Complex Frequency Research Articles

Review on measurement-based frequency dynamics monitoring and analyzing in renewable energy dominated power systems

The massive integration of clean energy and renewable energy source (RES) is one of the most important trends in the low carbon energy transition toward carbon neutrality. Such an important goal significantly alters the power system dynamic behavior. Consequently, monitoring and analyzing the complex frequency dynamic of RES-dominated power systems play an essential role in ensuring power system security and stability. The measurements, especially those supported by wide area measurement systems (WAMSs), can enable full state awareness and deep informatization of the power system and therefore provide effective solutions for monitoring and analyzing system frequency dynamic behaviors with complex features. This paper focus on the application of measurements in monitoring and modeling analysis technologies for the features of frequency dynamics of RES-dominated power systems. We summarize related research on online monitoring of frequency dynamic behavior features based on the information from measurements. Further, for system frequency security assessment, measurements can improve the traditional methods and promote new data-driven methods for more accuracy and effective frequency dynamics analysis. Finally, future directions and possible solutions for measurement-based frequency dynamics monitoring and analyzing are prospected.

Loss Compensation and Superresolution in Metamaterials with Excitations at Complex Frequencies

Loss Compensation and Superresolution in Metamaterials with Excitations at Complex Frequencies

Data augmentation based novel approach to automatic speaker verification system

In recent times, the Automatic Speaker Verification (ASV) systems have been gaining popularity among biometric systems. Feature extraction technique, classification model, and spoof dataset are the three main components that mainly affect the performance of such systems. In recent years, researchers have proposed integrated or complex feature extraction methods at front end and combination of two or more machine learning models at backend to classify the audio samples into spoofed or bonafide. This increases the overall complexity of ASV system. Moreover, most of the spoofing datasets are highly imbalanced. Hence, to solve these issues, this paper improves front-end feature extraction by combining data augmentation approach Synthetic Minority Oversampling Technique (SMOTE) with less complex feature extraction method Frequency Domain Linear Prediction (FDLP). In the proposed system, classification of the audio samples into bonafide or spoofed samples has been done by using different backend classification models such as Random Forest (RF), K-Nearest Neighbor (KNN), Naïve Bayes (NB), Convolutional Neural Network (CNN), Long Short-Term Memory, and Bidirectional LSTM (BiLSTM). The proposed system has been built using ASVspoof PA 2019, ASVspoof LA 2019 and VSDC datasets, and has been evaluated on Logical Access (LA) attacks, Presentation attacks (PA) and multi-order replay attacks (MA). The obtained results show that combination of SMOTE oversampling with FDLP at frontend, and BiLSTM at backend outperforms all other implemented models. It provides Equal Error Rate (EER) value 0.85 %, 0.91 % and 0.55 % for PA, LA and MA attacks scenarios respectively. The performance of the proposed system has also been evaluated in the presence Gaussian noise. It can be interpreted from the obtained results that proposed FDLP-SMOTE-BiLSTM system provides better performance in noisy environment, and under different spoofing attacks scenarios.

The Singlet: Direct Synthesis of Pseudo-Elliptic Inline Filters With Frequency Variant Couplings

