Accurate Amplitude Research Articles

Comparison of synergy extrapolation and static optimization for estimating multiple unmeasured muscle activations during walking

BackgroundCalibrated electromyography (EMG)-driven musculoskeletal models can provide insight into internal quantities (e.g., muscle forces) that are difficult or impossible to measure experimentally. However, the need for EMG data from all involved muscles presents a significant barrier to the widespread application of EMG-driven modeling methods. Synergy extrapolation (SynX) is a computational method that can estimate a single missing EMG signal with reasonable accuracy during the EMG-driven model calibration process, yet its performance in estimating a larger number of missing EMG signals remains unknown.MethodsThis study assessed the accuracy with which SynX can use eight measured EMG signals to estimate muscle activations and forces associated with eight missing EMG signals in the same leg during walking while simultaneously performing EMG-driven model calibration. Experimental gait data collected from two individuals post-stroke, including 16 channels of EMG data per leg, were used to calibrate an EMG-driven musculoskeletal model, providing “gold standard” muscle activations and forces for evaluation purposes. SynX was then used to predict the muscle activations and forces associated with the eight missing EMG signals while simultaneously calibrating EMG-driven model parameter values. Due to its widespread use, static optimization (SO) applied to a scaled generic musculoskeletal model was also utilized to estimate the same muscle activations and forces. Estimation accuracy for SynX and SO was evaluated using root mean square errors (RMSE) to quantify amplitude errors and correlation coefficient r values to quantify shape similarity, each calculated with respect to “gold standard” muscle activations and forces.ResultsOn average, compared to SO, SynX with simultaneous model calibration produced significantly more accurate amplitude and shape estimates for unmeasured muscle activations (RMSE 0.08 vs. 0.15, r value 0.55 vs. 0.12) and forces (RMSE 101.3 N vs. 174.4 N, r value 0.53 vs. 0.07). SynX yielded calibrated Hill-type muscle–tendon model parameter values for all muscles and activation dynamics model parameter values for measured muscles that were similar to “gold standard” calibrated model parameter values.ConclusionsThese findings suggest that SynX could make it possible to calibrate EMG-driven musculoskeletal models for all important lower-extremity muscles with as few as eight carefully chosen EMG signals and eventually contribute to the design of personalized rehabilitation and surgical interventions for mobility impairments.

Aerodynamic Analysis of Blade Stall Flutter Prediction for Transonic Compressor Using Energy Method

In this study, stall flutter onset prediction in a transonic compressor is carried out using the (uncoupled) energy method with Fourier transform. As the study is conducted computationally using computational fluid dynamics (CFD)-based simulations, the energy method was employed due to its higher computational efficiency by implementing the one-way FSI (Fluid Structure Interaction) model. The energy method is relatively uncommon for determining the aerodynamic damping and flutter prediction, specifically in blade stall conditions for the 3D blade passages. The NASA Rotor 67 was chosen for the validation of the study due to the availability of a wide range of experimental data. A flutter prediction analysis was performed computationally using CFD for the two-blade passages of the rotor in the peak efficiency and stall regions. Prior to this, the modal analysis on the prestressed blade was conducted, considering the centrifugal effects. The modal analysis provided accurate blade frequency and amplitude, which were the inputs of the flutter analysis. The first three modes of blade resonance were studied with a range of nodal diameters within near-peak efficiency and stall regions. The energy method implemented in this study for the flutter analysis was successfully able to predict the aerodynamic damping coefficients of the first three modes for a range of nodal diameters from the periodic-unsteady solution of the defined blade oscillation within the regions of interest (peak efficiency and stall point). The results of the study confirm the rotor blade’s stability within the near-peak region and, most importantly, the prediction of the flutter onset in the stall region. The study concluded that the computationally inexpensive and time-efficient energy method is capable of predicting the stall flutter onset. In the future, further validations of the energy method and investigations related to flow mechanism of stall flutter onset are planned.

An efficient pseudoelastic pure P‐mode wave equation and the implementation of the free surface boundary condition

