Measured Frequency Response Research Articles

Third-order optical bandpass filters based on structures of alternating layers of quartz and silver

Designs of optical bandpass filters have been developed on planar structures, which were obtained by vacuum deposition onto quartz glass (SiO2) substrates of three layers also of quartz, which are half-wavelength resonators separated from each other, from free space, and from the substrate by four layers of silver (Ag). The thicknesses of the Ag and SiO2 layers were determined based on the given parameters of the filter passband by parametric synthesis of one-dimensional models using electrodynamic analysis. In this case, experimental frequency dependences of the real and imaginary parts of the permittivity of silver were used. The measured frequency responses of the manufactured prototypes of red, green and purple filters are in good agreement with the responses obtained during synthesis.

Wideband microwave frequency response measurement based on optical phase-locked loop.

Frequency response measurement, or the forward transmission coefficient (S21) measurement for a two-port network, is the key function of a vector network analyzer (VNA). In this paper, a broadband and high dynamic range (DR) microwave S21 parameter measurement scheme based on an optical phase-locked loop (OPLL) is proposed. By heterodyning two phase-locked hybrid integrated ultra-narrow linewidth lasers, a microwave signal with low phase noise and spurious level is generated as the incident signal and reference signal, and the signal frequency can be easily manipulated over a wide range by tuning the master laser wavelength. In the receiver, the radio frequency (RF) signals are down-converted to intermediate frequency (IF) signals with the phase-locked lasers. By sampling and processing the IF signals the S21 parameter of the DUT can be acquired. A proof-of-concept experiment is performed, and with available photodetectors, phase modulators and phase-locked loops, a measurable range of 2 to 18 GHz is achieved. The demonstrated minimum frequency resolution of the OPLL-based RF signal synthesizer is 10 Hz. The system DR exceeds 68 dB at an equivalent resolution bandwidth of 1 kHz. The S21 parameters of a power divider and a bandpass filter are measured, and the results are well consistent with those of a commercial VNA. The DR and measurable range limit factors and possible extension methods are discussed. The proposed approach offers a high potential way to develop a wideband, high DR, and fully integrated VNA.

Experimental analysis of wheel and bogie frame transfer functions for on-board measurements of rail roughness

Acceleration measurements on in-service rail vehicles give many valuable insights into track condition. These measurements are favourable in terms of measurement frequency, no need for additional track possession for measurements, operator safety, etc. The collected acceleration data however needs to be further processed to extract more detailed information on rail surface defects. To derive rail roughness from bogie frame acceleration, a complex signal processing approach is required, as well as determining the dynamic parameters of the track, vehicle, and operational conditions. In this paper, a method to evaluate the influence of resilient wheel and bogie frame on the acceleration data received from bogie frame-mounted accelerometers is described. The method is based on a standstill measurement of frequency response functions on wheel and bogie frame positions using an impact hammer and accelerometers. Following the preliminary results of bogie acceleration measurements, in-situ wheel receptance measurements were carried out on the same tramway vehicle in a standstill position, to determine the transfer function between the wheel-rail contact point and the position of the accelerometer mounted on the wheel frame. After the experimental study, a discussion of their potential application in the method for deriving rail roughness from vibration data is presented.

Compact quad-channel filtering diplexer using meander hairpin ring resonator aided by grey wolf algorithm

Abstract In this paper, a compact quad-channel filtering diplexer using meander hairpin ring resonators (M-HRR) aided by grey wolf algorithm (GWA) is proposed. To realize a compact size of the multi-channel diplexer, the form of a meander-line structure is applied to the hairpin ring resonator for the miniaturization of the proposed quad-channel diplexer. Then, using the coupling topology of the 0° feeding structure, a transmission zero (TZ) is generated between two resonant frequencies of M-HRR to improve the band-edge selectivity and band-to-band isolation of the diplexer. To address the problematic challenge of the complexity in designing the multi-channel diplexer with a time-consuming optimization manually, an intelligent GWA is utilized to optimize the physical layout of the designed circuit to achieve the desired performance of the diplexer rapidly. Furthermore, different kinds of intelligent algorithms are implemented and compared under identical conditions. Finally, a quad-channel filtering diplexer centering at 3.28/3.75/4.32/4.75 GHz with 3-dB fractional bandwidth (FBW) of 5.4%, 2.9%, 4.9%, and 3.2% respectively is fabricated and measured. The circuit occupies a compact size of 0.22λg × 0.20λg. Good accordance is observed between the simulated and measured frequency responses.

