Frequency Plane Research Articles

POWER QUALITY ANALYIS FOR POWER LED DRIVES

DC micro grids have grown increasingly popular in the energy grid in recent years, as distributed generation has increased. Distributed generation refers to small or large-scale renewable energy that is linked to the main power system. Renewable energy sources like solar and wind power help the local grid, but their output is inherently intermittent and unpredictable, interfering with regular grid operation. Some of these issues can be mitigated by using energy storage in conjunction with renewable energy. Renewable energy is often linked to the grid using power electronic converters. 
 The goal of this research is to simulate and evaluate transmitted emissions in the time and frequency planes using IEEE 1459 to investigate the impacts of DC / DC converters on DC lines, particularly for renewable energy generation. While there are standards and norms for frequencies up to 2 kHz and beginning at 150 kHz, the frequency range 2-150 kHz only has suggested techniques and propagation restrictions. As a result, the emission conveyed in the frequency range of 2-150 kHz is a subject that must be comprehended. The structure of the generation model, as well as the idea of power quality in electricity generating models, will be investigated using data collected through experimental and computer simulations on a medium-scale hybrid network connected to the grid. The technological advances acquired will subsequently be utilized to evaluate the power quality of various DC and AC single/three phase power systems (such as computer servers, airplanes, and so on).

Feature extraction by enhanced time–frequency analysis method based on Vold-Kalman filter

The time–frequency analysis method can extend a one-dimensional signal to a two-dimensional time–frequency plane, revealing the signal's time-varying characteristics. The time–frequency representation (TFR) obtained by the time–frequency postprocessing algorithm has the characteristics of energy aggregation and high resolution. The generalized S-synchroextracting transform (GS-SET) stands out for its strong adaptability. However, this method cannot obtain effective information when analyzing multicomponent complex signals. We propose an enhanced time–frequency analysis method to solve this problem. First, the multicomponent complex signal is decomposed into multiple mono-component signals by the Vold-Kalman time-varying filtering technique. Second, these signals are processed by the GS-SET method. Last, the obtained TFRs are linearly superimposed to obtain the results of the enhanced method. The simulated signal verifies that the proposed method can effectively represent its time-varying characteristics. The experimental signal of the rolling bearing verifies the practicability of this method.

Quantitative analysis of terahertz signals using CWT-based spectrogram and Zernike image moments

The combination of terahertz (THz) spectroscopic measurements and multivariate calibration techniques has become a well-established technique in many research fields. However, intentional or unintentional changes in environmental conditions, THz instruments and/or of the substance itself make the established calibration model becoming insufficient and inadequate for the further application. In this article, we introduce, discuss, and evaluate a new multivariate calibration method, the CWT-ZM, that combines the merits of the Zernike moment (ZM) invariance and the continuous wavelet transform (CWT) time–frequency analysis. With the help of a wavelet time–frequency analysis, the THz pulse is expanded into a two-dimensional (2D) time–frequency plane that provides richer and more direct characteristic information in the time and frequency domain simultaneously. In addition, Zernike moments provide linearly independent descriptors for the 2D time–frequency intensity image and are invariant to THz signal affine transformations, such as peak shifting, baseline drifting, and scaling. In this manner, we obtain a set of features that exhibit a high capability to capture the concentrations of the target compounds and a high invariance of the different measuring instruments and the variable environment. This approach results in a more robust regression system with improved generalization properties with respect to standard methods. Experiments were then conducted on a THz dataset of pharmaceutical tablets acquired by two different THz instruments, and these confirmed the effectiveness of the proposed approach. Furthermore, CWT-ZM is an extensible framework that can be combined with various spectral qualitative and quantitative analysis algorithms.

Spherical Bragg resonators for lasing applications: a theoretical approach.

This work considers a perfect 3D omnidirectional photonic crystal; Spherical Bragg Resonators (SBR), for lasing applications. We use the recursive transfer matrix method to study scattering in an Er3+ doped SBR. We find the threshold gain factor for lasing by scanning poles and zeros of the S-matrix in the complex frequency plane. For a six Si/SiO2 bilayer SBR, the threshold gain factor corresponds to a dopant density of Er3+ of 5.63 × 1020ions/cm3. We believe, our work is the first theoretical demonstration of the ability to engineer optical amplification and threshold gain for lasing in SBRs.

