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A new automated algorithm for picking the arrival times of the global P -, SH - and SV -wave phases from multi-component seismic waveform data is presented. This picker is based on a sequential approach using autoregressive prediction of the filtered waveform in a sliding time window, the Akaike Information Criterion and the Hilbert transform of the original waveform. The quality of the individual picks is computed by combining signal-to-noise ratios and higher order statistics into a single measure. Synthetic tests are used to find values for high and low quality thresholds. The algorithm is applied to a global data set of waveforms from teleseismic events with magnitude 6 or higher that occurred between 1990 and 2019. This resulted in approximately 4 million P-phase arrival times as well as approximately 3 million SH- and SV-phase arrival times each. These automatic picks are compared to approximately |$830\, 000$| manual P-picks as well as approximately |$70\, 000$| manual S-picks from the ISC-EHB catalogue. An upper bound for the picking errors of the automatic picks is estimated by using high quality picks of neighbouring stations. This upper bound is found to be 0.55 s for the P-picks and 4.3 s for the S-picks. If only high quality picks are considered, this represents 50 per cent of the P-picks and 25 per cent of the S-picks, then these errors decrease to 0.35 s for the P-picks and 1.5 s for the S-picks, respectively. As a by-product of the picking, the dominant periods of the arriving signals are determined as well. [ABSTRACT FROM AUTHOR]

The paper concerns the weighted Hilbert transform of locally continuous functions on the semiaxis. By using a filtered de la Vallée Poussin type approximation polynomial recently introduced by the authors, it is proposed a new "truncated" product quadrature rule (VP- rule). Several error estimates are given for different smoothness degrees of the integrand ensuring the uniform convergence in Zygmund and Sobolev spaces. Moreover, new estimates are proved for the weighted Hilbert transform and for its approximation (L-rule) by means of the truncated Lagrange interpolation at the same Laguerre zeros. The theoretical results are validated by the numerical experiments that show a better performance of the VP-rule versus the L-rule. [ABSTRACT FROM AUTHOR]

A Field Programmable Gate Array (FPGA) is a semiconductor device based around a Configurable Logic Blocks (CLB) matrix connected by programmable interconnects. FPGA has numerous applications in biomedical signal processing due to its flexible programming and low power consumption. An Electrocardiogram (ECG) is a medical test used to determine heart rates, cardiac activity, and classify arrhythmias. All pass filters have Low Pass Filter (LPF), High Pass Filter (HPF), Band Stop Filter (BSF), and Band Pass Filter (BPF) to produce the exact amplitude in peak detection. However, the separate coefficient for individual filters increases the area in traditional all-pass filters. To overcome this issue, a Reconfigurable All-Pass Filter (RAPF) which considers a single coefficient for all filters and minimizes memory usage, consuming less area and power is employed. The LPF coefficient is utilized to perform the LPF operation, and then the two's complement of this LPF coefficient is computed to produce the HPF coefficient. Next, the two's complement is fed into the Hilbert Transform (HT) to produce the BSF coefficient and determine BSF operations. A RAPF is designed to perform these operations effectively. The RAPF performance is determined using Register, Look Up Table (LUT), Global Buffer (BUFG), Digital Signal Processing (DSP), Power, and Flip Flop (FF). RAPF consumes lesser power of 34 mW for Artix 7 XC7A200TFBG676-2 FPGA device, as opposed to the existing technique, Single Node Reservoir Computing (SNRC) using cumulative mean filter. [ABSTRACT FROM AUTHOR]

Expressing distributions in Euclidean space in terms of spherical coordinates gives rise to an alternative class of continuous linear functionals, termed signumdistributions, acting on test functions showing a pointwise singularity at the origin. In this paper the theory of signumdistributions is further explored from the viewpoint of integral transforms, viz. the Fourier and Hilbert transforms, and the interplay between them. [ABSTRACT FROM AUTHOR]

In this study, we are analyzing the effect of the Hilbert Transform (HT) on diffraction of a plane wave by an oscillating half-plane. Both the incident wave and oscillating half-plane have different oscillating frequencies. After the necessary mathematical computations for several types of time-dependent oscillating functions, it is verified graphically that the HT induces a shift of 90 ∘ , which can be observed from the flipping effect in the magnitude of the sinusoidal components occurring in their respective diffracted fields. Graphical illustrations presenting the effects of the HT are presented and discussed. [ABSTRACT FROM AUTHOR]

