Complex Frequency Response Research Articles

Harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a capacitive voltage transformer

AbstractHarmonic state estimation, which highly depends on accurate synchronised phasors, is a crucial basis for the location, traceability, and governance of harmonics in power systems. However, most existing synchronous phasor measurement units (PMUs) provide power frequency phasors rather than harmonic phasors. In addition, as the dominant voltage signal provider for PMUs in power systems, capacitive voltage transformers (CVTs) have complex frequency responses and cannot be directly used for harmonic measurement. Therefore, accurate harmonic state estimation is difficult to achieve in applications. A method for harmonic voltage phasor reconstruction and harmonic state estimation based on the measurement data of a CVT is proposed. First, the reasons for harmonic voltage measurement errors were analysed. Second, the scattering parameter method was used to measure the wideband voltage transfer characteristics of CVT. Third, a voltage reconstruction method was proposed to improve the measurement accuracy and expand the frequency range of synchronous phasor measurement. Fourth, this method was applied to harmonic state estimation, and the performance of harmonic state estimation before and after voltage reconstruction was quantitatively compared. Results showed that the proposed method can remarkably improve the accuracy of harmonic state estimation. Finally, some factors, such as state observability, complex error disturbances, CVT structure, and harmonic order, influencing the performance of the proposed method were investigated. Results further demonstrated that the method has high accuracy, strong anti‐interference, and adaptability, and can provide basic information for harmonic localisation and traceability.

A comparative analysis of damping models for the vibratory properties of a bent beam

Much of Eric Unger's career was devoted to the study of dissipation mechanisms. This paper will explore the effect of various ways that damping effects have been incorporated in the solution of equations of motion. The analytical model of an L-shaped beam, cantilvered at one end and loaded at its free end by a force that is transverse to the plane of the bent beam, is the basis for the study. Equations of motion that account for coupling of flexure and torsion are created by merging the Ritz series method and the method of Lagrange multipliers. Energy is dissipated by a dashpot transversely mounted at the corner. An “exact” solution of the equations of motion using state-space modal analysis provides the reference for approximate methods including proportional damping, modal decoupling, and structural damping. Impulse response and complex frequency response at various levels of damping will be addressed.

Frequency Domain UWB Channel Characterization and Modeling in Indoor Static Environment

In this article, distance and frequency‐dependent indoor wireless channel characterization and modeling are presented in C, X, and Ku bands at the line of sight (LOS) and nonline of sight (nLOS) scenarios. Complex frequency responses of the indoor radio channel are measured using the frequency‐domain approach. The terminal and measurement setup dependencies of the propagation channel are deconvoluted using closed‐form expressions devised from a two‐port network model approach of the antenna transreceiver system. Subsequently, terminal independent frequency‐domain channel transfer functions (CTFs) and time‐domain channel impulse responses (CIRs) are derived for accurate statistical analysis of large‐ and small‐scale fading parameters of the propagation channel. A distance‐dependent statistical pathloss model is proposed. Successively, a frequency domain channel model using the fifth‐order autoregressive process is proposed. Subsequently, the existence of the multiple clusters in the environment is analyzed by the poles of the transfer functions of the model. Models are validated in both time and frequency domains by comparing the computer‐simulated synthetic model data with the empirical channel responses. The measurement data and the model data are seen to be in good agreement.

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.

Complex sparse Bayesian learning for guided wave dispersion curve estimation in plate-like structures

This paper proposes a new dispersion curve estimation method that employs the complex sparse Bayesian learning (CSBL). It is well accepted that guided wave packets are distorted because of the differences in propagation velocities at different frequencies; thus, the preceding velocity–frequency curve estimation is beneficial for wave packet recovery, feature recognition and defect localization. Conventional dispersion curve estimation methods, such as two-dimensional Fourier transform and multiple signal classification, are suitable for array signal and are restricted by the transducer aperture, leading to a small application scope. According to the frequency–response model of the guided wave, for each frequency, the responses obtained by the transducers can be sparsely represented based on an overcomplete dictionary matrix constructed using multiple discretized wavenumbers and known distances. A CSBL algorithm was developed to infer the posterior probability density function of the weight vector in the sparse representation. The non-zero elements in the sparse weight vector mean that the corresponding dictionary atoms indicated wavenumbers are contained in the frequency response, and the velocity–frequency curve can be finally derived from the wavenumber–frequency curve. The proposed CSBL method has a satisfactory capability to solve this sparse representation of the complex frequency response because a hierarchical form of the Laplace prior is employed to achieve a high degree of sparsity of the weight vector. This method effectively incorporates the real and imaginary parts of the complex frequency response by employing the same hyperparameter to integrate the known information. This method requires only a few randomly placed transducers; thus, it has a wide range of applications. The effectiveness of the proposed approach was validated using multiple guided-wave signals obtained through numerical simulations and an experimental study on a plate structure.