Modal analysis of electromagnetic resonators: User guide for the MAN program

All electromagnetic systems, in particular resonators or antennas, have resonances with finite lifetimes. The associated eigenstates, also called quasinormal modes, are essentially non-Hermitian and determine the optical responses of the system. We introduce MAN (Modal Analysis of Nanoresonators), a software with many open scripts, which computes and normalizes the quasinormal modes of virtually any electromagnetic resonator, be it composed of dispersive, anisotropic, or non-reciprocal materials. MAN reconstructs the scattered field in the basis formed by the quasinormal modes of the resonator and provides a transparent interpretation of the physics.The software is implemented in MATLAB and has been developed over the past ten years. MAN features many toolboxes that illustrate how to use the software for various emblematic computations in low and high frequency regimes. A specific effort has been devoted to interface the solver with the finite-element software COMSOL Multiphysics. However, MAN can also be used with other frequency-domain numerical solvers. This article introduces the program and summarizes the relevant theoretical background. MAN includes a comprehensive set of classical models and toolboxes that can be downloaded from the web. Program summaryProgram title: MAN (Model Analysis of Nanoresonators)CPC Library link to program files:https://doi.org/10.17632/wdz5pd4sb4.1Licensing provisions: GNU General Public License 3Developer's repository link:https://doi.org/10.5281/zenodo.7400937Programming language: MatlabNature of problem: Compute and normalize the quasinormal modes of resonators and antennas of any type, be they composed of dispersive, anisotropic, or non-reciprocal materials, or be they operated at high or low frequencies. Use the quasinormal modes to reconstruct the resonator responses in the near field and far field.Solution method: Two methods are gathered. The quasinormal modes are computed and normalized either by solving the linearized Maxwell equations or searching poles in the complex frequency plane. The reconstruction is then performed analytically with closed form expressions of the excitation coefficients. A presentation of the software capabilities is found in the video (https://www.youtube.com/watch?v=SOdQsXdBGv0). To see how to use the software, please also watch the demo (https://www.youtube.com/watch?v=BSf9A1qyUBE).

Excitation of mirror symmetry higher-order rational soliton in modulation stability regimes on continuous wave background.

We study the relationship between the structures of the nonlinear localized waves and the distribution characteristics of the modulation stability regime in a nonlinear fiber with both third-order and fourth-order effects. On the background frequency and background amplitude plane, the modulation stability region consists of two symmetric curves on the left and right and a point on the symmetry axis. We find that the higher-order excitation characteristics are obviously different at different positions in the modulation stability region. Their excitation characteristics are closely related to the modulation instability distribution characteristics of the system. It is shown that asymmetric high-order rational solitons are excited at the left and right stable curves, and the symmetric one is excited at the stable points. Interestingly, the asymmetric higher-order rational solitons on the left and right sides are mirror-symmetrical to each other, which coincides with the symmetry of the modulation instability distribution. These results can deepen our understanding of the relationship between nonlinear excitation and modulation instability and enrich our knowledge about higher-order nonlinear excitations.

Forward fitting STIX visibilities

Aims. We seek to determine to what extent the problem of forward fitting visibilities measured by the Spectrometer/Telescope Imaging X-rays (STIX) on board Solar Orbiter becomes more challenging with respect to the same problem in the case of previous hard X-ray solar imaging missions. In addition, we aim to identify an effective optimization scheme for parametric imaging for STIX. Methods. This paper introduces a global search optimization for forward-fitting STIX visibilities and compares its effectiveness with respect to the standard simplex-based optimization used so far for the analysis of visibilities measured by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). We made this comparison by considering experimental visibilities measured by both RHESSI and STIX, as weel as synthetic visibilities generated by accounting for the STIX signal formation model. Results. We found that among the three global search algorithms for parametric imaging, particle swarm optimization (PSO) exhibits the best performances in terms of both stability and computational effectiveness. This method is as reliable as the simplex method in the case of RHESSI visibilities. However, PSO is significantly more robust when applied to STIX simulated and experimental visibilities. Conclusions. A standard optimization based on local search of minima is not effective enough for forward-fitting the few visibilities sampled by STIX in the spatial frequency plane. Therefore, more sophisticated optimization schemes based on global search must be introduced for parametric imaging in the case of the Solar Orbiter X-ray telescope. The forward-fitting routine based on PSO proved to be significantly robust and reliable, and it could be considered as an effective candidate tool for parametric imaging in the STIX context.