A multi-frequency instantaneous wavenumber damage imaging method based on ultrasonic guided waves induced by laser point-by-point excitation is proposed in this paper. The experiment involved using the Nd:YAG pulsed laser is used as the excitation source to excite ultrasonic guided waves point-by-point in the detection area, and the piezoelectric ceramic transducer is used to receive ultrasonic guided wavefield at a fixed position. The wavefield information at different frequencies is extracted by a three-dimensional Fourier transform. The spatial phase distribution of the extracted guided wavefield with different frequencies is obtained by the Hilbert transform and phase unwrapping method. Then, the wavenumber of each detection point and the dispersion relations of the test piece with different thicknesses are calculated. Based on the calculated dispersion relation, the mapping relationship between the wavenumber and the thickness of the test piece is obtained. Furthermore, based on the obtained wavenumber information and wavenumber thickness mapping relationship, the thickness reduction depth of the defect can be calculated. Finally, the quantitative detection of defects is achieved through data fusion. The proposed method is verified through quantitative detection of the rectangular groove defects and the flat bottom defects with variable thickness and complex contour in the aluminium plate. At the same time, the detection results of the proposed method are compared with those of the single-frequency instantaneous wavenumber imaging method, single-frequency local wavenumber imaging method, and multi-frequency local wavenumber imaging method. In the detection results, the method proposed in this paper presents a better defect detection effect. [ABSTRACT FROM AUTHOR]

A general rethinking of the mathematical foundations of water surface waves from the perspective of the Hilbert transform uncovers shortcomings of the standard multiple-scale approach as well as elucidates the interplay of non-local and dispersive effects. Application of the Hilbert transforms to planar and cylindrical settings allows us to deduce new weakly nonlinear models, including an alternative to Zakharov's equation and an envelope equation for cylindrical waves on deep water, as well as to highlight the crucial differences between these geometries. [ABSTRACT FROM AUTHOR]

This paper presents a robust scheme to detect and isolate faults quickly to prevent significant damage to the DC microgrid. The proposed technique uses the joint framework of Hilbert–Huang transform and empirical mode decomposition for feature extraction and bagging tree classifier to accurately and swiftly identify DC faults, which is challenging due to the limited time available to interrupt them. The intermittency pertaining to PV source and outage of distributed energy resources (DERs) may further complicate the protection task. In this regard, this paper proposes an intelligent scheme for fast fault detection and classification in DC microgrid. The joint framework of Hilbert transform and empirical mode decomposition has been used to calculate discriminatory attributes for characterizing the fault behavior in the signal. The ensemble strategy of efficient bagging tree classifier has been exploited after extensive testing and comparison with other modern approaches in this framework. Compared to other methods, the proposed scheme is more precise and faster which ascertain its efficacy in providing resilient protection to the DC microgrid with immunity to stochastic behavior pertaining to weather intermittency and DER outage. The performance of developed protection technique has also been validated on OPAL-RT digital simulator for authenticating its applicability in field applications. [ABSTRACT FROM AUTHOR]

Electroencephalography (EEG) helps to assess the electrical activities of the brain so that the neuronal activities of the brain are captured effectively. EEG is used to analyze many neurological disorders, as it serves as a low-cost equipment. To diagnose and treat every neurological disorder, lengthy EEG signals are needed, and different machine learning and deep learning techniques have been developed so that the EEG signals could be classified automatically. In this work, five ensemble models are proposed for EEG signal classification, and the main neurological disorder analyzed in this paper is epilepsy. The first proposed ensemble technique utilizes an equidistant assessment and ranking determination mode with the proposed Enhance the Sum of Connection and Distance (ESCD)-based feature selection technique for the classification of EEG signals; the second proposed ensemble technique utilizes the concept of Infinite Independent Component Analysis (I-ICA) and multiple classifiers with majority voting concept; the third proposed ensemble technique utilizes the concept of Genetic Algorithm (GA)-based feature selection technique and bagging Support Vector Machine (SVM)-based classification model. The fourth proposed ensemble technique utilizes the concept of Hilbert Huang Transform (HHT) and multiple classifiers with GA-based multiparameter optimization, and the fifth proposed ensemble technique utilizes the concept of Factor analysis with Ensemble layer K nearest neighbor (KNN) classifier. The best results are obtained when the Ensemble hybrid model using the equidistant assessment and ranking determination method with the proposed ESCD-based feature selection technique and Support Vector Machine (SVM) classifier is utilized, achieving a classification accuracy of 89.98%. [ABSTRACT FROM AUTHOR]