Calibration-free scheme for frequency response measurement of a Mach–Zehnder modulator with low-frequency detection

This paper presents a novel, to the best of our knowledge, calibration-free scheme for measuring the frequency response of Mach–Zehnder modulation (MZM) using low-frequency detection. An auxiliary MZM1 modulated by a MHz-level electrical signal f1 is utilized to generate a double-sideband optical signal, which is subsequently directed into the device under test (MZM2). The MZM2 is biased at its minimum point and driven by a frequency-swept microwave signal f m . After photoelectric converting, a fixed low-frequency electrical signal f L carrying the frequency response information of the MZM2 is generated. By sweeping f m while extracting the amplitude of f L , the frequency response of the MZM2 free from the response of the photodetector (PD) is thus determined. In the experiment, the frequency response of a commercial MZM is characterized in the frequency range from 0.1 GHz to 20 GHz with a resolution of 50 MHz. The measurement result is consistent with the vector network analyzer swept method. In addition, the new method eliminates errors introduced by the PD and reduces the requirement for a high-bandwidth PD.

Damage identification of reinforced concrete slabs using experimental modal testing and finite element model updating

Condition assessment and health monitoring of reinforced concrete structures is an essential part of their effective maintenance throughout their service life. Vibration-based damage detection and health monitoring is one of the most popular global approaches where experimentally measured modal parameters, such as frequencies, mode shapes, etc. are compared to their corresponding finite element counterparts to estimate possible stiffness loss. The present investigation implements a vibration-based parameter estimation algorithm for updating a finite-element (FE) model for damage assessment of reinforced concrete slabs using measured frequency response functions (FRF) data through a mixed numerical-experimental technique. An inverse eigen-sensitivity algorithm has been implemented to minimize the error function realized as the weighted differences in the mode shapes and frequencies of the FE model and the modal test data. Three reinforced concrete slabs were subjected to real physical damage conditions to verify the efficacy of the proposed methodology. The technique is found to be resilient in the presence of modal and coordinate sparsity. In general, damage can be assessed even if the portions of the structure are inaccessible to the users, thereby extending the possibility of its application to most of the practical configurations of reinforced concrete slabs.

Frequency response based identification of nonlinear oscillators

Experimental modal analysis is commonly used to identify models for the vibratory behavior of structures. This is done by conducting a set of experiments to obtain the structure’s governing equations and information in the form of eigenfrequencies, mode shapes, and damping. However, linearity of the test structure is assumed within this identification procedure. Hence, as it stands, experimental modal analysis is not readily applicable to build models when nonlinearities are present through, for example, friction, (electro-) magnetic fields, or large deformations. To identify governing equations for such systems, a robust and systematic identification procedure is proposed in this article. The identification routine is formulated in the frequency domain, and a noise reduction scheme and a simplification routine are employed to obtain sparse and robust models. The identification procedure is implemented in an automated script (FrID), which is applied to forced response measurements stemming from structures with magnets, clamps, and bolted joints as well as systems with multiple active modes and internal resonances. The identified governing equations accurately fit the experimentally obtained frequency response measurements and can also be utilized to extrapolate the response for different forcing amplitudes. Moreover, nonlinear modes of the underlying conservative system can be computed from the identified governing equations.

Automated characterisation and operational insights of superconducting travelling wave parametric amplifiers: unveiling novel behaviours and enhancing tunability

Superconducting travelling wave parametric amplifiers (TWPAs) exhibit great promise across various applications, owing to their broadband nature, quantum-limited noise performance, and high-gain operation. Whilst their construction is relatively simple, particularly for thin-film-based TWPAs, challenges such as the requirement for an extremely long transmission line, current fabrication limitations, and their sensitivity to fabrication tolerances, mean that their optimal operating conditions often differ from those anticipated during the design stage. As a result, manual fine-tuning of numerous operational parameters becomes necessary to recover optimal performance; a process that is both labour-intensive and time-consuming. This paper introduces an automated methodology designed to significantly accelerate the characterisation of a TWPA by several orders of magnitude without requiring human intervention. Additionally, we have developed metrics to condense the multitude of measured frequency responses of the TWPA, obtained in data cube form, into an easily-understandable format for further scientific interpretation. To demonstrate the efficacy and speed of our methodology, we utilise an existing NbTiN (niobium titanium nitride) TWPA as an example. This showcases the capability of our approach to unveil both broad- and fine-scale behaviours of the device, highlighting the importance of an automated experimental setup for the in-depth investigation of TWPAs for future developments.