A general and direct synthesis of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$</tex-math> </inline-formula> poles pseudo-elliptic inline filters having <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N_{p}$</tex-math> </inline-formula> purely real and/or imaginary frequency transmission zeros is presented. Using an appropriate model of the resonators (bandpass distributed or lumped element) and shifting the reference planes at the input and output of the filter network, a novel direct synthesis and realization of filters based on frequency variant coupling (inductive or capacitive) in the distributed domain is demonstrated for accurate modeling of narrow and broadband filters. First, a complete general synthesis procedure is described that allows for flexible or mixed topologies realizing transmission zeros anywhere on the frequency plane (including complex and infinite frequencies). Furthermore, by exploiting the power of modular design, a synthesis procedure that enables simultaneous extraction of reflection zero (a pole) and a transmission zero in the form of a symmetrical and physically realizable singlet as an elementary unit is showcased. The physical dimensions of the extracted singlets are independently determined in any chosen technology, and the overall filter is obtained by directly cascading the physical singlets. To validate this novel synthesis technique, three design examples are shown: a narrowband four-pole, four transmission zeros (fully canonical) filter from literature is synthesized and physically dimensioned, a wideband three-pole, three transmission zero (fully canonical) filter, and a broadband three-pole, one transmission zero, filter. In the first two examples, each of the singlet blocks was implemented in an overmoded rectangular waveguide cavity operating at the TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{201}$</tex-math> </inline-formula> mode coupled at the input and output to the fundamental nonresonating TE <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{10}$</tex-math> </inline-formula> mode. The third example was implemented in a re-entrant coaxial resonator operating at the fundamental mode. The simulation of the electromagnetic (EM) high-frequency structure simulator (HFSS) models of the overall example filters was in excellent agreement with the synthesized models, thereby validating the effectiveness of the proposed synthesis technique. Furthermore, the measured results of the fabricated wide bandpass filter showed close agreement with synthesis and EM model.

Principles of progressive slow-sound and critical coupling condition in broadband sonic black hole absorber

Recent advances in sonic black hole (SBH) provide new opportunities for controlling sound waves and designing wave manipulation devices. SBH is a device that consists of partitions with gradually decreasing inner radii inserted into an acoustic duct. Several studies have reported that SBH can achieve a broadband sound absorption coefficient close to 1, avoiding the issue of alternating high and low absorption coefficients observed in traditional sound absorbers. However, the fundamental mechanisms and principles behind this behavior are not yet fully understood. This study aims to investigate the detailed sound absorption mechanisms of SBH, including the progressive slow-sound effect and the critical coupling condition that leads to broadband sound absorption. To achieve this goal, an analytical model based on the effective medium approach is developed to investigate the layer-by-layer retardation in sound propagation. The sound absorption coefficient is then determined based on the surface impedance calculation. The effective medium analysis reveals that SBH enables a unique condition to progressively decelerate wave propagation across its layers. As a result, the critical coupling condition becomes more easily established with smoothly increasing SBH partitions and more discretised layers, as elucidated by the complex frequency analysis results. The physical insights gained from this study reveal the distinctive features of SBH compared to classical sound absorbers, paving the way for its engineering applications.

Frequency veering and nonlinear coupled vibration analysis of variable stiffness composite plates with curvilinear fiber paths

The coupling forced vibration behaviors of a variable stiffness plate with curvilinear fiber paths at mode veering regions caused by variations of fiber angle have been rarely found in previous papers, especially in the presence of considering the complex material nonlinearity of composite materials. In this paper, the variable stiffness plate of carbon fiber reinforced composites (CFRC) with curvilinear fiber paths is taken as the research object, and the influence of curvilinear fiber paths on its natural characteristics and vibration responses are studied in detail on the basis of considering the material nonlinearity of CFRC. Firstly, it is found that the variations of curvilinear fiber paths can cause complex frequency veering behavior of the variable stiffness plate, and lead to the appearance of irregular modal shapes formed by modal interaction. Then, the forced vibration response of the variable stiffness plate in the frequency veering region is analyzed methodically, and the variation rules of the vibration response under modal interaction is obtained. After analyzing the nonlinear vibration response of the variable stiffness plate under the combined influence of modal interaction and CFRC material nonlinearity, the mechanism of complex nonlinear dynamic behavior of variable stiffness plate in frequency veering region is further investigated.