Aiming at the rolling bearing non-stationary and low signal-to-noise ratio under the strong background noise interference condition, resulting in the problem about weak fault features cannot be extracted effectively, this paper uses the improved beluga whale optimization algorithm (IBWO) to optimize the selection for both the key parameters of the variational modal extraction (VME) and the maximum correlation kurtosis deconvolution (MCKD) at the same time. A bearing weak fault feature extraction method is proposed based on IBWO and VME-MCKD. Firstly, to enhance the randomness of the initial position, the BWO algorithm is improved by incorporating Logistic mapping and constructing a composite metric as a fitness function using the envelope entropy and fractal dimension. Then, the penalty factor and initial center frequency, both key parameters of the VME, are optimally selected using IBWO, and the optimized VME is used to extract the optimal desired mode of the bearing fault signal. On this basis, the optimal desired mode is noise-reduced using the IBWO-optimized MCKD algorithm to further highlight the fault shock component. Finally, the Hilbert transform is utilized to perform envelope demodulation processing on the noise-reduced signal, and the fault eigenfrequency is extracted and compared with the fault theoretical eigenfrequency for diagnosis. The analysis of simulated and measured fault signals show that compared with VMD, MCKD, MED, MOMEDA, FSK, and other methods, the approach proposed herein is able to more clearly and accurately extract the rich fault octave components, and there is little interference near the peak. The accuracy of classification and diagnosis of bearing faults using the fault features extracted by the method in this paper can reach 99.937 %. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Local control parameters such as instantaneous delay and instantaneous amplitude play an essential role in evaluating the performance and maintaining the stability of real-time hybrid simulation (RTHS). However, existing methods have limitations in obtaining this local assessment in either the time domain or frequency domain. In this study, the instantaneous frequency is introduced to determine local control parameters for actuator tracking assessment in a real-time hybrid simulation. Instantaneous properties, including amplitude, delay, frequency and phase, are then calculated based on analytic signals translated from actuator tracking signals through the Hilbert transform. Potential issues are discussed and solutions are proposed for calculation of local control parameters. Numerical simulations are first conducted for sinusoidal and chirp signals with time varying amplitude error and delay to demonstrate the potential of the proposed method. Laboratory tests also are conducted for a predefined random signal as well as the RTHS of a single degree of freedom structure with a self-centering viscous damper to experimentally verify the effectiveness of the proposed use of the instantaneous frequency. Results from the ensuing analysis clearly demonstrate that the instantaneous frequency provides great potential for local control assessment, and the proposed method enables local tracking parameters with good accuracy. [ABSTRACT FROM AUTHOR]

Bridge engineering structures play a crucial role in transportation. Traditional methods of road and bridge closures for inspection and evaluation, while effective, increase bridge inspection costs and disrupt normal traffic flow. Therefore, a rapid detection and evaluation method for bridge structural modal parameters in the operational state is more suitable for practical engineering applications. However, under real operating conditions, bridge vibration signals typically contain a large amount of noise and interference, and modal identification must overcome issues of non-stationarity and non-linearity in the vibration signals caused by vehicle loads and environmental changes to ensure the accuracy of the identification. This study replaces the traditional Empirical Mode Decomposition algorithm in the Hilbert-Huang Transform with the Variational Mode Decomposition algorithm. It proposes a new method that combines the VMD algorithm with the Hilbert Transform, referred to as the Variational Mode Decomposition-Hilbert Transform method. Compared to the EMD algorithm, it offers significant improvements in suppressing mode mixing and endpoint effects. A vehicle-bridge coupling model was constructed, and the bridge’s natural modal information was successfully extracted from the vibration response signals. The research results indicate that the improved algorithm offers higher accuracy and faster computational speed compared to traditional identification algorithms. [ABSTRACT FROM AUTHOR]

This document is a list of references related to the topic of variational mode decomposition (VMD) and its applications in various fields such as structural health monitoring, fault diagnosis, and time series analysis. The references include research papers and articles that discuss the theory, methodology, and practical applications of VMD. The document also includes a list of nomenclature used in the referenced papers. [Extracted from the article]

We study minimal and toroidal compactifications of p -integral models of Hilbert modular varieties. We review the theory in the setting of Iwahori level at primes over p , and extend it to certain finer level structures. We also prove extensions to compactifications of recent results on Iwahori-level Kodaira–Spencer isomorphisms and cohomological vanishing for degeneracy maps. Finally we apply the theory to study q -expansions of Hilbert modular forms, especially the effect of Hecke operators at primes over p over general base rings. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of phase retrieval with short-time linear canonical transform (STLCT). The relation between signal, window and their STLCT is provided through Fourier transform. Based on this theorem, a uniqueness result is established for all square integrable functions. For nonseparable real continuous signal, we prove the uniqueness theorems under some weaker conditions. In complex bandlimited and cardinal B -spline spaces, uniqueness results are provided with magnitude-only STLCT. [ABSTRACT FROM AUTHOR]

Fingerprints play a significant role in various fields due to their uniqueness. In order to effectively utilize fingerprint information, it is necessary to enhance image quality. This paper introduces a method based on Radial Hilbert transform (RHLT), which simulates the vortex filter using the point spread function (PSF) of spiral phase plate (SPP) with a topological charge l = 1 , for fingerprint edge enhancement. The experimental results show that the processed fingerprint image has more distinct edges, with an increase in information entropy and average gradient. Unlike classical edge detection operators, the fingerprint edge image obtained by the RHLT method exhibits a lower mean square error ( M S E ) and a higher peak signal-to-noise ratio ( P S N R ). This indicates that the RHLT method provides more accurate edge detection and demonstrates higher noise-resistance capabilities. Due to its ability to highlight edge information while preserving more original features, this method has great application potential in fingerprint image processing. [ABSTRACT FROM AUTHOR]