Transient frequency response test and measurement error prediction of DCTV based on adaptive inertial weight improved ACO

AbstractA temporary frequency response test and measurement error prediction method of direct current voltage transformer (DCTV) based on artificial intelligence (AI) is proposed. Firstly, the frequency characteristic of direct current (DC) side voltage of DCTV is analyzed. On this basis, a DCTV transient Frequency Response testing method based on transient alternating current (AC) & DC superposition was developed. Then, the method of voltage sudden change and phase correction is used to achieve transient process DCTV response time testing. Finally, the ant colony optimization (ACO) algorithm was improved by combining an adaptive inertia weight improvement strategy, achieving accurate prediction of the Measurement Error of DCTV. The proposed AI based DCTV transient Frequency Response testing and Measurement Error prediction method were compared and analyzed with the other three methods through simulation experiments. Compared to the other three comparison methods, the maximum transformation error in the evaluation indicators of mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE) decreased by 0.006, 0.0119, and 0.0085, respectively, while the maximum phase error decreased by 0.2794, 0.3004, and 0.2823, respectively.

Railway vibration – fast physics-based models for the prediction of ground vibration and the identification of track damage

The following applications of machine learning/AI for railway vibration will be discussed: 1. The prediction of the wave propagation from a railway line (completely physics based for surface lines, for tunnel lines (partially) physics-based ML for surface lines). 2. The track behaviour for the emission of train-induced ground vibration (physics based for homogeneous soil, ML for layered soil). 3. Track damage detection and quantification from FRF and moving load response. 4. Bridge damage detection and localisation from modal analysis and moving load response. 5. The use of axle-box acceleration for the identification of track/sub-soil condition and bridge resonances. Prediction calculation of railway vibration usually needs time-consuming finite element, boundary element and wavenumber domain calculations. For a user-friendly prediction software, fast calculations are needed. Several time-consuming detailed calculations should be used to develop simpler and fast models. The dynamic stiffness of isolated or un-isolated railway tracks from detailed calculations with a continuous soil is approximated with the simpler Winkler soil. The vehicle-track resonance (P2 resonance) rules the effect of the mitigation measures, and it can also be used for the on-board monitoring of the track and sub-soil condition. For the identification of track damage such as gaps between sleepers, track slabs and layers, detailed models with a continuous soil have been updated to get the best fit to the measured frequency response functions from hammer tests and the deformation pattern from the moving load response. Whereas the track damage can be locally identified, this is more difficult for bridges where the modal analysis gives mainly global information. The influence lines of the inclination for statically passing vehicles (locomotive, truck, compaction ) have been used to localise bridge damage (stiffness variations). The on-board monitoring of rail bridges needs special conditions (regular trains with special speeds) to excite and measure the bridge resonance.

Vibration analysis of anisogrid composite lattice sandwich truncated conical shells: Theoretical and experimental approaches

Drawing upon both theoretical and experimental methodologies, this study investigates the vibrational characteristics of lattice sandwich truncated conical shells featuring composite ribs made of carbon and E-glass fibers. Toward this aim, the equations of motion along with the corresponding boundary conditions of such sandwich shells are derived using classical Donnell’s shell theory and the smeared stiffness technique. Subsequently, the governing equations are solved to obtain a closed-form expression for natural frequencies employing the Galerkin method. In addition, ABAQUS simulations are presented to study the vibration behavior of single-skin and three-skin conical shells. To validate the theoretical methods, the specimens of three-layer sandwich conical shells were fabricated from two Kevlar fabric laminates and a composite lattice core with hexagonal cells using a manual filament winding process. The composite ribs consist of carbon and E-glass fibers with a ratio of 3:1. Finally, experimental modal tests were conducted to extract natural frequencies and mode shapes by measuring frequency responses at 40 points over a duration of 60 s using a laser vibrometer. A strong correspondence is observed between the theoretical outcomes (utilizing the Galerkin and FE methods) and the experimental findings (with a maximum discrepancy of approximately 16% for the initial four mode shapes). Findings indicate that the excellent performance of the composite lattice core in vibration behavior, which can increase approximately 19% and 16% the natural frequencies corresponding to the first and second mode shapes, respectively.

