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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]

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]

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]

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]

Copyright of Przegląd Elektrotechniczny is the property of Przeglad Elektrotechniczny 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.)

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]

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]

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]

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]

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]

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]

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.)

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]

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 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]

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]

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]

The effect of the off‐axis angle (note as θ) on compressive properties and failure mechanisms in needled carbon/quartz fiber reinforced phenolic resin (CF‐QF/PF) composite has been investigated. For this objective, a series of quasi‐static off‐axis compression tests were performed, and a more precise and general model for predicting the compressive modulus and strength has been proposed. Further, the acoustic emission (AE) technology, including parameter‐based analysis and the Hilbert Huang Transform (HHT) method, was also employed to scrutinize the intricate damage mechanisms. The results show that specimens with θ = 0° exhibit linear and brittle behavior and are the most dangerous scenarios because delamination (accounting for 58% of the total AE accumulative energy) dominates their failure. For specimens with small off‐axis angles (0° < θ ≤ 45°), the fiber‐matrix interface determines their compressive properties. While for specimens with large off‐axis angles(45° < θ ≤ 90°), the enhanced transverse load‐bearing capacity of fibers becomes the dominant factor, characterized by significant debonding (33% when θ = 60°) and fiber breakage (27% when θ = 90°). Finally, these results were verified by optical microscopy (OM) and scanning electron microscopy images (SEM). Highlights: Off‐axis compression behaviors of needled CF‐QF/PF composite are studied.A more precise and general model for predicting off‐axis compression properties is proposed.Acoustic emission technology is used to quantify different types of damage.Failure mechanisms are revealed by combining in‐situ and offline techniques. [ABSTRACT FROM AUTHOR]

Objective: The present pilot study aimed to propose an innovative scale-independent measure based on electroencephalographic (EEG) signals for the identification and quantification of the magnitude of chronic pain. Methods: EEG data were collected from three groups of participants at rest: seven healthy participants with pain, 15 healthy participants submitted to thermal pain, and 66 participants living with chronic pain. Every 30 s, the pain intensity score felt by the participant was also recorded. Electrodes positioned in the contralateral motor region were of interest. After EEG preprocessing, a complex analytical signal was obtained using Hilbert transform, and the upper envelope of the EEG signal was extracted. The average coefficient of variation of the upper envelope of the signal was then calculated for the beta (13–30 Hz) band and proposed as a new EEG-based indicator, namely Piqβ, to identify and quantify pain. Main results: The main results are as follows: (1) A Piqβ threshold at 10%, that is, Piqβ ≥ 10%, indicates the presence of pain, and (2) the higher the Piqβ (%), the higher the extent of pain. Conclusions: This finding indicates that Piqβ can objectively identify and quantify pain in a population living with chronic pain. This new EEG-based indicator can be used for objective pain assessment based on the neurophysiological body response to pain. Significance: Objective pain assessment is a valuable decision-making aid and an important contribution to pain management and monitoring. [ABSTRACT FROM AUTHOR]

Polyurethane (PU) mixture, which is a new pavement mixture, exhibits different dynamic properties compared to a hot-mixed asphalt mixture (HMA). This paper analyzed whether the Kramers–Kronig (K–K) relation and thermorheologically simple properties applied to the PU mixture. Based on the results, the PU mixture exhibited thermorheologically simple properties within the test conditions. The time–temperature superposition principle (TTSP) was applicable for the PU mixture to construct a dynamic modulus master curve using the standard logistic sigmoidal (SLS) model, the generalized logistic sigmoidal (GLS) model, and the Havriliak–Negami (HN) model. The Hilbert integral transformed SLS and GLS models for the phase angle can accurately fit the measured phase angle data with newly fitted shift factors and predict the phase angle within the viscoelastic range. The core–core and black space diagrams both displayed single continuous smooth curves, which can be utilized to characterize the viscoelastic property of the PU mixture. The K–K relation is applicable for the PU mixture to obtain the phase angle master curve model, storage modulus, and loss modulus from the complex modulus test results with the test temperatures and loading frequencies. The phase angle of the PU mixture at extremely high or low test temperatures cannot be derived from the dynamic modulus data. [ABSTRACT FROM AUTHOR]