Complex frequency analysis and source of losses in rectangular sonic black holes

The amount and practical source of losses required by rectangular sonic black holes in air to effectively absorb low-frequency sound are analyzed numerically and experimentally. In the sole presence of viscothermal losses, only high-order (high frequency) Fabry–Perrot resonances are likely to be critically coupled in realistic rectangular sonic black holes. This results in sharp absorption peaks that do not reach unity at low frequencies, because the quality factors of the associated resonances are high. To avoid these drawbacks, slits of rectangular sonic black holes are partially filled with porous materials so that a profile of porous filled slits is superimposed on the sonic black hole profile itself. The improvement in the absorption coefficient is significant, particularly at frequencies below the viscous/inertial transition frequency of the porous material. This transition frequency is assumed to be the limit of possible perfect absorption of the bulk porous material layer. The numerical results are supported by experimental results, which also show that the vibrations of the plates forming the acoustic black hole must be considered with caution.

Manipulating the quasi-normal modes of radially symmetric resonators.

The frequency response of a resonator is governed by the locations of its quasi-normal modes in the complex frequency plane. The real part of the quasi-normal mode determines the resonance frequency and the imaginary part determines the width of the resonance. For applications such as energy harvesting and sensing, the ability to manipulate the frequency, linewidth and multipolar nature of resonances is key. Here, we derive two methods for simultaneously controlling the resonance frequency, linewidth and multipolar nature of the resonances of radially symmetric structures. Firstly, we formulate an eigenvalue problem for a global shift in the permittivity of the structure to place a resonance at a particular complex frequency. Next, we employ quasi-normal mode perturbation theory to design radially graded structures with resonances at desired frequencies.

Thermoelastic damping analysis of functionally graded sandwich microbeam resonators incorporating nonlocal and surface effects

Functionally graded (FG) sandwich microstructures/nanostructures stand as one of the most promising composite structures due to the capability to resist thermal shock and high noise in extreme thermal environments. Meanwhile, accurately prediction quality-factor based on thermoelastic damping (TED) is of great significance for the design of high-performance microresonators /nanoresonators. However, the classical TED models fail to explain the size-dependent thermo-mechanical behavior. The nonlocal elasticity and surface elasticity are responsible for the size-dependent phenomenon. In this article, a modified TED model is proposed to estimate the impact of the size-dependent effect on the TED of FG sandwich microbeam resonators in unsteady heat transfer processes by combining the nonlocal elasticity model, surface elasticity model, and dual-phase-lag (DPL) heat conduction model. It is assumed that the FG sandwich microbeam resonators consist of a ceramic core and FG surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of TED is obtained by the complex frequency method. The influences of the factors including the nonlocal parameter, the surface effect, the power-law index, and the vibration modes on the TED are analyzed. These results provide a reasonable theoretical analysis to predicate TED in the design of FG sandwich microresonators/nanoresonators with high performance.

Temporal coupled-mode theory for PT-symmetric chiral metasurfaces.

We have developed a temporal coupled-mode theory based on quasi-normal modes to investigate the chiroptical effects in parity-time (PT) symmetric metasurfaces. The PT symmetry enforces a different constraint for the direct scattering matrix and the coupling constants, which is verified by calculating the transmission spectra originating from the chiral quasi-bound states in the continuum. What's more, the scattering matrix can be analytically continued to the complex frequency plane. We find that the zero and pole singularities of the transmission coefficients and scattering matrix play an important role in the optical chirality. The pole singularities carry a quantized topological charge of -1. Our work paves the way for studying the enhanced optical chirality in non-Hermitian metasurfaces.

Investigation on wave-body interactions by a coupled High-Order Spectrum method with fully nonlinear Rankine source method

The complex frequency components of ocean waves inherently result in energy transfer during the evolution of wave spectra. This paper introduces a High-order spectrum method coupled with a fully nonlinear hydrodynamic solver (HOS-FNL), for modeling wave-structure interaction within a modulated nonlinear wave train. The approach combines the high-order spectrum method for modeling the incident wave field in a large water domain, with the nonlinear Rankine source method for calculating the disturbed wave field around the floating structure. We validated the HOS code through simulations of free and locked wave cases, and the entire modulation process is analyzed and compared with existing literature. Experimental measurements of the loads acting on a container ship in regular waves are used to validate the core algorithm of the hydrodynamic solver, yielding satisfactory results. Additionally, the behavior of a ship due to finite-amplitude uniform wave train is investigated, visualizing the motion and load response of the ship, wave run-up, diffraction wave patterns, and velocity vectors of the free surface to emphasize the nonlinear characteristics. The HOS-FNL method demonstrates remarkable effectiveness and efficiency, showcasing its potential for a wide range of practical marine applications.