AbstractBased on the elastic wave equation, a pseudoelastic pure P‐mode wave equation has been recently derived by projecting the wavefield along the wavefront normal direction. This pseudoelastic pure P‐mode wave equation offers an accurate simulation of P‐wave fields with accurate elastic phase and amplitude characteristics. Moreover, considering no S‐waves are involved, it is computationally more efficient than the elastic wave equation, making it an excellent choice as a forward simulation engine for P‐wave exploration. Here, we propose a new pseudoelastic pure P‐mode wave equation and apply the stress image method to it to implement the free surface boundary condition. The new pseudoelastic wave equation offers significantly improved computational efficiency compared to the previous pseudoelastic wave equation. Additionally, the wavefields simulated by this new pseudoelastic wave equation exhibit clear physical interpretations. We evaluate the accuracy of the new wave equation in simulating elastic P‐waves by employing a model with high‐velocity contrasts. We find that this new equation, which purely admits P‐waves, though having exact amplitude and phase behaviour as the elastic waves for transmission components, the amplitudes slightly suffer in the scattering scenario. The difference in amplitude between the elastic and our pseudoelastic increases as the contrast in velocity at the interface (interlayer velocity ratio) increases, especially the S‐wave velocities. This has negative implications on scattering from the free surface boundary condition or the sea bottom interface, especially if the shear wave velocity below the surface or the sea bottom is high. However, in cases where, like for land data in the Middle East, the transition to a free surface is smoother, the accuracy of the pseudoelastic equation is high. In all cases, regardless of the interlayer velocity ratio, the accuracy of the pseudoelastic wave equation in simulating the elastic case, for scattered waves, exceeds that of the acoustic wave equation in phase and amplitude.

Computational vibration mitigation using phase interpolation in digital holographic microscopy for overlay metrology.

Digital holographic microscopy retrieves amplitude and phase information of an image which allows us to computationally correct for imperfections in the imaging optics. However, digital holographic microscopy is an interferometric technique that is inherently sensitive to undesired phase variations between object and reference beam. These phase variations lower the fringe contrast if they are integrated over a finite exposure time which leads to a reduced amplitude of the retrieved image. This results in significant errors in applications that rely on a stable and accurate amplitude measurement, such as optical overlay metrology in the semiconductor industry. We present experimental results on a computational vibration mitigation method for the application of overlay metrology using phase interpolation between a sequence of measured holograms and demonstrate its capability to improve metrology precision in an overlay metrology application that uses digital holographic microscopy.

Compensating Acquisition Footprint for Amplitude-Preserving Angle Domain Common Image Gathers Based on 3D Reverse Time Migration

Angle domain common image gathers (ADCIGs) play a crucial role in seismic exploration, offering prestack underground illumination information that aids in validating migration velocity and conducting prestack amplitude versus angle (AVA) analysis for reservoir characterization. This paper introduces an innovative approach for compensating amplitude errors caused by irregular seismic acquisition geometries in ADCIGs. By incorporating an angle domain illumination compensation factor, the proposed method effectively modifies these errors, preserving the amplitude of seismic reflectivity in the prestack angle domain. The effectiveness of the proposed approach is validated through comprehensive tests conducted on synthetic and field data examples. The results demonstrate the capability of the method to enhance the quality of ADCIGs derived from 3D reverse time migration (RTM), yielding accurate and reliable amplitude preservation. While the illumination compensation factor assumes a vertically linear velocity model, the method holds promise for extension to more complex media and diverse migration techniques. This suggests its applicability and adaptability beyond the specific assumptions considered in this study. In conclusion, this paper presents an innovative angle domain illumination compensation factor that significantly improves the quality of ADCIGs by addressing amplitude errors arising from irregular seismic acquisition geometries. The experimental validation using synthetic and field data confirms the effectiveness of the proposed method within the context of 3D RTM. Furthermore, the technique holds potential for broader application in more complex subsurface scenarios and various migration methodologies.

From 3D to 5D tracking: SMX ASIC-based double-sided micro-strip detectors for comprehensive space, time, and energy measurements

We present the recent development of a lightweight detector capable of accurate spatial, timing, and amplitude resolution of charged particles. The technology is based on double-sided double-metal p+ – n – n+ micro-strip silicon sensors, ultra-light long aluminum-polyimide micro-cables for the analogue signal transfer, and a custom-developed SMX read-out ASIC capable of measurement of the time (Δt ≲ 5 ns) and amplitude. Dense detector integration enables a material budget > 0.3 % X 0. A sophisticated powering and grounding scheme keeps the noise under control.In addition to its primary application in Silicon Tracking System of the future CBM experiment in Darmstadt, our detector will be utilized in other research applications.

Lensless Imaging Based on Dual‐Input Physics‐Driven Neural Network

Lensless imaging, as a novel computational imaging technique, has attracted great attention due to its simplicity, compactness, and flexibility. This technique analyzes and processes the diffraction of an object to obtain complex amplitude information. However, traditional algorithms such as Gerchberg‐Saxton (G–S) algorithm tend to exhibit significant errors in complex amplitude retrieval, particularly for edge information. Additional constraints have to be incorporated on top of amplitude constraints to enhance the accuracy. Recently, deep learning has shown promising results in optical imaging. However, it requires a large amount of training data. To address these issues, a novel approach called dual‐input physics‐driven network (DPNN) is proposed for lensless imaging. DPNN utilizes two diffractions recorded at different distances as inputs and uses an unsupervised approach that combines physical imaging model to reconstruct object information. DPNN adopts a U‐Net 3+ architecture with a loss function of mean absolute error (MAE) to better capture diffraction features. DPNN achieves highly accurate reconstruction without requiring extensive data and being immune to background noise. Based on different diffraction intervals, noise levels, and imaging models, DPNN exhibits superior capabilities in peak signal‐to‐noise ratio and structural similarity compared with conventional methods, effectively achieving accurate phase or amplitude information reconstruction.