Modal Identification of Bladed Disks by Time–Frequency Analysis of the Nonsynchronous Response

Abstract In some circumstances, it is impossible to exploit resonance crossings to identify the modal properties of rotor disks. In these cases, the identification process must rely on nonsynchronous vibrations and becomes challenging for two reasons. First, the signals are weak (compared to the levels measured during resonance crossings) and random, thus an averaging procedure is necessary. Second, the dynamical system is time-variant due to the variation of the rotor speed. This paper presents a modal identification procedure formulated in the framework of the time–frequency analysis. A region of the time–frequency plane is stretched to map the system into a fictitious linear time-invariant (LTI) system. Then, the power spectral density function (PSD) of the response is computed by an averaging procedure. Finally, the modal properties are estimated through an output-only modal identification algorithm. The procedure is applied to simulated and experimental data regarding a bladed disk of a steam turbine.

TMSST-CK fault feature extraction method for flexible thin-wall bearing based on the Gini index principle

A flexible thin-wall bearing (FTB) is forced to deform with the elastic deformation of the flexspline in motion, resulting in a completely different fault characteristic frequency (FCF) from ordinary rolling bearings. However, current extraction methods treat FTBs as ordinary ones and they are analyzed based on the spectrum, without considering the time-varying nature of the FCF in an FTB. In an effort to address this concern, this paper proposes a Gini index-based time-reassigned multisynchrosqueezing transform, where the window size is determined by the period impulses feature in the noise-removed signal. In addition, a frequency point selection method that contains fault characteristics of the FTB is proposed by calculating the maximum correlated kurtosis in the time–frequency (TF) plane. Furthermore, the instantaneous frequency is extracted by calculating the time interval between two consecutive impulses. The extracted fault frequency agrees well with the experimental result and outperforms other TF analysis techniques in demonstrating its time-varying nature.

Time-Scale Localization Operators in the Weinstein Setting

In this paper, we introduce the notion of Weinstein two-wavelet and we define the two-wavelet localization operators in the setting of the Weinstein theory. Then we give a host of sufficient conditions for the boundedness and compactness of the two-wavelet localization operator on $L^{p}_{\alpha}(\mathbb{R}^{d+1}_+)$ for all $1\leq p\leq \infty$, in terms of properties of the symbol $\sigma$ and the functions $\varphi$ and $\psi$. In the end, we study some typical examples of the Weinstein two-wavelet localization operators.

Inter-turn fault detection of induction motors using a method based on spectrogram of motor currents

Steady-state signatures seem more reliable than incipient fault signatures for detection of inter-turn short circuit (ITSC) fault in induction motors (IMs). An efficient detection approach is proposed based on the deviation of the histogram relevant to the time–frequency plane’s image of the steady-state modal current signal from the standard normal distribution. First, the misleading frequency components like 3rd, 5th, and 7th harmonics are excluded using Kalman Filter (KF). Then, from the time–frequency spectrogram of the signal, the converted gray-level image and its histogram are obtained. A considerable deviation of the histogram distribution from a normal distribution is observed in the case of ITSC fault, used for the detection. A cumulative index including normalized skewness and kurtosis of the histogram is used as the criterion of the detection. Finally, a novel threshold setting method based on Otsu’s threshold principle is proposed, which efficiently distinct faulty conditions from healthy operations. The required data for assessment of the approach is gathered from different experiments carried out on a test bench, subjected to various fault percentages and different load levels. The results confirm the effectiveness of the proposed methodology.