Aiming at the problem that the existing harmonic detection methods are susceptible to noise interference in the actual working environment, which leads to the reduction of detection accuracy, this paper introduces a novel harmonic detection technique utilizing a RIME optimization algorithm (RIME) to enhance variational mode decomposition (VMD) combined with an improved wavelet threshold (IWT) approach. Initially, RIME optimization refines VMD for the decomposition of harmonic current signals, yielding several modal components. Subsequently, a correlation coefficient method distinguishes between effective and ineffective modal components, discarding the latter. The effective components undergo noise reduction through an enhanced wavelet thresholding technique, and these denoised components are then reconstructed to produce the final noise-reduced signal. Finally, the Hilbert transform is applied to the denoised signal to extract harmonic parameters. Verification through both simulated and actual signal measurements demonstrates that the proposed method not only surpasses other noise reduction algorithms in signal-to-noise ratio and root-mean-square error, but also shows superior accuracy and robustness compared to alternative detection techniques. This method effectively filters out signal noise under noise interference, minimizes detection errors, and achieves precise harmonic signal detection with improved accuracy. [ABSTRACT FROM AUTHOR]

A Microgrid Protection Scheme proposed in this paper is based on the Hilbert-Huang Transform (HHT) and a Machine Learning model. The obtained phasor current signals at first, along with its fundamental components undergo empirical mode decomposition. Decomposing signals into mono components using the Empirical Mode Decomposition (EMD) technique are IMF stands for intrinsic mode function. To derive various practical insights from the chosen IMF, the Hilbert Transform is employed. An approach to machine learning utilization for training the protective system should successfully function and prove best for the protection of the Microgrid System. [ABSTRACT FROM AUTHOR]

Modal decomposition techniques are important tools for the analysis of unsteady flows and, in order to provide meaningful insights with respect to coherent structures and their characteristic frequencies, the modes must possess a robust spatial support. In this context, although widely used, methods based on singular value decomposition (SVD) may produce modes that are difficult to interpret when applied to problems dominated by intermittent and transient events. Fortunately, specific modal decomposition techniques have been recently developed to analyze such problems, but a proper comparison between them is still lacking from the literature. Therefore, this work compares two recent methods: the fast adaptive multivariate empirical mode decomposition (FA-MVEMD) and the multiresolution dynamic mode decomposition (mrDMD). These techniques are employed here for the study of flow databases involving transient and intermittent dynamics. Specifically, the investigated problems include an SD7003 airfoil subjected to deep dynamic stall conditions, and a steady NACA0012 airfoil operating at a transitional Reynolds number. In the former case, the methods are employed to investigate the onset and evolution of the dynamic stall vortex (DSV), while in the latter case, intermittent vortex pairing is analyzed. We show that the combination of a multidimensional EMD with the Hilbert transform provides modes with superior spatial support when compared to the mrDMD, also allowing the characterization of instantaneous frequencies of coherent structures. Moreover, the EMD also condenses a larger amount of information within a single intrinsic mode function (IMF). [ABSTRACT FROM AUTHOR]

In this article we characterize the range of the attenuated and non-attenuated X-ray transform of compactly supported symmetric tensor fields in the Euclidean plane. The characterization is in terms of a Hilbert-transform associated with A-analytic maps in the sense of Bukhgeim. [ABSTRACT FROM AUTHOR]

The Hilbert transform (HT) is an important method for signal demodulation and instantaneous frequency (IF) estimation. The modulus of the analytic signal constructed by the HT is considered as the amplitude, and the derivative of the instantaneous phase of the extracted pure frequency modulation signal is the IF. When the spectra of the amplitude function and the oscillation term overlap each other and fail to satisfy the Bedrosian condition, the instantaneous amplitude and frequency calculated by the HT will contain errors. The recursive Hilbert transform (RHT) is an effective method to overcome this problem. The RHT considers the pure frequency modulation signal obtained by the previous HT as a new signal and recursively computes its HT until convergence. The final pure frequency modulation signal of the recursive procedure has the same zero-crossing points as the original signal, and its corresponding quadrature error signal vanishes. We emphasize the convergence analysis of the algorithm and study the convergent tendency of the quadrature error signal in each recursive step. The key to the proof is that the discrete Fourier transform value of the quadrature error signal is regarded as a vector, and the length/norm of the vector decreases with the recursion process. Finally, we used three examples to demonstrate the effectiveness of this method in signal demodulation, IF identification and damped vibrating signal analysis, which indicate the application potential of the RHT method in mono-component signal processing. [ABSTRACT FROM AUTHOR]