Extraction and evaluation of cable forces of a cable-stayed bridge based on amplitude and phase estimation method

In order to identify the time-varying frequency and amplitude of structural vibration based on the bridge structural health monitoring data and obtain the cable force of cable-stayed bridges in real time, a spectrum analysis method based on amplitude and phase estimation (APES) was proposed in this study. The amplitude spectrum of the acceleration data is first calculated by the APES method, the real-time spectrogram of the cable is obtained by the sliding window method. Then the modal frequency and amplitude are automatically extracted from the real-time spectrum by using a frequency extrusion post-processing technique, which can be regarded as the average value of the instantaneous frequency and amplitude respectively. Next, the fundamental frequency of the cable is extracted by using an automatic identification method, and the performance of the proposed method is verified. Finally, real-time scoring of cable forces and structural condition assessment is achieved with consideration of the moderation index model as well as the material strength. The results show that the APES method can use shorter calculation samples than the traditional Fast Fourier Transform (FFT) to obtain higher resolution and more accurate amplitude, which provides a theoretical basis for the real-time identification of fundamental frequency based on short-term monitoring data. The frequency extrusion post-processing-algorithm can reduce the spectrum recognition delay and improve timeliness of the cable force evaluation. The time-varying cable force with an interval of 10 s can be used to reflect the health status of the cable in time. The research results can provide technical support for the real-time extraction of cable force of long-span cable-stayed bridges, and can also provide an effective basis for component condition evaluation and bridge maintenance decision-making.

VELOcities of CEpheids (VELOCE)

We present the first data release of VELOcities of CEpheids (VELOCE), dedicated to measuring the high-precision radial velocities (RVs) of Galactic classical Cepheids (henceforth, Cepheids). The first data release (VELOCE DR1) comprises 18 225 RV measurements of 258 bona fide classical Cepheids on both hemispheres collected mainly between 2010 and 2022, along with 1161 observations of 164 stars, most of which had previously been misclassified as Cepheids. The median per-observation RV uncertainty for Cepheids is 0.037 km s−1 and reaches 2 m s−1 for the brightest stars observed with Coralie. Non-variable standard stars were used to characterize RV zero-point stability and to provide a base for future cross-calibrations. We determined zero-point differences between VELOCE and 31 literature data sets using template fitting, which we also used to investigate linear period changes of 146 Cepheids. In total, 76 spectroscopic binary Cepheids and 14 candidate binary Cepheids were identified using VELOCE data alone, which are investigated in detail in a companion Paper (VELOCE II). VELOCE DR1 provides a number of new insights into the pulsational variability of Cepheids, most importantly: a) the most detailed description of the Hertzsprung progression based on RVs to date; b) the identification of double-peaked bumps in the pulsation curve; and c) clear evidence that virtually all Cepheids feature spectroscopic variability signals that lead to modulated RV variability at the level of tens to hundreds of m s−1 and that cannot be satisfactorily modeled using single-periodic Fourier series. We identified 36 stars exhibiting such modulated variability, of which 4 also exhibit orbital motion. Linear radius variations depend strongly on pulsation period and a steep increase in slope of the ΔR/p vs. log P-relation is found near 10 days. This effect, combined with significant RV amplitude differences at fixed period, challenges the existence of a tight relation between Baade-Wesselink projection factors and pulsation periods. We investigated the accuracy of RV time series measurements, υγ, and RV amplitudes published by Gaia’s third data release (Gaia DR3) and determined an offset of 0.65 ± 0.11 km s−1 relative to VELOCE. Whenever possible, we recommend adopting a single set of template correlation parameters for distinct classes of large-amplitude variable stars to avoid systematic offsets in υγ among stars belonging to the same class. The peak-to-peak amplitudes of Gaia RVs exhibit significant (16%) dispersion. Potential differences of RV amplitudes require further inspection, notably in the context of projection factor calibration.