Simultaneous non-convex low rank regularization for fast magnetic resonance spectroscopy reconstruction

2D magnetic resonance spectroscopy (MRS) is extensively used to analyze the components, structures, and interactions of substances in chemistry and bioengineering. To reduce data acquisition time, the spatiotemporally encoded ultrafast (STEU) MRS employs a fast means to acquire data in the hybrid time and frequency (HTF) plane, but relies on non-uniform sampling (NUS) technique. After that, a proper reconstruction method is essential to recover a high quality 2D MRS from undersampled HTF data. In this work, each column and row of 2D MRS are converted into Hankel matrices, by which a simultaneous low rank regularization model is proposed to exploit the bivariate exponential structure of 2D MRS signal. Additionally, a non-convex surrogate function for rank is integrated in the proposed model to more precisely enforce the low rank property of Hankel matrices. To ensure computational accuracy and convergence, an efficient numerical algorithm is further deduced based on alternating direction method of multipliers (ADMM) iteration. The experimental results have shown that the proposed method significantly outperforms existing 2D MRS reconstruction methods, and presents a strong robustness to low sampling rates, various sampling patterns, and measurement noise with a favorable complexity.

Experimental study of the bistatic acoustic scattering from cylindrical shell

The acoustic scattering technique is a powerful tool in the non-destructive control and evaluation of structures. In many real applications, it is important to study the acoustic scattering in bistatic configuration (the emitter is far from the receiver) since it allows to give multiple viewpoints of the considered structure. The present paper investigates both theoretically and experimentally the acoustic scattering in different viewpoints of a cylindrical shell. To analyse the bistatic evolution of the acoustic scattering, we call upon the clockwise and counterclockwise waves propagating on the cylindrical shell. The use of time–angle representation gives a map of the different waves circumnavigating around the shell. This representation allows to show the chronological evolution of the acoustic scattering as a function of the azimuthal angle. The conducted spectral analysis reveals that the frequency content of the scattered acoustic response varies from one location to another. The majority of the resonant frequencies can be detected in the monostatic configuration (the emitter and receiver are co-located). The application of the time–frequency method on the experimental acoustic signals recorded in different viewpoints of the shell allows to analyse and follow the time and frequency shifts of the clockwise and counterclockwise waves propagating on the cylindrical structure. The echo patterns observed in the time–frequency plane are used to estimate the arrival times of the clockwise and counterclockwise waves as a function of the azimuthal angle. Based on the obtained arrival times, we estimate the delay between the clockwise and counterclockwise waves and therefore their group velocities.

Experimental investigation of three-dimensional modes in the wake of a rotationally oscillating cylinder

Three-dimensionalities in the wake of flow past a circular cylinder executing sinusoidal rotary oscillations about its axis is studied experimentally. The results of water tunnel experiments on a rotationally oscillating cylinder for Reynolds number of 250 with varying amplitude and forcing frequency are discussed. Qualitative studies using hydrogen bubble and laser-induced fluorescence flow visualisation techniques are performed. Observation made for oscillating amplitude, $\theta _{0} = {\rm \pi}/4$ and $\theta _{0}=3{\rm \pi} /4$ , and a low normalised forcing frequency, $FR$ , of 0.75 and 0.5, respectively, confirmed a mode having a spanwise non-dimensional wavelength of $\sim$ 1.8 which is also observed for a rotating cylinder. On increasing forcing frequency this mode disappears and a new mode with a bean-shaped structure and a much smaller spanwise normalised wavelength of $\sim$ 0.8 appears at an $FR$ of 1 and an oscillation amplitude of ${\rm \pi} /2$ . This mode remains almost stable until a forcing frequency of $FR=1.4$ . At higher forcing frequency, $FR=2.75$ , and oscillation amplitude of $3{\rm \pi} /4$ , a mode with cellular structure and a normalised spanwise wavelength of $\sim$ 1.6 is identified. The cells in this mode flatten up with increasing downstream distance and are shed alternately with respect to the adjacent cell. Certain combinations of forcing parameters resulted in a forced two-dimensionality of the wake. Quantitative studies using hot-wire measurements and particle image velocimetry confirm the presence of these modes and wake characteristics. Wake mode map in the forcing frequency and amplitude plane is presented showing regions of newly discovered modes and wake lock-on boundaries.