Purpose: The classification of sleep stages based on Electroencephalogram (EEG) changes has significant implications for evaluating sleep quality and sleep status. Most polysomnography (PSG) systems have a limited number of channels and do not achieve optimal classification performance due to a paucity of raw data. To leverage the data characteristics and enhance the classification accuracy, we propose and evaluate a novel dual-link deep neural network model, 'DoubleLinkSleepCLNet'. Methods: The DoubleLinkSleepCLNet model performs feature extraction and efficient classification on both the raw EEG and the EEG processed with the Hilbert transform. It leverages the frequency domain and time domain feature modules, resulting in superior performance compared to other models. Results: The DoubleLinkSleepCLNet model, using the 2 Raw/2 Hilbert data modes, achieved the highest classification performance with an accuracy of 88.47%. The average accuracy of the EEG was improved by approximately 4.08% after the application of the Hilbert transform. Additionally, Convolutional Neural Network (CNN) demonstrated superior performance in processing phase information, whereas Long Short-Term Memory (LSTM) excelled in handling time series data. Conclusion: The application of the Hilbert transform to EEG data, followed by processing it with a convolutional neural network, enhances the accuracy of the model. These findings introduce novel concepts for accelerating sleep stage prediction research, suggesting potential applications of these methods to other EEG analyses. [ABSTRACT FROM AUTHOR]

For any nonempty set U ⊂ R + , we consider the maximal operator H U defined as H U f = sup u ∈ U | H (u) f | , where H (u) represents the Hilbert transform along the monomial curve u γ (s) . We focus on the L p (R d) operator norm of H U for p ∈ (p ∘ (d) , ∞) , where p ∘ (d) is the optimal exponent known for the L p boundedness of the maximal averaging operator obtained by Ko–Lee–Oh (Invent Math 228:991–1035, 2022, Forum Math Pi 11:Paper No. e4, 33, 2023) and Beltran–Guo–Hickman–Seeger (Am J Math, ). To achieve this goal, we employ a novel bootstrapping argument to establish a maximal estimate for the Mihlin–Hörmander-type multiplier, along with utilizing the local smoothing estimate for the averaging operator and its vector-valued extension to obtain crucial decay estimates. Furthermore, our approach offers an alternative means for deriving the upper bound established in Guo–Roos–Seeger–Yung (Math Ann 377:69–114, 2020). [ABSTRACT FROM AUTHOR]

Acoustic emission (AE) technology, as a non-destructive testing methodology, is extensively utilized to monitor various materials' structural integrity. However, AE signals captured during experimental processes are often tainted with assorted noise factors that degrade the signal clarity and integrity, complicating precise analytical evaluations of the experimental outcomes. In response to these challenges, this paper introduces an unsupervised deep learning-based denoising model tailored for AE signals. It juxtaposes its efficacy against established methods, such as wavelet packet denoising, Hilbert transform denoising, and complete ensemble empirical mode decomposition with adaptive noise denoising. The results demonstrate that the unsupervised skip autoencoder model exhibits substantial potential in noise reduction, marking a significant advancement in AE signal processing. Subsequently, the paper focuses on applying this advanced denoising technique to AE signals collected during the tensile testing of steel fiber-reinforced concrete (SFRC), the tensile testing of steel, and flexural experiments of reinforced concrete beam, and it meticulously discusses the variations in the waveform and the spectrogram of the original signal and the signal after noise reduction. The results show that the model can also remove the noise of AE signals. [ABSTRACT FROM AUTHOR]

Numerous works have been dedicated to the topic of m -isometries, including [2–6,14,18–20,27,47,48]. In this article, we introduce the concept of (m , N A) -isometry, where A is a non-zero operator and m is a positive integer, as an extension of the m -isometry class created by J. Alger and M. Stankus in the 1980s. We present some algebraic and spectral characteristics of (m , N A) -isometries. Additionally, we investigate the product of an (m , N A) -isometry by an (n , N B) -isometry, which enhances and broadens the previous work of Gu et al. on m -isometries [40]. Finally, we apply our main findings to elementary operators defined on the Hilbert-Schmidt class, which can be identified with a tensor product. This provides a new, less complicated, and non-combinatorial proof of Theorem 2.10 of [30]. [ABSTRACT FROM AUTHOR]

In the late 1980's, Böttcher and Silbermann asked whether the boundedness of the Toeplitz operator T (a) on the space ℓ μ p (Z +) implies boundedness of the Laurent operator M (a) on the space ℓ 0 , μ p , p (Z). We give the negative answer to this question. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for detecting high-impedance faults (HIF) in distribution systems that uses the Hilbert transform. Our approach is based on determining the instantaneous frequency of signals and detecting deviations from a reference frequency. Our technique is very sensitive to fault fluctuations because it makes use of the Hilbert transform's ability to capture dynamic signal properties like phase and frequency alterations. This sensitivity enables the extraction of unique features that identify fault signals, providing critical insights into fault detection and location. Notably, our method is appropriate for the analysis of non-stationary signals, which are typical in power systems where signal attributes vary fast during fault conditions. Furthermore, our method resolves deviations by comparing them to a predefined range and displaying essential features such as basic frequency, RMS (Root Mean Square), Crest Factor, Minimum and Maximum Deviations, and Maximum Current Amplitude. These values offer unique insights into the present signal's qualities, which aids in defect detection and diagnostics, particularly in HIF settings. Our proposed technique detects high-impedance flaws by evaluating deviations from the nominal frequency, even in environments with weaker features and variable surface conditions. To improve our system's robustness and usefulness, we recommend performing additional study on adaptive thresholding algorithms and real-time implementation choices. Future research areas could involve investigating the integration of machine learning algorithms for automatic fault categorization and localization, which would enhance the capabilities of distribution system fault detection approaches. [ABSTRACT FROM AUTHOR]