The high precision identification of coal–rock layers is a significant challenge in intelligent mining. There is a large amount of electromagnetic noise and metal reflector signals in the full space detection environment of mining roadway, which makes it hard to distinguish the reflected waves at interface from a set of echo signals generated by the interface due to the similar amplitudes among them. So the method of identifying layers solely based on amplitude characteristics has poor stability and accuracy in coal mining environments. This paper proposes a method for identifying coal–rock layers based on Hilbert transform and tracking–scanning–stacking technology. There are two steps to achieve the recognition of air–coal–rock interfaces. First, by analysing the instantaneous amplitude spectrum obtained from the Hilbert transform, the first extreme point that is always the maximum value within a wavelength range is determined as the rough position of the air–coal interface. To solve the problem of recognition errors caused by noise and energy dispersion, the density difference method is used to remove discrete points. Second, the precise position of the air–coal interface is determined by tracking the extreme points within the 1.5 wavelength range around the rough position, and using the amplitude stacking method to quantitatively analyse and compare the degree of energy concentration. The data between zero time and the reflected waves at the air–coal interface is removed to avoid the impact of them on the recognition of the coal–rock interface. Results of physical model experiments and actual coal mine experiments show that this method yields better results and has high stability compared to conventional recognition method. Moreover, the average relative thickness errors are 4.5% for air layer and 4.2% for coal layer. [ABSTRACT FROM AUTHOR]

We investigate the vortex-shedding modes of a streamwise and transversely rotating sphere undergoing vortex-induced vibration (VIV). At Reynolds number Re = 500, we have conducted direct numerical simulations for reduced velocities U ∗ = 6 , 8 , and 11, considering dimensionless streamwise (α x) and transverse (α z) rotation rates set at α x , z = 1. At α x = 1 , the vortex-shedding mode exhibits twisted spiral-like structures, while at α z = 1 , ring-like structures form through the stretching and twisting of hairpins. For α x = 1 , the dimensionless circulation (Γ x) decreases with increasing U ∗ , showing negative growth at U ∗ = 6. Conversely, for α z = 1 , Γx remains negative except at U ∗ = 8 , where counterclockwise vortex rotation results in positive circulation. At α z = 1 , VIV is periodic for U ∗ = 6 and 8 but intermittent at U ∗ = 11. Phase analysis using the Hilbert transform reveals anti-phase synchronization in the phase between the sphere's displacements and the vortex force coefficient (Δ ϕ V) and phase slip in the phase between the sphere's displacements and the total force coefficient (Δ ϕ T) along the y direction for α x = 1. At α z = 1 , phase slip with distinct phase-locking epochs is observed along the z direction for all U ∗ cases. Pre-lock-in behavior with phase slip is also noted for U ∗ = 11 along the y direction. [ABSTRACT FROM AUTHOR]

This paper explores the concept of approximate Birkhoff–James orthogonality in the context of operators on semi-Hilbert spaces. These spaces are generated by positive semi-definite sesquilinear forms. We delve into the fundamental properties of this concept and provide several characterizations of it. Using innovative arguments, we extend a widely known result initially proposed by Magajna [17]. Additionally, we improve a recent result by Sen and Paul [24] regarding a characterization of approximate numerical radius orthogonality of two semi-Hilbert space operators, such that one of them is A -positive. Here, A is assumed to be a positive semi-definite operator. [ABSTRACT FROM AUTHOR]

This paper presents a study to accurately evaluate defects in concrete decks using ultrasonic pulse-echo signals. A reinforced concrete deck with void defects was designed and evaluated for validation, and a commercial ultrasonic pulse-echo (UPE) device was used to obtain the 2D images of the void defect inside the deck. The UPE image is based on the ultrasonic shear-wave test method and an extended synthetic aperture focusing technique (SAFT). To enhance the accuracy of the defect location in the SAFT imaging, the recorded A-scan data from UPE was analyzed using an advanced denoising approach and defect echo peak extraction, which are based on empirical modal decomposition, Hurst exponent characterization, and Hilbert envelope estimation. The results demonstrated that the location and depth of the void defect in the deck can be accurately assessed by using the developed approach. The new method provides quantitative information of the anomalies inside the deck, which can be used to calibrate the qualitative images of UPC devices with the SAFT. [ABSTRACT FROM AUTHOR]

Featured Application: This study belongs to the field of intelligent non-destructive testing and proposes a CNN-based method for accurate quantification of defect characterized by ultrasonic diffraction method. The innovation in this study lies in several key aspects: (1) Development of a CNN architecture that automatically classifies A-scan signals in the scan path; (2) Connectivity region solving algorithm to accurately calculate the defect-region size according to the classification results; (3) An intelligent noise reduction framework that enables accurate identification of defective areas in complex noise situations. The purpose of this paper is to automate the interpretation of data during ultrasonic diffraction using a non-destructive testing (NDT) technique to accurately size defects for assisting in decision-making. A convolutional neural network (CNN) architecture was developed to automatically measure the length of the defect. Using the architecture, the population of A-scan signals in the scanning path was classified. The defect region was extracted and its size in the scanning direction was obtained by the connected region solution algorithm based on the classification results. The arrival time of diffraction waves was accurately identified by the intelligent denoising framework proposed, combined with Hilbert transform, and then the height of defects was calculated by corresponding geometric relations. The estimation results demonstrate that the measurement method can be considered as a useful technique for crack sizing in industrial structures, even in the case of complex noise. [ABSTRACT FROM AUTHOR]