Microseismic data denoising in the sychrosqueezed domain by integrating the wavelet coefficient thresholding and pixel connectivity

SUMMARY Microseismic monitoring is crucial for risk assessment in mining, fracturing and excavation. In practice, microseismic records are often contaminated by undesired noise, which is an obstacle to high-precision seismic locating and imaging. In this study, we develop a new denoising method to improve the signal-to-noise ratio (SNR) of seismic signals by combining wavelet coefficient thresholding and pixel connectivity thresholding. First, the pure background noise range in the seismic record is estimated using the ratio of variance (ROV) method. Then, the synchrosqueezed continuous wavelet transform (SS-CWT) is used to project the seismic records onto the time–frequency plane. After that, the wavelet coefficient threshold for each frequency is computed based on the empirical cumulative distribution function (ECDF) of the coefficients of the pure background noise. Next, hard thresholding is conducted to process the wavelet coefficients in the time–frequency domain. Finally, an image processing approach called pixel connectivity thresholding is introduced to further suppress isolated noise on the time–frequency plane. The wavelet coefficient threshold obtained by using pure background noise data is theoretically more accurate than that obtained by using the whole seismic record, because of the discrepancy in the power spectrum between seismic waves and background noise. After hard thresholding, the wavelet coefficients of residual noise exhibit isolated and lower pixel connectivity in the time–frequency plane, compared with those of seismic signals. Thus, pixel connectivity thresholding is utilized to deal with the residual noise and further improve the SNR of seismic records. The proposed new denoising method is tested by synthetic and real seismic data, and the results suggest its effectiveness and robustness when dealing with noisy data from different acquisition environments and sampling rates. The current study provides a useful tool for microseismic data processing.

Universal properties of boundary and interface charges in multichannel one-dimensional continuum models

We generalize our recent results for the boundary and interface charges in one-dimensional single-channel continuum [Phys. Rev. B 104, 155409 (2021)] and multichannel tight-binding [Phys. Rev. B 104, 125447 (2021)] models to the realm of the multichannel continuum systems. Using the technique of boundary Green's functions, we give a rigorous proof that the change in boundary charge upon the shift of the system towards the boundary by the distance $x_{\varphi}\in[0, L]$ is given by a perfectly linear function of $x_{\varphi}$ plus an integer-valued topological invariant $I$ -- the so called boundary invariant. For systems with weak potential amplitudes, we additionally develop Green's function-based low-energy theory, allowing one to analytically access the physics of multichannel continuum systems in the low-energy approximation.

Realizing the perfect sound absorption and broadening effective band using porous material and micro-perforated plate

The noise attenuation ability of a single material or structure, especially for low-frequency noise, is limited by its thickness. Aiming to achieve high-efficiency noise attenuation at low frequencies, this paper proposes the methods of porous material filling and micro-perforated plate (MPP) embedding to design a perfect sound absorber at different frequencies using the under-loss Helmholtz resonator (HR). Based on the transfer matrix method, the theoretical calculation models of the sound absorption coefficients of the HR, Helmholtz resonator with porous material (HRP), and Helmholtz resonator with micro-perforated plates (HRM) are constructed. Based on the theoretical models, the under-loss absorber HR1 with the peak absorption at 243 Hz, and the HRP and HRM with perfect absorption at 212 Hz and 157 Hz are designed, respectively. The impedance analysis and complex frequency plane method are used to analyze the sound absorption mechanisms of the HR1, HRP, and HRM. The accuracy of the theoretical model is verified by the finite element method. Finally, the three acoustic absorbers are manufactured using 3D printing technology, and the absorption coefficients are evaluated experimentally. The experimental results show that the HR1 has a high working frequency at 245 Hz and a narrow bandwidth of high-efficiency sound absorption ([Formula: see text]), which is only 12 Hz. The working frequency of the HRP is 214 Hz, and its high-efficiency sound absorption bandwidth is 54 Hz. The HRP has the lowest working frequency at 157 Hz and the widest high-efficiency sound absorption bandwidth of 58 Hz among the three absorbers. The research results presented in this paper provide a reference for the realization of low-frequency broadband noise attenuation designs and have certain application potential in noise control.