In order to nondestructively and accurately identify unplasticized polyvinyl chloride windows, a classification method based on multi-feature algorithm selection modeling was developed. Confocal Raman microspectroscopy was used to obtain the spectral profiles of 150 samples from five brands. The differences in model recognition accuracy were compared among three preprocessing methods: Savitzky-Golay filtering, Hilbert transform, and wavelet transform. The best preprocessing method was selected, and the competitive adaptive reweighted sampling was used to extract feature wavelengths. Furthermore, a Bayesian classification model was constructed to classify and differentiate each sample. The results showed that confocal Raman microspectroscopy can reflect the differences in physicochemical information among different samples. Preprocessing can improve the model's recognition accuracy, with wavelet transform (96%) > Hilbert transform (90%) > Savitzky-Golay filtering (76%) > untreated (72%). Wavelet transform can remove noise from spectral data without changing the peak region and its absorbance. Based on wavelet transform processing and competitive adaptive reweighted sampling (CARS) combined with Bayesian discriminant analysis, a 100% accurate classification of 150 samples was successfully achieved. [ABSTRACT FROM AUTHOR]

In this paper, we introduce proximal groups that are a generalization of topological groups. A straight-forward application of proximal groups is given in the concise representation of collections of overlapping Hilbert envelope lobes attached to the peak points on oscillatory motion waveforms that occur in sequences of video frames that track object movements. [ABSTRACT FROM AUTHOR]

Mean-Variance (MV) is a method that collects several assets using appropriate weight intending to maximize profits and to reduce risk. Stock market conditions are very volatile, mean variance method does not reach stock market fluctuation well because MV method is only limited to one time period. This study proposes a mean variance complex-based approach that transforms real returns into complex returns by using Hilbert transform to construct an optimal mean-variance portfolio based on complex returns and then find its dynamic asset allocation. The results show that with the same risk tolerance, the mean variance complex-based approach outperforms MV method in profits, losses, and portfolio performance tests. [ABSTRACT FROM AUTHOR]

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Previous studies have revealed that both AGC (automatic gain control) and AFC/PLL (automatic frequency control/phase-locked loop) circuits for demodulating SSB/ISB (single sideband/independent sideband) modulated signals cannot cope with severe fading at all. The author therefore decided to develop an asynchronous demodulation scheme for SSB/ISB signals using a DSP processor, i.e. without AGC or AFC/PLL circuits. The adverse effects of fading on the amplitude and phase components of the received signal must be first removed at the receiver side. The introduction of the Hilbert transform has certainly enabled successful asynchronous demodulation. The paper presents asynchronous demodulation methods for three modulated signals such as RZ SSB (Real Zero SSB), multi-channel ISB and ISB-based AM (amplitude modulation) stereo signals propagating along a fading path. The demodulation circuit can be implemented in a feedforward configuration. [ABSTRACT FROM AUTHOR]

Earthquake is one of the main factors causing structural disasters in current buildings. Under earthquake action, adjacent building structures are generally in different vibration stages, and collisions may occur in the structures, which may cause serious damage to the structure. In order to prevent certain earthquakes from damaging the designed buildings, this article mainly introduced the design and analysis of a numerical algorithm for seismic nonlinear structural dynamic response based on the HVSR algorithm. This article evenly divided the acceleration response time series into 15 time periods and then selected the position corresponding to the peak point of instantaneous amplitude within each period as the selected data point position. The same seismic load can be applied at the bottom of the established nonlinear model to extract the dynamic response data of the top layer of the structure, and then, the instantaneous amplitude and corresponding instantaneous phases and frequencies of the main components of the structural dynamic response can be extracted through the time-varying filter and Hilbert transform based on the discrete analytic mode decomposition. Under the influence of these four ground motions, the collision force within the range of 0–50 kN accounted for over 87% of the total number of collisions. In the comparison results of collision response to peak displacement, the four ground motions all led to structural collision, and the collision inhibited the positive peak displacement response of node 1512. Compared with noncollision, the peak displacement was reduced by 27.273, 33.675, 27.727, and 37.248%, respectively. The peak displacement of 1512 nodes was suppressed and reduced by 18.856%. The results indicate that the HVSR algorithm can obtain the instantaneous characteristic parameters of nonlinear structural dynamic response and achieve model correction. [ABSTRACT FROM AUTHOR]