Performance Improving of Wind Power Generation Systems Through Parameter Optimization and Dynamic Analysis of the Speed-Regulating Differential Transmission

Abstract Hybrid drive wind power generation systems (WPGSs) equipped with speed-regulating differential mechanisms (SRDMs) have emerged as a promising solution for integrating large-scale wind energy into the power grid without the need for partially or fully rated converters. This article presents a comprehensive study on the dynamic analysis and parameter optimization of the SRDM-based transmission, with the aim of providing a sound foundation for the design and performance improvement of hybrid drive WPGSs. This study first formulates the kinematics, power flow, and mechanical efficiency of the SRDM and then proposes an effective parameter configuration model for optimizing the speed ratios of the key link units. The objective function is set as the minimum peak power required for speed regulation by the SRDM. Furthermore, to deal with the unique mechanical features such as dual power inputs, continuously variable transmission, and time-varying steering mechanism, an appropriate nonlinear dynamic modeling method of the SRDM transmission is developed. The torsion–translation vibration equations are derived and solved using the Runge–Kutta numerical integral method, considering randomly changing wind speed inputs and time-varying internal/external excitations. Results reveal that the sun gear experiences severe vibrations with the maximal and average vibration displacements of 0.563 mm and 0.112 mm, respectively, in the circumferential direction, while the planet gear exhibits complex frequency responses. Finally, specialized case studies are demonstrated to verify the proposed approaches, showing the satisfactory on-grid operating performance of the proposed SRDM-based WPGSs.

H-Shaped Radial Phononic Crystal for High-Quality Factor on Lamb Wave Resonators.

In this paper, a novel H-shaped radial phononic crystal (H-RPC) structure is proposed to suppress the anchor loss of a Lamb wave resonator (LWR), which has an ultra-high frequency (UHF) and ultra-wideband gap characteristics. Compared to previous studies on phononic crystal (PC) structures aimed at suppressing anchor loss, the radial phononic crystal (RPC) structure is more suitable for suppressing the anchor loss of the LWR. By using the finite element method, through the research and analysis of the complex energy band and frequency response, it is found that the elastic wave can generate an ultra-wideband gap with a relative bandwidth of up to 80.2% in the UHF range when propagating in the H-RPC structure. Furthermore, the influence of geometric parameters on the ultra-wideband gap is analyzed. Then, the H-RPC structure is introduced into the LWR. Through the analysis of the resonant frequency, it is found that the LWR formed by the H-RPC structure can effectively reduce the vibration energy radiated by the anchor point. The anchor quality factor was increased by 505,560.4% compared with the conventional LWR. In addition, the analysis of the LWR under load shows that the LWR with the H-RPC structure can increase the load quality factor by 249.9% and reduce the insertion loss by 93.1%, while the electromechanical coupling coefficient is less affected.

Evaluation and analysis of optically injection-locked semiconductor laser characteristics for optical complex signal generation

In this paper, we present an investigation of the optical injection-locked parameters which utilize an approach to creating optical complex signals using optically injection-locked (OIL) semiconductor lasers. Subsequently, we discuss the impact of the OIL parameters on the locking map, manufacturing the corresponding complex signal area, pole-zero diagram, and frequency response of the system. The steady-state analysis of the rate equations indicates that changing OIL parameters can result in simultaneous optical AM and PM of the OIL laser while preserving the injection locking state. Based on the simulation results, we found that using strong R inj and high negative Δfinj (which are mandatory for generating high-quality complex modulation) along with α = 3; can improve the performance in producing complex signal area as well as the frequency response, while using other settings does not lead to the development of both. Therefore, we achieve the maximum generated complex signal area and the -3dB frequency by using an adjusted parameter value for the system, which results in a faster modulation speed and higher quality of the optical complex modulation.