Fleet-based early fault detection of wind turbine gearboxes using physics-informed deep learning based on cyclic spectral coherence

The development of a reliable and automated condition monitoring methodology for the detection of mechanical failures in rotating machinery has garnered much interest in recent years. Thanks to the rise in popularity of machine learning techniques, the number of purely data-driven approaches that try to tackle the issue of vibration-based condition monitoring has also drastically improved. Instead of directly using the vibration measurement data as input to a machine learning model, this work first exploits the cyclostationary characteristics inherent to vibration waveforms originating from rotating machinery. The proposed methodology first estimates the two-dimensional cyclic spectral coherence map of a vibration signal in order to decompose the cyclic modulations on the cyclic and carrier frequency plane. While this provides an effective tool to visualize any potential modulation signatures of faulty gears or bearings, it does not allow for easy inspection over time due to its dimensions. To tackle this issue, this paper proposes an unsupervised deep learning approach to wield this vast amount of data as a tool for detecting persistent changes in the modulation characteristics of the vibration signals. In the first phase, a deep autoencoder learns to reconstruct predictions of the cyclic coherence maps based on unlabeled healthy vibration data and the machine operating conditions. Two post-processing steps improve the predictions by mitigating frequency shifts and outlier or noisy measurements. Lastly, the residual error between the predicted and the actual coherence map is then aggregated and employed for further alarming based on thresholds. The autoencoder model is trained using five years of gearbox vibration data from five different wind turbines. The methodology is then validated on two faulty and eight healthy turbines. The results confirm that the proposed approach can deliver clear indications of failure for the faulty turbine while being completely devoid of any significant alarm trends for the healthy turbines. Thanks to the combination of highly effective cyclostationary signal processing with deep learning while using the operating conditions, the proposed methodology can detect and track incipient mechanical faults from non-stationary vibration data of rotating machinery. Lastly, it is important to emphasize that the proposed method is capable of learning the healthy behavior on one turbine and predicting the expected behavior on another turbine.

Spectroscopy ofKerr−AdS5spacetime with the Heun function: Quasinormal modes, greybody factor, and evaporation

We investigate quasinormal modes, greybody factor, and Hawking evaporation of a five-dimensional Kerr-anti--de Sitter (${\mathrm{AdS}}_{5}$) black hole by solving a wave equation for a test massive scalar field in terms of the local Heun function. We clarify the distribution of the quasinormal modes satisfying the ingoing and decaying boundary conditions at the event horizon and conformal infinity, respectively, and their splitting behaviors in the complex frequency plane with respect to a variation of spin parameters. We also point out the existence of purely imaginary modes. Further, we develop a method to extract in/outgoing waves near the AdS boundary, which enables us to define the greybody factor for a wide range of parameter space complementary to previous works. Using the greybody factor, we compute evaporation rates for mass and spins for the Kerr-${\mathrm{AdS}}_{5}$ black hole via the Hawking radiation of the scalar field.

Time–frequency domain local spectral analysis of seismic signals with multiple windows

For a non-stationary seismic signal, time–frequency analysis methods often include a time window function that serves as a weighting function and by which the signal is multiplied to form a segment. The time window function often has the highest weighting coefficient for the central sample of the signal segment. For the rest of the segment, there is no adequate representation in the frequency spectrum. Here, I propose to use multiple orthogonal window functions to properly represent the local spectral property in the time–frequency plane and recover the information lost due to time windowing before applying the Fourier transform. First, I propose to construct multiple window functions directly using a stack of Gaussian functions. The weighted average spectrum of the multiple window functions has a flat passband, which is better than the conventional multiple windows. Taking advantage of the linearity of the Fourier transform, we can apply each window to the analytic signal to generate the instantaneous autocorrelation accordingly and form an averaged instantaneous autocorrelation by a weighted sum before performing the Fourier transform to generate the Wigner–Ville distribution (WVD). This multi-window WVD method successfully represents the local spectrum of the non-stationary seismic signal in the time–frequency plane.