This paper proposes a method for harmonic time–frequency analysis and detection based on an improved multi-synchrosqueezing transform (MSST). The aim is to address the significant endpoint problem of the synchrosqueezing transform (SST) in power harmonic analysis. This approach initially employs the Burg method to estimate the parameters of the auto-regressive (AR) model for the harmonic signal. Subsequently, it conducts multiple iterative computations on the SST results of the extended harmonic signal, further compressing the time–frequency spectrum energy to obtain a more precise time–frequency spectrum of the harmonic signal. Additionally, it utilizes the robust reconstruction capability of MSST to decompose the harmonic signal and obtain a series of intrinsic mode functions (IMF) with different frequencies. Finally, the Hilbert Transform is applied to identify the harmonic parameters of each IMF component and accomplish harmonic detection. The simulation experiments and measured data results demonstrate that the proposed method outperforms the Hilbert-Huang Transform (HHT) and SST methods in achieving more accurate time–frequency analysis and detection of harmonic signals. It also reveals the time–frequency characteristics and variation patterns of power grid harmonics, making it of great significance for harmonic control. [ABSTRACT FROM AUTHOR]

In this paper, a simple formula is derived for the modal damping ratio of the bridge using the correlation between the instantaneous amplitudes of the related front and rear contact responses of a two-axle test vehicle by the Hilbert transform (HT). To start, closed-form solutions were derived for the dynamic response of the damped bridge and vehicle-bridge contact responses. Next, the HT was employed to generate the instantaneous amplitudes of the two contact points. Based on their correlation, a simple formula is derived for the bridge damping ratio. Finally, the reliability of the derived formula was verified in the numerical study. It was demonstrated that the proposed formula can be successfully used to determine the first bridge damping ratio, even in the presence of rough pavement, but with the aid of random traffic. [ABSTRACT FROM AUTHOR]

Diagnosing bearing defects (BFs) in squirrel cage induction machines (SCIMs) is essential to ensure their proper functioning and avoid costly breakdowns. This paper presents an innovative approach that combines intelligent direct torque control (DTC) with the use of Hilbert transform (HT) to detect and classify these BFs. The intelligent DTC allows precise control of the electromagnetic torque of the asynchronous machine, thus providing a quick response to BFs. Using HT, stator current is analyzed to extract important features related to BFs. The HT provides the analytical signal of the current, thus facilitating the detection of anomalies associated with BFs. The approach presented incorporates an intelligent DTC that adapts to stator current variations and characteristics extracted via the HT. This intelligent control uses advanced algorithms such as neural networks (ANN-DTCs) and fuzzy logic (FL-DTCs). In this paper, a comparison between these two algorithms was performed in the MATLAB/Simulink environment for a three-phase asynchronous machine to evaluate their effectiveness under the proposed approach. The results obtained demonstrated a high ability to detect and classify BFs, confirming the effectiveness of each algorithm. In addition, this comparison highlighted the specific advantages and disadvantages of each approach. This information is valuable in choosing the most suitable algorithm according to the constraints and specific needs of the application. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new complexity computation based on the complex function. This measure exploits the dispersion Lempel–Ziv complexity (DLZC) and the dispersion statistical complexity measure based on Jensen–Shannon divergence (DCJS) of the analytic signal and constructs the binary complex function, called complex number complexity (CNC). The statistical measure depicts the complex system from different angle and mines more potential information. Through simulation experiments, we prove that the proposed method is able to detect data fluctuations more sensitively and accurately. For an application, the CNC is applied to fault detection which has different fault diameters and rotational speeds. The results deliver that the CNC measure can well represent the complexity of faulty bearings and has significant differences in any two fault types. The technique is effective to characterize different fault. [ABSTRACT FROM AUTHOR]

This manuscript proposes a hybrid technique for fault detection and classification in a three-phase induction motor (IM). The proposed hybrid technique combines enhanced ladder spherical evaluation (ELSE) and recurrent neural networks (RNN); hence, it is called the ELSE–RNN method. The main goal of the manuscript is to detect and categorize the faults that occur in the IM. The key objective of the proposed method is to enhance the performance of supercapacitor (SC) storage technology and fuzzy-tuned proportional–integral (PI) supervision over conventional control. The main contribution of this paper is developing an effective fault diagnosis method for three-phase IMs. The presence of stator, rotor, winding, and bearing faults is employed using signal processing techniques, such as the Hilbert transform and SIFT. The proposed ELSE–RNN technique is utilized with the end goal of detecting and classifying faults. Here, the proposed ELSE–RNN technique recognizes motors' healthy or unhealthy conditions in many situations to distinguish faults for protection. The proposed ELSE–RNN technique reduces the complexity of detecting and classifying faults with a validated system and increases the system's accuracy. The ELSE–RNN technique is implemented in MATLAB, and its performance is compared to existing techniques. [ABSTRACT FROM AUTHOR]

When analyzing a narrowband signal, the Hilbert transform is often used, which makes it possible to describe the process through slowly changing functions: the envelope (amplitude) and, weakly dependent on time, the characteristic signal frequency—the "instantaneous" frequency. Based on the smoothness of these characteristics, one can evaluate the process and compare it at different periods. This approach was used to analyze the spectral components of a series of average monthly Wolf numbers. This description of the main and second harmonics, supplemented by the properties of the long-period component, gives a fairly complete picture of the entire series of monthly averages. The work examines the correspondence of the characteristics of reliable data, with this approach, to the accepted description in terms of the parameters of cycles (maximum of the cycle, duration of the cycle, and its growth branches) and constructs an "envelope" of the maxima of the cycles. The time dynamics of the instantaneous frequencies of the fundamental and second harmonics of the entire series are also presented, and significant differences in their behavior are noted in the intervals corresponding to the reconstructed and reliable parts. [ABSTRACT FROM AUTHOR]