Multiple-order singularity expansion method

Physical systems and signals are characterized by complex functions of the frequency in the harmonic domain. The extension of such functions to the complex frequency plane, and in particular expansions and factorized forms of the harmonic-domain functions in terms of their poles and zeros, is of high interest to describe the physical properties of a system, and study its response dynamics in the temporal and harmonic domains. In this work, we start from a general property of continuity and differentiability of the complex functions to derive the multiple-order singularity expansion method. We rigorously derive the common singularity and zero expansion and factorization expressions, and generalize them to the case of singularities of arbitrary order, while deducing the behavior of these complex frequencies from the simple hypothesis that we are dealing with physically realistic signals.

Generalized Kelvin-Voigt viscoelastic modeling and numerical study of Free-Damped vibrations in MR elastomer reinforced with graphene platelets

This study focuses on the modeling and numerical analysis of a novel composite plate, which consists of a laminated magnetorheological elastomer (MRE) reinforced with graphene platelets (GPLs). The investigation begins with the determination of the mechanical properties of the MRE, utilizing a modified generalized Kelvin-Voigt viscoelastic model. Through nonlinear regression analysis and the nonlinear least squares technique, the dependencies of the storage and loss modulus of the magnetorheological (MR) matrix are evaluated, considering factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is validated by comparing the obtained results with existing experimental data from the literature, employing root mean square error and correlation coefficients as metrics of consistency. Next, the homogenization process is applied to the composite media, which involves integrating the MR elastomer matrix and GPL reinforcements using the Halpin-Tsai micromechanical approach. This procedure enables the extraction of effective material properties governing the behavior of the composite structure. The theoretical framework, encompassing third-order plate theory, linear elasticity, and viscoelasticity, is then employed to derive the dynamic equations of the composite plate, employing Hamilton's principle as a guiding principle. To solve the dynamic problem and obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. This numerical technique offers a robust and accurate solution approach, providing comprehensive insights into the vibrational behavior of the composite plate. The study conducts a thorough investigation, exploring the performance achieved by incorporating GPL reinforcements within the MRE matrix. Specifically, the effects of different volume fractions of iron particles and varying magnetic fields are comprehensively examined and analyzed. Through this comprehensive exploration, a profound understanding of the behavior of the composite plate and its response to external stimuli is attained. The findings highlight the potential advantages of integrating GPL reinforcements and offer valuable insights for optimizing the design and performance of such composite structures in practical applications. The research contributes to the advancement of knowledge in the field of composite materials and opens up new possibilities for innovative and high-performance structural designs.

Evaluating the effect of spinal cord stimulation on patient with disorders of consciousness: A TMS-EEG study