Lumped Parametric Model for Skin Impedance Data in Patients with Postoperative Pain.

The societal and economic burden of unassessed and unmodeled postoperative pain is high and predicted to rise over the next decade, leading to over-dosing as a result of subjective (NRS-based) over-estimation by the patient. This study identifies how post-surgical trauma alters the parameters of impedance models, to detect and examine acute pain variability. Model identification is performed on clinical data captured from post-anesthetized patients, using Anspec-PRO prototype apriori validated for clinical pain assessment. The multisine excitation of this in-house developed device enables utilizing the complex skin impedance frequency response in data-driven electrical models. The single-dispersion Cole model is proposed to fit the clinical curve in the given frequency range. Changes in identified parameters are analyzed for correlation with the patient's reported pain for the same time moment. The results suggest a significant correlation for the capacitor component. Clinical Relevance- Individual model parameters validated on patients in the post-anesthesia care unit extend the knowledge for objective pain detection to positively influence the outcome of clinical analgesia management.

Complex Frequency Domain Analysis of Memristor Based on Volterra Series

At present, the application of different types of memristors in electronics is being deeply studied. Given the nonlinearity characterizing memristors, a circuit with memristors cannot be treated by classical circuit analysis. In this paper, memristor is equivalent to a nonlinear dynamic system composed of linear dynamic system and nonlinear static system by Volterra series. The nonlinear transfer function of memristor is derived. In the complex frequency domain, the n-order complex frequency response of memristor is established by multiple Laplace transform, and the response of MLC parallel circuit is taken as an example to verify. Theoretical analysis shows that the complex frequency domain analysis method of memristor transforms the problem of solving nonlinear circuit in time domain into n times complex frequency domain analysis of linear circuit, which provides an idea for nonlinear dynamic system analysis.

Spatial Assessment of Heterogeneous Tissue Natural Frequency Using Micro-Force Optical Coherence Elastography.

Analysis of corneal tissue natural frequency was recently proposed as a biomarker for corneal biomechanics and has been performed using high-resolution optical coherence tomography (OCT)-based elastography (OCE). However, it remains unknown whether natural frequency analysis can resolve local variations in tissue structure. We measured heterogeneous samples to evaluate the correspondence between natural frequency distributions and regional structural variations. Sub-micrometer sample oscillations were induced point-wise by microliter air pulses (60–85 Pa, 3 ms) and detected correspondingly at each point using a 1,300 nm spectral domain common path OCT system with 0.44 nm phase detection sensitivity. The resulting oscillation frequency features were analyzed via fast Fourier transform and natural frequency was characterized using a single degree of freedom (SDOF) model. Oscillation features at each measurement point showed a complex frequency response with multiple frequency components that corresponded with global structural features; while the variation of frequency magnitude at each location reflected the local sample features. Silicone blocks (255.1 ± 11.0 Hz and 249.0 ± 4.6 Hz) embedded in an agar base (355.6 ± 0.8 Hz and 361.3 ± 5.5 Hz) were clearly distinguishable by natural frequency. In a beef shank sample, central fat and connective tissues had lower natural frequencies (91.7 ± 58.2 Hz) than muscle tissue (left side: 252.6 ± 52.3 Hz; right side: 161.5 ± 35.8 Hz). As a first step, we have shown the possibility of natural frequency OCE methods to characterize global and local features of heterogeneous samples. This method can provide additional information on corneal properties, complementary to current clinical biomechanical assessments, and could become a useful tool for clinical detection of ocular disease and evaluation of medical or surgical treatment outcomes.