A method is proposed for analyzing the tremor of the earth's surface, measured by GPS, in order to highlight prognostic effects. The method is applied to the analysis of daily time series of vertical displacements in Japan. The network of 1047 stations is divided into 15 clusters. The Huang Empirical Mode Decomposition (EMD) is applied to the time series of the principal components from the clusters, with subsequent calculation of instantaneous amplitudes using the Hilbert transform. To ensure the stability of estimates of the waveforms of the EMD decomposition, 1000 independent additive realizations of white noise of limited amplitude were averaged before the Hilbert transform. Using a parametric model of the intensities of point processes, we analyze the connections between the instants of sequences of times of the largest local maxima of instantaneous amplitudes, averaged over the number of clusters and the times of earthquakes in the vicinity of Japan with minimum magnitude thresholds of 5.5 for the time interval 2012–2023. It is shown that the sequence of the largest local maxima of instantaneous amplitudes significantly more often precedes the moments of time of earthquakes (roughly speaking, has an "influence") than the reverse "influence" of earthquakes on the maxima of amplitudes. [ABSTRACT FROM AUTHOR]

This research aimed to investigate the accuracy of picking of P-wave arrival times in rock fracture acoustic emission signals. In order to simulate the mining scenario, Gaussian white noise and pulse noise were added to the data collected in the laboratory. Complete ensemble empirical mode decomposition with adaptive noise + Wavelet (CEEMDAN + Wavelet) was improved in this paper, where the Spearman rank correlation coefficient was adopted to effectively select intrinsic mode functions for denoising which retained the inherent characteristics of the rock fracture signal. The absolute amplitude and energy change rate of the envelope signal, calculated based on the Hilbert transform, were used as the input of the short term average/long term average (STA/LTA) normalization algorithm to pickup the P-wave arrival time. The reliability of this method was tested on 30 groups of recorded rock fracture laboratory data and 60 groups of added noise data. Taking the manual pickup results as the standard, the errors of CEEMDAN + Wavelet + STA/LTA + AIC (Akaike information criterion) method with the absolute amplitude of the signal as the input are all within 10 ms, and 86.67% of the results are within 5 ms. The method proposed in this paper effectively addressing the issue of false pickup caused by the sensitivity of AIC and traditional STA/LTA method for strong noise, and achieving relatively high accuracy and stability in processing low signal-to-noise ratio signals. This work contributes to monitor microscopic changes in rock bodies and is of great significance for the prediction and monitoring of geological disasters. [ABSTRACT FROM AUTHOR]

Practical combustors in furnaces, industrial heaters, and gas turbine engines face a sudden loss of flame due to rich blowout (RBO) at an extremely rich fuel-air mixture or lean blowout (LBO) at an extremely lean fuel-air mixture. Thus, the stability limits of the combustion regime are governed by RBO and LBO. In the present study, we focus on the dynamics of swirl-stabilized premixed combustion near lower and higher flammability limits, where the possibilities of LBO and RBO, respectively, are observed. Near RBO and LBO, we employ metrics from statistics and dynamical systems theory to characterize the transition in flame dynamics. We observe that the range of frequencies obtained using Fourier Transform near RBO and LBO is alike. The emergence of dominantly low-frequency oscillation near those blowout limits is investigated using Hilbert Transform. The mean frequency of the combustion system gradually reduces near both blowout limits due to behavioral oscillations prominently observed. The scaling property of flame oscillation is examined using the Hurst exponent, and we observe a decreasing trend of the parameter as combustion approaches both LBO and RBO. Therefore, for the gradual reduction of the Hurst exponent near both flammability limits, we can use the parameter as a precursor for both RBO and LBO. [ABSTRACT FROM AUTHOR]

In view of the low signal-to-noise ratio (SNR) of shear wave electromagnetic acoustic transducers (EMAT) in the detection of high-temperature equipment, the use of low excitation voltage (LEV) further deteriorates the detection results, resulting in the echo signal containing defects being drowned in noise. For the extraction of the EMAT signal, an adaptive noise reduction method is proposed. Firstly, the minimum envelope entropy is taken as the fitness function for the Harris Hawks Optimizer (HHO), and the optimal successive variational mode decomposition (SVMD) balance parameter is searched by HHO adaptive iteration to decompose LEV EMAT signals at high temperatures. Then the filter is carried out according to the excitation center frequency and correlation coefficient threshold function. Then, improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN) is used to decompose the filtered signal and combine the kurtosis factor to select the appropriate intrinsic mode functions. Finally, the signal is extracted by the Hilbert transform. In order to verify the effectiveness of the method, it is applied to the low-voltage detection of 40Cr from 25 °C to 700 °C. The results show that the method not only suppresses the background noise and clutter noise but also significantly improves the SNR of EMAT signals, and most importantly, it is able to detect and extract the 2 mm small defects from the echo signals. It has great application prospects and value in the LEV detection of high-temperature equipment. [ABSTRACT FROM AUTHOR]