ObjectiveThe application of spinal cord stimulation (SCS) in the treatment of disorders of consciousness (DOC) has attracted attention, but its effect on brain activity is still unknown. Transcranial magnetic stimulation combined with EEG (TMS-EEG) can measure cortical activity, which can evaluate the effect of SCS on DOC. MethodsWe record 20 DOC patients' CRS-R values and TMS-EEG data before and after one-session SCS (Pre-SCS and Post-SCS). 20 DOC patients including 10 patients with unresponsive wakefulness syndrome (UWS) and 10 patients with minimally conscious states (MCS). TMS evoked potential (TEP) was used to measure the changes of cortical activity in DOC patients between Pre-SCS and Post-SCS. Firstly, we used the global mean field potential (GMFP) and fast perturbational complexity index (PCIst) to compare the temporal changes of patients' cortical activity. Then, we obtained the frequency feature (natural frequency, NF) based on the TEP time-frequency analysis, and compared the changes of natural frequency between Pre-SCS and Post-SCS. Finally, the study explored the relationship between the patient's baseline CRS-R values and changes of TMS evoked cortical activity in time and frequency domains. ResultsAfter SCS, MCS and UWS groups almost have no changes of CRS-R values (MCS: 9.9 ± 1.52 at Pre-SCS, 10.2 ± 1.48 at Post-SCS; UWS: 5.6 ± 1.26 at Pre-SCS, 5.7 ± 1.34 at Post-SCS). MCS group showed significant increases of GMFP amplitude (around 100 ms and 300 ms) and PCIst values at Post-SCS (p < 0.05). UWS group had no significant changes (p > 0.05). Besides, SCS induced the significant increases of natural frequency for MCS group(p < 0.05), but not for UWS group. At last, the study found that all patient's baseline CRS-R values were significantly correlated with ΔPCIst (r = 0.67, p < 0.005), and ΔNF (r = 0.72, p < 0.001). ConclusionsSCS can modulate cortical activity of DOC patient, including temporal complexity and natural frequency. The changes of cortical activity caused by SCS are related to patients’ consciousness level. TMS-EEG can evaluate the effect of SCS on DOC patients.

Asymmetric phase modulation of light with parity-symmetry broken metasurfaces

The design of wavefront-shaping devices is conventionally approached using real-frequency modeling. However, since these devices interact with light through radiative channels, they are by default non-Hermitian objects having complex eigenvalues (poles and zeros) that are marked by phase singularities in a complex frequency plane. Here, by using temporal coupled mode theory, we derive analytical expressions allowing to predict the location of these phase singularities in a complex plane and as a result, allowing to control the induced phase modulation of light. In particular, we show that spatial inversion symmetry breaking—implemented herein by controlling the coupling efficiency between input and output radiative channels of two-port components called metasurfaces—lifts the degeneracy of reflection zeros in forward and backward directions, and introduces a complex singularity with a positive imaginary part necessary for a full 2π-phase gradient. Our work establishes a general framework to predict and study the response of resonant systems in photonics and metaoptics.

Hydrodynamic and non-hydrodynamic excitations in kinetic theory — a numerical analysis in scalar field theory

Viscous hydrodynamics serves as a successful mesoscopic description of the Quark-Gluon Plasma produced in relativistic heavy-ion collisions. In order to investigate, how such an effective description emerges from the underlying microscopic dynamics we calculate the hydrodynamic and non-hydrodynamic modes of linear response in the sound channel from a first-principle calculation in kinetic theory. We do this with a new approach wherein we discretize the collision kernel to directly calculate eigenvalues and eigenmodes of the evolution operator. This allows us to study the Green’s functions at any point in the complex frequency space. Our study focuses on scalar theory with quartic interaction and we find that the analytic structure of Green’s functions in the complex plane is far more complicated than just poles or cuts which is a first step towards an equivalent study in QCD kinetic theory.

Stable parameters identification for rational approximation of Single degree of freedom frequency response function of semi‐infinite medium

AbstractThe rational approximation is an important tool for establishing a dynamic analysis model in time domain for semi‐infinite water and soil. It accurately represents the interaction between the semi‐infinite medium and an engineering structure. Current research on rational approximation method focuses mainly on the establishment of time‐domain analysis models. However, the stability, accuracy, and calculation efficiency of the rational approximation model cannot be guaranteed simultaneously. Based on linear system control theory, this work decomposes the continuous‐time rational approximation (CRA) and the discrete‐time rational approximation (DRA) into a combination of first‐ and second‐order subsystems, and the stability boundaries for the identified parameters are established according to the stability conditions of each subsystem. A genetic algorithm and a sequential quadratic programming algorithm are used to construct a parameter identification method that can ensure stability in the time domain. Through parameter identification of complex frequency response functions, it is demonstrated that the method proposed in this work can guarantee the stability and accuracy simultaneously, and the calculation efficiency is also substantially improved over that of the existing methods.