Fixing Measured Frequency Response Near Underdamped Dynamics for Loaded-Motor Feedback Design

Fixing Measured Frequency Response Near Underdamped Dynamics for Loaded-Motor Feedback Design

Design of 2.5-D miniaturized frequency selective surface with enhanced oblique stability

This paper presents a miniaturized 2.5-D frequency selective surface (FSS) that exhibits a band stop response at frequency of 1.5 GHz. In the unit cell, the meander patterns on both side of the substrate are connected in series by four vias. Moreover, the meandered pattern in each quadrant is also connected with one of the meander patterns of the adjacent unit cell. In this manner, a 2.5-D closed loop is created with large perimeter. The enlarged perimeter amplifies the effective inductance and leads to a decrease in both the resonant frequency and the dimensions of unit cell. Subsequently, the proposed FSS demonstrates excellent miniaturization with an overall size of 0.038 λ 0 × 0.038 λ 0. Moreover, the frequency response is highly stable up to 86° for both TE and TM polarization. The resonance mechanism of the designed FSS is explicated through distribution of surface current and electric field. The testing board of the proposed FSS has been fabricated for the verification of the design. The measured frequency response of the prototype are congruent with the simulation results. The distinguished features of the constructed structure are enhanced angular stability, miniaturized unit cell, low profile, simple geometry and easy fabrication.

Stiffness increase in main spindles by using tapered roller bearings for aluminum cutting tests

Due to increasing demands regarding higher manufacturing accuracy and the machining of high-strength materials, the stiffness and load-carrying capacity of main spindles must be enhanced. One approach is to replace the conventionally used angular contact ball bearings, so called spindle bearings, with tapered roller bearings of the same size, which have a higher stiffness and load carrying capacity due to their larger rolling contact. In case the speed requirement is below a speed parameter n·dm=0.9×106\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\cdot d_{m}=0.9\ imes 10^{6}$$\\end{document} mm/min, the poorer speed parameter of tapered roller bearings can be compensated by a sufficiently high lubrication quantity. However, the stiffness increase by using this bearing type in main spindles has not yet been quantified in field tests. Therefore, the aim of this paper is to demonstrate the stiffness advantage of a spindle with an elastically arranged tapered roller bearing compared to a conventional spindle with angular contact ball bearings by machining tests. First, the radial load displacement characteristic of the newly developed tapered roller bearing spindle is tested in advance on an isolated test rig. In machine cutting tests, full slots are milled in an aluminum block. During the tests, the axial and radial displacements of the spindle shaft relative to the housing are measured and evaluated in radial and axial direction. These tests are repeated and compared with the conventional spindle. By varying the process parameters such as cutting depth, feed rate or rotational speed, the increased stiffness of the tapered roller bearing spindle compared to the conventional spindle is illustrated based on the measured displacements. Moreover, frequency response measurements at different speeds underpin the improved damping of the tapered roller bearing spindle. Assuming that the speed requirements are not too high and the tapered roller bearing is sufficiently lubricated, the use of this type of bearing can significantly increase the stiffness and thus the manufacturing precision in the long term for main spindles.

Stability Analysis via Impedance Modelling of a Real-World Wind Generation System with AC Collector and LCC-Based HVDC Transmission Grid

Stability Analysis via Impedance Modelling of a Real-World Wind Generation System with AC Collector and LCC-Based HVDC Transmission Grid

Enhancing rational approximation of wideband resonant MIMO systems with frequency-domain data

Vector Fitting (VF) is a successful methodology for both time and frequency domain estimation of dynamic systems. These algorithms have gained popularity as a system identification tool due to their ability to provide a practical procedure for accurately approximating the measured frequency response behavior of complex and highly resonant dynamic systems using rational models. Instrumental Variable (IV) techniques can also be added to the VF algorithm to enhance the optimality of the solutions in the presence of measurement noise. In this context, this paper presents a multiple-input multiple-output (MIMO) generalization of instrumental variable (IV-)VF. The proposed algorithm can be applied to accurately estimating models formed by either continuous- or discrete-time rational basis functions (RBFs). We show that such a generalization preserves the main implementation features observed in Standard VF, but with improved optimality property for its solutions. Additionally, in order to alleviate convergence problems that may arise from the fixed high-frequency normalization, we also present in this paper how to incorporate in the proposed IV-VF method the relaxed formulation found in standard VF for both the continuous and discrete-time cases. The resulting MIMO IV-VF algorithm can be easily understood by VF users, and its applicability is discussed by using an estimation case study with two power system pieces of equipment (an 88 kV Transformer and a 550 kV Instrument Transformer) for which actual frequency domain measurements were collected in the field. It is shown that the proposed algorithm significantly improves the modeling accuracy when compared to standard VF algorithms.