The twin-jet configuration allows two different scenarios to close the screech feedback. For each jet, there is one loop involving disturbances which originate in that jet and arrive at its own receptivity point in phase (self-excitation). The other loop is associated with free-stream acoustic waves that radiate from the other jet, reinforcing the self-excited screech (cross-excitation). In this work, the role of the free-stream acoustic mode and the guided-jet mode as a closure mechanism for twin rectangular jet screech is explored by identifying eligible points of return for each path, where upstream waves propagating from such a point arrive at the receptivity location with an appropriate phase relation. Screech tones generated by these jets are found to be intermittent with an out-of-phase coupling as a dominant coupling mode. The instantaneous phase difference between the twin jets computed by the Hilbert transform suggests that a competition between out-of-phase and in-phase coupling is responsible for the intermittency. To model wave components of the screech feedback while ensuring perfect phase locking, an ensemble average of leading spectral proper orthogonal decomposition modes is obtained from several segments of large-eddy simulation data that correspond to periods of invariant phase difference between the two jets. Each mode is then extracted by retaining relevant wavenumber components produced via a streamwise Fourier transform. Spatial cross-correlation analysis of the resulting modes shows that most of the identified points of return for the cross-excitation are synchronised with the guided jet mode self-excitation, supporting that it is preferred in closing rectangular twin-jet screech coupling. [ABSTRACT FROM AUTHOR]

Skin cancer is the process of identifying and diagnosing, a disease in which abnormal skin cells grow and spread uncontrollably. An innovative deep learning-based skin cancer detection model is introduced in this research work. The proposed model is divided into five main phases: (a) Pre-Processing (b) Segmentation (c) Feature Extraction (d) 3-Tier Classification (e) post-processing. Initially, the collected raw image is pre-processed via contrast enhancement, decimal scaling, and augmentation methods. From the pre-processed image, the important feature is extracted by using the statistical features like mean, variance, and information gain. Then, from the extracted image, the region of interest ROI is identified via fuzzy assisted Kapur's multi-level thresholding. The optimal features are selected using the hybrid Self-Improved Chimp Optimization algorithm with Glow Swarm Optimization algorithm (HSCGS). The three-tier classification using the BERT based Transformer with HSCGS based Gated Recurred Unit (GRU), BiLSTM, and Graph Neural Network is projected for classification. The proposed model is implemented using the PYTHON platform. The findings are evaluated in terms of accuracy, sensitivity, precision, FPR, FNR, etc. using the present models. The proposed model has recorded the highest detection accuracy as 97% and highest MCC and NPV values. Proposed model has shown the best performance and has outperformed other models. [ABSTRACT FROM AUTHOR]

This article deals with a classes of singular integral–differential equations with convolution kernel and reflection. By means of the theory of boundary value problems of analytic functions and the theory of Fourier analysis, such equations can be transformed into Riemann boundary value problems (i.e., Riemann–Hilbert problems) with nodes and reflection. For such problems, we propose a novel method different from classical one, by which the explicit solutions and the conditions of solvability are obtained. [ABSTRACT FROM AUTHOR]

Accurate traffic flow prediction plays a crucial role in the development of intelligent traffic management. Despite numerous investigations into spatio-temporal methods, achieving high accuracy in traffic flow prediction remains challenging. This challenge arises from the complex dynamic spatio-temporal correlations within the traffic road network and the limitations imposed by the selection of hyperparameters based on experiments and manual experience, which can affect the performance of the network architecture. This paper introduces a novel transformer-based adaptive graph convolutional recurrent network. The proposed network automatically infers the interdependencies among different traffic sequences and incorporates the capability to capture global spatio-temporal correlations. This enables the dynamic capture of long-range temporal correlations. Furthermore, the whale optimization algorithm is employed to efficiently design an optimal network structure that aligns with the requirements of the traffic domain and maximizes the utilization of limited computational resources. This design approach significantly enhances the model's performance and improves the accuracy of traffic flow prediction. The experimental results on four real datasets demonstrate the efficacy of our approach. In PEMS03, it improves MAE by 2.6% and RMSE by 1.4%. In PEMS04, improvements are 1.6% in MAE and 1.4% in RMSE, with a similar MAPE score to the best baseline. For PEMS07, our approach shows a 4.1% improvement in MAE and 2.2% in RMSE. On PEMS08, it surpasses the current best baseline with a 3.4% improvement in MAE and 1.6% in RMSE. These results confirm the good performance of our model in traffic flow prediction across multiple datasets. [ABSTRACT FROM AUTHOR]