A Digital Pre-Equalizer For Optical Wireless Links

The range of transmitters, detectors and other components that can be used in optical wireless links means that they can have a wide variety of frequency responses. Both pre- and post- equalization have been used in optical wireless systems to increase data rates. Pre-equalization has the advantage that noise impairments due to equalization can be minimised. However, the variety of pre-equalizer transfer functions, which can be easily created using analog circuits, is limited by the frequency responses of these circuits. Consequently, it may not be possible to equalize some optical wireless links with analog circuit-based pre-equalizers. In this paper a flexible digital pre-equalization scheme that can equalize complex frequency responses is described. The flexibility and the applicability of the scheme is also demonstrated using two example systems, including one that incorporates a fluorescent optical fiber to create a wide-field-of-view receiver for handheld devices. In particular, the bandwidths of the two example systems have been increased to over 500 MHz and to 350 MHz, resulting in at least a three-fold increase in data rate without any post-equalization. The authors believe that this is the first time such significant improvements in on-off-keying data rates have been demonstrated in systems with a relatively complex frequency response and a limited dynamic range.

SOME RECENT DEVELOPMENTS ON DYNAMICAL ℏ-DISCRETE FRACTIONAL TYPE INEQUALITIES IN THE FRAME OF NONSINGULAR AND NONLOCAL KERNELS

Discrete fractional calculus ([Formula: see text]) is significant for neural networks, complex dynamic systems and frequency response analysis approaches. In contrast with the continuous-time frameworks, fewer outcomes are accessible for discrete fractional operators. This study investigates some major consequences of two sorts of inequalities by considering discrete Atangana–Baleanu [Formula: see text]-fractional operator having [Formula: see text]-discrete generalized Mittag-Leffler kernels in the sense of Riemann type ([Formula: see text]). Certain novel versions of reverse Minkowski and related Hölder-type inequalities via discrete [Formula: see text]-fractional operators having [Formula: see text]-discrete generalized Mittag-Leffler kernels are given. Moreover, several other generalizations can be generated for nabla [Formula: see text]-fractional sums. The proposing discretization is a novel form of the existing operators that can be provoked by some intriguing features of chaotic systems to design efficient dynamics description in short time domains. Furthermore, by combining two mechanisms, numerous new special cases are introduced.

Concurrent Topology Optimization of Composite Plates for Minimum Dynamic Compliance.

This paper proposes a novel density-based concurrent topology optimization method to support the two-scale design of composite plates for vibration mitigation. To have exceptional damping performance, dynamic compliance of the composite plate is taken as the objective function. The complex stiffness model is used to describe the material damping and accurately consider the variation of structural response due to the change of damping composite material configurations. The mode superposition method is used to calculate the complex frequency response of the composite plates to reduce the heavy computational burden caused by a large number of sample points in the frequency range during each iteration. Both microstructural configurations and macroscopic distribution are optimized in an integrated manner. At the microscale, the damping layer consists of periodic composites with distinct damping and stiffness. The effective properties of the periodic composites are homogenized and then are fed into the complex frequency response analysis at the macroscale. To implement the concurrent topology optimization at two different scales, the design variables are assigned for both macro- and micro-scales. The adjoint sensitivity analysis is presented to compute the derivatives of dynamic compliance of composite plates with respect to the micro and macro design variables. Several numerical examples with different excitation inputs and boundary conditions are presented to confirm the validity of the proposed methodologies. This paper represents a first step towards designing two-scale composite plates with optional dynamic performance under harmonic loading using an inverse design method.

Analytical Representation of the Complex Frequency Response of a Hydrophone

Analytical Representation of the Complex Frequency Response of a Hydrophone

Bayesian parameter updating in linear structural dynamics with frequency transformed data using rational surrogate models

The identification of parameters of structural models through measurements of the system’s response is of interest in many contexts. In Bayesian system identification the underlying inverse problem is formulated in a probabilistic setting, and Bayes’ rule is applied to update a prior conjecture on the parameters. We apply the Bayesian framework to identify the parameters of structural systems using dynamic measurement data. The likelihood function is formulated in terms of the misfit of the frequency transformed data and the model frequency response function. We introduce a novel formulation that accounts for the correlation of the model error in both spatial and frequency domain. The proposed formulation is able to handle dense data sets in the frequency domain without need to manually select data points. Due to the high computational demands of sampling-based approaches for solving the Bayesian updating problem with expensive structural dynamics models, we resort to surrogate models. We apply a recently introduced rational surrogate model that approximates the complex frequency response as a rational of two polynomials with complex coefficients. Samples of the posterior distribution of the model parameters are then obtained through an adaptive sequential sampling approach using the surrogate instead of the original dynamic model. The proposed method is successfully applied to identify the orthotropic stiffness and damping parameters of a finite element model of a cross laminated timber plate.