Shaping of the Frequency Response of Photoacoustic Cells with Multi-Cavity Structures

In the great majority of cases, the design of resonant photoacoustic cells is based on the use of resonators excited at the frequencies of their main resonances. This work presents a solution in which the use of a multi-cavity structure with the appropriate selection of the mechanical parameters of the cavities and the interconnecting ducts allows for the shaping of the frequency response of the cell. Such solutions may be particularly useful when the purpose of the designed cells is operation at multiple frequencies, e.g., in applications with the simultaneous detection of multiple gaseous compounds. The concept is tested with cells made using 3D printing technology. The measured frequency responses of the tested cells show very good agreement with the simulation results. This allows for an approach in which the development of a cell with the desired frequency response can be initially based on modeling, without the need for the time-consuming and expensive process of manufacturing and measuring numerous modifications of the cell.

Structured barycentric forms for interpolation-based data-driven reduced modeling of second-order systems

An essential tool in data-driven modeling of dynamical systems from frequency response measurements is the barycentric form of the underlying rational transfer function. In this work, we propose structured barycentric forms for modeling dynamical systems with second-order time derivatives using their frequency domain input-output data. By imposing a set of interpolation conditions, the systems’ transfer functions are rewritten in different barycentric forms using different parametrizations. Loewner-like algorithms are developed for the explicit computation of second-order systems from data based on the developed barycentric forms. Numerical experiments show the performance of these new structured data-driven modeling methods compared to other interpolation-based data-driven modeling techniques from the literature.

An applicator for high-power rock comminution using microwave technology in the megawatt range

Abstract The mining industry is heavily dependent on energy-intensive processes, such as rock breakage, which leads to significant operational costs. This paper explores microwave-assisted rock breakage as an innovative method to enhance the efficiency of comminution within the mining industry. It introduces a system that employs a Klystron microwave power source with a maximum output of 7.5 MW, using a $\mathrm{TM}_{010}$ single-mode cavity at 3 GHz, to channel energy inside a specially designed rock cavity. The paper emphasizes the importance of designing an efficient microwave cavity for this system, focusing on the cavity’s design and simulation. Through both simulated results (using HFSS software) and experimental observations, the study reveals the promising application of microwave technology in the field of mining. The simulated frequency response of the designed cavity (S11) is −22 dB, it demonstrates significant potential for reducing both energy consumption and associated costs. Additionally, the designed cavity is fabricated from aluminum and filled with polyether ether ketone material. The measured frequency response (S11) of the cavity at 3 GHz is −17 dB.

Evaluation of the thermo-acoustic instability frequency and growth rate via input reflection coefficient measurement for central heating equipment

Experimental measurement methods and theoretical evaluations based on low-order modeling approaches for both the growth rate and frequency at the onset of thermo-acoustic combustion instability are proposed, and their performance is evaluated. The developed techniques are demonstrated through a systematic measurement of the linear growth rate and frequency of evolving oscillations in the laboratory setup and also applied for the thermo-acoustic qualification of an industrial domestic boiler and a heat cell unit (combination of a burner with a heat-exchanger). Generic measurements have been done for a burner deck with premixed surface-stabilized Bunsen-type flames. The industrial domestic boiler and the heat cell unit are equipped with burners of a similar type but differ by their perforation pattern. They have been tested at different conditions and the experimental and theoretical results are compared. Two modeling strategies are tested: 1- in Laplace domain, with estimating a rational function in the complex domain to fit the measured frequency response, 2- exclusively in frequency domain, without estimating a rational function. Both methods include measurement of the frequency response of two reflection coefficients from i) the upstream part of the system, Rup, and ii) burner with flame completed by the downstream part of the appliance, Rin. Within the first approach, a procedure for an analytic continuation of the measured frequency response to the complex domain is applied and complex eigenfrequencies are calculated by solving the corresponding dispersion equation. An alternative approach was proposed by Kopitz and Polifke and allows estimating both the frequency of oscillation and the growth rate from the analysis of the polar plot of the system's characteristic equation in the frequency domain. The comparison shows that the unstable frequencies can be predicted accurately by both tested modeling strategies. This conclusion holds also for the tested industrial applications. The prediction of the instability growth rates is closer to the measured one when the modeling method in the complex domain is used. However, the frequency domain analysis provides less accurate, but still reasonable estimates of the growth rates and frequencies. Moreover, a good overview of thermo-acoustic performance of each industrial boiler/burner at different conditions is obtained via Rin measurements.