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The complex damping model can only be used to calculate the steady-state responses, while the transient responses are divergent. Based on the complex damping model, the Hilbert transform is introduced to establish a hysteretic damping model, eliminating the divergence phenomenon. However, with the increase of the loss factor, the damped natural frequency also increases. To overcome this shortcoming, a frequency-independent damping model is proposed based on the hysteretic damping model. However, traditional time-domain methods are no longer applicable to frequency-independent damping models. Therefore, the transient response and steady-state response are separated, and the assumption of external excitation acceleration is introduced. Time-domain methods-based linear polynomial assumption, quadratic polynomial assumption and trigonometric function assumption are proposed, respectively. Numerical examples show that the time-domain methods based on linear polynomial assumption and quadratic polynomial assumption have high computational efficiency. But these two methods cannot take into account the vibration frequency of external excitation acceleration. Hence, the computational accuracy is low. Compared with them, the time-domain method based on trigonometric function assumption has the lowest computational efficiency and the highest computational accuracy. [ABSTRACT FROM AUTHOR]

We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multiwavelet frame coefficients \[ \{\lvert \mathcal {W}_{\phi _i} f(\alpha ^{m}\beta n,\alpha ^{m}) \rvert : i\in \{1,2,3\}, m,n\in \mathbb {Z}\} \] for every \alpha >1,\beta >0 with \beta \ln (\alpha)\leq 4\pi /(1+4p), p>0, when the three wavelets \phi _i are suitable linear combinations of the Poisson wavelet P_p of order p and its Hilbert transform \mathscr {H}P_p. For complex-valued signals we find that this is not possible for any choice of the parameters \alpha >1,\beta >0, and for any window. In contrast to the existing literature on wavelet sign retrieval, our uniqueness results do not require any bandlimiting constraints or other a priori knowledge on the real-valued signals to guarantee their unique recovery from the absolute values of their wavelet coefficients. [ABSTRACT FROM AUTHOR]

In the field of geological exploration and wave propagation theory, particularly in heterogeneous attenuating media, the stability of numerical simulations is a significant challenge for implementing effective attenuation compensation strategies. Consequently, the development and optimization of algorithms and techniques that can mitigate these numerical instabilities are critical for ensuring the accuracy and practicality of attenuation compensation methods. This is essential to reveal subsurface structure information accurately and enhance the reliability of geological interpretation. We present a method for stable forward modeling in strongly attenuating media by reapplying the Hilbert transform to eliminate increasing negative frequency components. We derived and validated new constant-Q wave equation (CWE) formulations and a stable solving method. Our study reveals that the original CWE equations, when utilizing the analytic signal, regenerate and amplify negative frequencies, leading to instability. Implementing our method maintains high accuracy between analytical and numerical solutions. The application of our approach to the Chimney Model, compared with results from the acoustic wave equation, confirms the reliability and effectiveness of the proposed equations and method. [ABSTRACT FROM AUTHOR]

The Hilbert transform plays an important role in the theory and practice of signal processing operations in continuous system theory because of its relevance to such problems as envelope detection and demodulation, as well as its use in relating the real and imaginary components, and the magnitude and phase components of spectra. The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. It is also the main part of the theory of singular integral equations on the real line. Therefore, approximations of Hilbert transform are of great interest. Many papers have dealt with the numerical approximation of singular integrals in case of bounded intervals. On the other hand, the literature concerning the numerical integration on unbounded intervals is much sparser than the one on bounded intervals. There is very little literature concerning the case of Hilbert transform. This article is dedicated to the approximation of Hilbert transform in Hölder spaces by the operators introduced by V.R.Kress and E.Mortensen to approximate the Hilbert transform of analytic functions in a strip. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Vortex-Induced Vibration (VIV) is a complex fluid–structure interaction in offshore structures. Traditionally, this phenomenon is considered periodic; however, many of its signals show chaotic behavior. The basic model already employed by other researchers is a rigid circular cylinder with linear springs and dampers. In this work, nonlinear snapping support is used to model nonlinearity in the system. To numerically simulate the flow, Reynolds-Averaged Navier–Stokes (RANS) equations for two-dimensional incompressible unsteady flows are applied. The degree of nonlinearity of the system can be changed by manipulating γ , which is one of the geometric properties of the spring and takes values between 0 and 1. The 0–1 test, Poincaré section, and Fast Fourier Transform are used to analyze the cylinder and lift force behavior. Also, the Hilbert transform is applied to the signals, and the phase shift between displacement and lift force is obtained. The results show that the system behavior consists of branches: branch I and branch II. The large amplitudes occur in branch II. It is found that chaos emerges at the beginning of branch II, regardless of the value of γ. By raising the γ value, the span of branch II becomes more expansive, and its first point is placed at lower reduced velocities. Also, the wake dynamics becomes more regular at the end of branch I and more irregular at the beginning of branch II with the increase in γ. When the cylinder displacement signal is chaotic, the lift force behavior is also chaotic, but not vice versa. [ABSTRACT FROM AUTHOR]