Damping and tuning of inerter-based dampers for cable vibration mitigation considering girder vibrations

As the spans of cable-stayed bridges increase, and with the use of steel towers and girders, bridge stiffness decreases, the bridge frequencies approach the frequencies of the cables. The effect of girder–cable coupling vibrations cannot be ignored in cable vibration control. This study focuses on the performance of inerter-based dampers (IBDs) in cable vibration control when considering girder vibrations. Two types of IBD, a viscous inerter damper (VID) and a tuned inerter damper (TID), are studied. The system dynamics are formulated through complex modal analysis. Damping effects of the VID and TID are evaluated and optimized based on the complex frequency loci of the damped system. The results indicate that the control performance of the VID and TID for the target cable mode is drastically reduced when the ratio between the girder and target cable frequencies is approximately 1. The effects of the girder–cable coupling vibration on the optimal parameters and control performance of the VID and TID for the target cable mode are found to be significant even when the girder-cable frequency ratio is not close to 1, and the effect can be increased for a smaller girder–cable mass ratio. The different evolution characteristics of the girder–cable coupling effect are revealed by comparing the designs and performances of the VID and TID. The effectiveness of the VID and TID to control the system model considering dynamic cable force and cable sag is verified using a numerical model.

Low-frequency broadband absorber with coherent coupling based on perforated panel and space-coiling channels

Efficient broadband absorption of low-frequency sound via ultra-thin structure remains challenging due to the narrow-band property generated by the dispersive nature of resonance. In this study, we investigate the absorption mechanism of a component composed of a perforated panel and space-coiling channels through the coupling effect, acoustic impedance matching, and complex frequency analysis. In addition, the influence of geometrical parameters, resonance frequency intervals, and number of components in the coupled system on the band is investigated. Accordingly, the strategy for developing absorbers is to design individual components in the under-damped state by adjusting the geometrical parameters, then put together multiple components with different channel lengths in parallel. On the basis of this strategy, a low-frequency and broadband absorber is theoretically proposed and experimentally demonstrated, which can achieve broadband absorption from 250 Hz to 450 Hz. The design strategy has potential applications in low-frequency noise control engineering, such as plants, automotive and aerospace industries.

Modeling of a Magnetorheological Elastomer-Based Nanocomposite Higher-Order Beam: Tunable Dynamic and Damping Characteristics

This study involves the comprehensive modeling of material properties and a numerical investigation of the free-damped vibrations exhibited by an innovative composite beam. The beam under consideration is a laminated magnetorheological (MR) elastomer, strategically reinforced with graphene platelets (GPLs). Initially, the mechanical properties of the MR matrix are meticulously calculated using a modified generalized Kelvin–Voigt viscoelastic model. To ensure the accuracy and credibility of the proposed model, nonlinear regression analysis based on the nonlinear least squares technique is employed. This modeling approach enables the tunability of the MR matrix’s storage and loss modulus, which depend on factors such as the magnetic field, iron particles, and excitation frequency. The proposed model is verified by comparing the results with experimental data from the literature, using analyses of root mean square error (RMSE) and correlation coefficients. Subsequently, the composite media, comprising the magnetorheological elastomer (MRE) matrix and GPL reinforcements, undergoes homogenization through the application of the Halpin–Tsai micromechanical procedure. Theoretical formulations, encompassing third-order beam theory, strains, linear elasticity, and viscoelasticity, are then utilized to derive the motion equations governing the dynamic behavior of the composite beam. Hamilton’s principle guides the derivation of these equations. To obtain the complex frequencies characterizing the system, the generalized differential quadrature (GDQ) method is implemented. In this study, particular emphasis is placed on investigating the performance achieved by adding GPL reinforcements to the MRE with different iron particle volume fractions under various magnetic fields.