF) and residuals based on the ensemble empirical mode decomposition (EEMD). The sum of variance contribution rates of IMF1 (4 days), IMF2 (10 days), and IMF3 (12.1 days) of salinity was more than 75%. All measured TDICs have highlighted strong correlations between salinity and discharge. Furthermore, we used spatial interpolation techniques to map salinity data along rivers. This allowed the investigation of dynamic changes in saltwater intrusion patterns during periods of severe drought. Outcomes show a significant negative correlation between salinity and normalized difference vegetation index (NDVI), indicating that the study area's agricultural greening was affected by saltwater intrusion.

High-frequency fluctuation of air temperature during a heatwave event in urban environment and the physical mechanism behind

Heatwaves threaten human health and power systems. Urban climate is non-stationary and wide-spectrum, with high-frequency temperature and wind-speed variations that could overload power grids and expose people to extreme heat. In this study, Hilbert-Huang transform (HHT) was unprecedentedly used to decompose the urban-scale temperature (IMFθ1 to IMFθ6) and wind-speed (IMFW1 to IMFW6) signals during a 5-day heatwave event into 6 intrinsic mode functions (IMFs). The spatio-temporal characteristics, physical mechanism, and effective ranges of high-frequency components (IMF1 to IMF4) were unveiled. Temperature (wind speed) IMFθ1 to IMFθ4 (IMFW1 to IMFW4) had a temporal scale of 2.63 h (2.53 h), 5.88 h (5.78 h), 13.16 h (9.84 h), and 22.72 h (19.05 h); as well as a spatial scale of 2.31 km (0.99 km), 4.29 km (1.65 km), 5.94 km (2.64 km), and 6.6 km (2.97 km), respectively. The physical mechanisms of IMF1 to IMF4 were composed of turbulence and heat storage/release; disturbance induced by mountainous terrain and slope flows; land/sea breeze, together with anthropogenic heat. Besides, the peaked amplitudes of IMFθ1 were most risky in compact/open high-rise urban (1.4 °C–1.6 °C) rather than rural (0.6 °C–1.0 °C) areas. The foothill areas within 8-km coverage were susceptible to IMFθ2 (1 °C–2.1 °C). IMFθ3 (0.6 °C–3.6 °C) was effective in urban areas within 10 km from coastline. IMFθ4 (2.5 °C–3.5 °C) exhibited the most intense fluctuation in urban/suburban areas. The outcome provides references for policy makers to mitigate heat-related risks.

Study on the Safety of Tunnel Structure Vibration in Dry Ice Powder Thermal Shock Rock Breaking

The application of explosive blasting for rock breaking works was not possible in densely populated areas, which caused problems in urban tunnel construction. In the application of dry ice powder thermal shock breaking in tunnel excavation, a vibration monitoring system was employed to monitor the vibration response of the tunnel structure during the breaking process, and it was used to extract the signal characteristics by Hilbert-Huang transformation. Experimental results are as follows: 1) The peak vibration speed was below 50 mm/s for concrete structures safe as long as it was farther than 10 m from the burst hole in the support concrete. 2) Aggregate decay of vibration velocities caused by thermal shock breaking of rock with dry ice powder corresponded to the decay law of the power function. The range of influence of the vibration was considerably smaller compared to that of drilling and blasting the rock; 3) The new rock-breaking technology induced damage can be divided into three regions, with radial fractures generated by high-energy fluids dominating. 4) Hilbert Huang transform extracted signal features more objectively and accurately, with excellent reference for the safety monitoring of tunnel structures.

Non-destructive compaction quality evaluation of runway construction based on GPR data

ABSTRACT Assessing the compaction quality of rockfill materials is an essential link in the runway construction. However, traditional on-site limited sampling detection is not only time-consuming and labour-intensive, but also destructive. Common ground penetrating radar (GPR) calculates the relative permittivity of a material by measuring its thickness. Nonetheless, assessing the thickness of runway construction materials poses a significant challenge. To address this challenge, this paper focuses on the Hilbert -Huang transform (HHT) analysis of GPR signal of different compacting materials, and then replaces the traditional method of calculating the relative permittivity by measuring the thickness of materials. At the same time, taking the runway as an example, this work verified a crest factor (CF) index effectiveness in predicting the relative compaction of rockfill material through HHT analysis of GPR signals collected in the field, with an average error rate of 4.03%. Finally, Kriging interpolation method is used to estimate the compaction quality of any point, and the corresponding heat map of compaction quality evaluation is generated to determine the area of insufficient compaction in the construction process. Highlights The GPR method is used for non-destructive testing of the compaction quality of runway rockfill materials; Compaction quality evaluation by multiple indicators of GPR data signal processing. The influence of number of roller passes, materials mix ratios and different rockfill materials on the compaction quality of runway are analysed. The applicability of the GPR method is verified by runway construction tests.

Damage identification of Chi River bridge based on vehicle excitation and WPEVCR

In order to identify damage of Chi River bridge’s superstructure, a damage identification indicator is implemented in the field test, which involves the wavelet packet energy analysis with the feature of dynamic response signals caused by vehicle excitation. On the basis of the field test, a series of numeric models with varied service conditions were developed. The wavelet packet analysis method was utilized to decompose the bridge’s acceleration signals at both healthy and damaged status, and the values of Wavelet Packet Energy Variance Change Rate (WPEVCR) were obtained. Then, according to the acceleration signal data measured from the field test, the damage assessment of the condition of Chi River bridge was performed by means of the obtained WPEVCR. The results demonstrate the capability of WPEVCR in localizing and quantifying the bridge damage status. Moreover, another damage indicator based on the Hilbert-Huang Transform (HHT) has been also employed to verify the assessment of WPEVCR, and both damage identification approaches indicate that the Chi River bridge is in a healthy service condition.