In situ broadband acoustic measurements of age-0 walleye pollock and pointhead flounder in Funka Bay, Hokkaido, Japan

Measurements of the broadband acoustic backscattering from fish should improve acoustic discrimination between species. The pulse compression processing of broadband systems can be used to measure acoustic backscattering with high range resolution and improve signal-to-noise ratio. This may increase opportunities for in situ target strength (TS) measurements, the preferred method of collecting TS data. To evaluate the availability of TS spectra for acoustic discrimination, three Simrad EK80 wideband transceivers and split-beam transducers of 70, 120, and 200 kHz were used to collect in situ frequency responses of TS from age-0 juvenile walleye pollock and pointhead flounder, a swimbladderless flat-fish, distributed in and around Funka Bay, Hokkaido, Japan. The single echoes were extracted from backscattering data, and the TS spectra of the two species were obtained. However, processing of the broadband acoustic data is under discussion. To ensure the reliability of our data, the TS spectra of standard targets were also calculated. The measured TS spectra of the standard targets were close to the theoretical TS spectra. The individual TS spectra of two species included complex frequency response; however, the mean TS spectrum was relatively stable. The different characteristics of the frequency responses observed for the two species were in good agreement with reported observations. The results available for the acoustic discrimination were similar to the multi-frequency method, which uses two or more single frequencies. The raw TS spectra should aid in not only discriminating between species but also Q3 estimating the size of the fish.

High-Resolution Optical Vector Analysis With Enhanced Sensitivity

High-resolution and high-sensitivity optical vector analysis (OVA) is highly desired by many applications, such as optical sensors and photonic integrated circuits (PICs). However, it is difficult to achieve high resolution and high sensitivity simultaneously. Here, we propose and experimentally demonstrate a high sensitivity OVA using coherent detection to achieve the complex frequency responses (including magnitude and phase responses) of a device under test (DUT). Carrier phase noise (CPN) cancellation is employed to eliminate the carrier phase fluctuation induced by the coherent detection. In an experiment, the frequency responses of a fiber Bragg grating (FBG) is accurately measured by the proposed method when the probe light is suppressed by ~18 dB. As a comparison, the method using coherent detection without CPN cancellation can only achieve the magnitude response, and the method using direct detection cannot obtain an effective measurement. The influence of the linewidth and time delay on the measurement is discussed. The proposed OVA provides a stable, high resolution, high sensitivity and low cost approach for characterizing optical devices with arbitrary response, especially for optical devices with large loss or bandpass response.

Model and long-term coherent accumulation basic algorithm for the reflected signal with non-zero higher derivative range to radar target

The purpose of the work was to substantiate a mathematical model of the signal reflected from moving radar target at the time of its observation, which determines the need to take into account the range migration and its derivatives up to the third order, inclusive, and the Doppler frequency migration, and the basic algorithm of long-term coherent accumulation for the reflected signal. The algorithm provides for the calculation of the “fast” spectra samples, within each repetition period, time, the phase alignment of the spectra samples by multiplying by the correcting phase factors determined by the expected parameters of the target movement and the number of the repetition period, the summation of the spectral samples in the “slow” time, the multiplication of the result by complex frequency response of a matched filter of a single signal and performing an inverse Fourier transform. The performance of the algorithm is illustrated by the results of computer simulation.

Error in the calibration of the receive paths due to nonlinear distortion of the transmitter at a multi-frequency control signal

Errors of amplitude calibration of the receive paths due to nonlinearities of the transmitter by simulation are considered. Calibration shall be carried out using a multi-frequency signal with elongated orthogonal subcarrier corresponding to the reference frequencies. Calibration is performed by evaluating the complex frequency response of the receiving path at control frequencies by dividing the samples of the output signal spectrum of the path by the corresponding samples of the input signal spectrum. To describe the terminal amplifier of a non-inertial transmitter, a polynomial model is used that takes into account the distortion of the amplitudes of the output signals.