Quantitative Measurement and Evaluation of High-Resolution Ultrasonic Sound Fields using a Novel Automated Ultrasonic Immersion Scanner

Ultrasonic probes are an integral part of the automated ultrasonic non-destructive testing and evaluation (NDT&E) systems to detect and size the defects in a wide range of structural materials in production lines. A complete quantitative assessment of the performance characteristics of an application-specific UT probe is needed to be evaluated on the basis of the international standard DIN EN ISO 22232-2. This requirement of full assessment not only improves the quality assurance of the manufactured probes by evaluating the acceptance criteria but also provides the useful technical information to the end-user to optimize the automated ultrasonic testing on-site. In addition, the evaluation of probe characteristics should be carried periodically throughout their service life. In this work, we developed a novel high-precision ultrasonic immersion scanner to evaluate the full ultrasonic probe characteristics which include the squint angle measurement in three different reference planes (XY, XZ, and YZ), RF-signal and its frequency spectrum at water-steel interface, focal distance, focal range, focal width, focal length and also the angle of beam divergence in different planes of the sound field distribution. In the newly developed UT immersion scanner, for the first time, we successfully integrated the high-precision Hexapod with six axes to achieve a few micrometer (~15 µm) spatial-resolution in the measured sound field patterns and a good angular resolution (~0.05°) in the squint angle measurement. In addition, we used a verified UT instrument in accordance with the standard DIN EN ISO 22232-1 to obtain more accurate amplitude values (±0.5 dB) while scanning a test block. The automated scanning, data acquisition, evaluation, visualization and the automated test report generation are carried based on the standard DIN EN ISO 22232-2. The measured sound beam characteristics of both focused and non-focused application-specific ultrasonic probes with center frequencies ranging from 0.2 - 15 MHz using the pulse-echo technique on a 3 mm half-ball steel reflector are presented. In addition, the measured sound beams of an application-specific 5 MHz multi-element transmit-receive (TR) probe using the 3 mm flat-bottomed-hole (FBH) reflector in a steel reference plate are discussed. Finally, the quantitative analysis of the measured sound field results and the acceptance criteria in accordance with DIN EN ISO 22232-2 are discussed.

Multiwavelength photometric study of RR lyrae variables in the globular cluster NGC 5272 (Messier 3)

ABSTRACT We present a comprehensive photometric study of RR Lyrae stars in the M3 globular cluster, utilizing a vast data set of 3140 optical (UBVRI) CCD images spanning 35 yr from astronomical data archives. We have successfully identified previously known 238 RR Lyrae stars from the photometric data, comprising 178 RRab, 49 RRc, and 11 RRd stars. Multiband periodogram was used to significantly improve the long-term periods of 65 per cent of RR Lyrae stars in our sample, thanks to the unprecedentedly long temporal coverage of the observations. The light curve templates were used to obtain accurate and precise mean magnitudes and amplitudes of all RR Lyrae variables. We combined optical (UBVRI) and near-infrared (NIR, JHKs) photometry of RR Lyrae variables to investigate their location in the colour-magnitude diagrams as well as the pulsation properties such as period distributions, Bailey diagrams and amplitude ratios. The period–luminosity relations in R and I bands and Period–Wesenheit relations were derived after excluding outliers identified in CMDs. The Period–Wesenheit relations calibrated via the theoretically predicted relations were used to determine a distance modulus of $\mu = 15.04 \pm 0.04 \, {\rm (stats)} \pm 0.19 \, {\rm {(syst.)}}$ mag (using metal-independent WBV Wesenheit) and $\mu = 15.03 \pm 0.04 \, {\rm (stats)} \pm 0.17 \, {\rm {(syst.)}}$ mag (using metal-dependent WVI Wesenheit). Our distance measurements are in excellent agreement with published distances to M3 in the literature. We also employed an artificial neural network based comparison of theoretical and observed light curves to determine physical parameters (mass, luminosity, and effective temperature) for 79 non-Blazhko RRab stars that agree with limited literature measurements.

Numerical characterization of piezoelectric energy harvesting from an L-shaped frame

An L-shaped structure, intended for piezoelectric energy harvesting, is being characterized numerically to obtain extended insight into the effect of various parameters and metrics that are hard to track from experimental setups and simplified analytical models and to show the underlying mechanism of efficient piezoelectric harvesting. A numerical model was developed to analyze the structure under harmonic base excitation to obtain voltage frequency response and strain distribution data. The model takes into effect the load resistance applied between the piezoelectric patch electrodes and the damping ratio of each mode for accurate resonance amplitude evaluation. The validity of the model was confirmed by comparisons with previous experiments and showed strong agreement. The approach demonstrated that piezoelectric energy harvesting modeling, in general, is sensitive to inaccurate estimations, especially in the damping parameters, which emphasizes that rough assumptions made in analytical models will not yield results that can be discussed in correlation with experimental outcomes. This work states the guidelines for accurate piezoelectric modeling using numerical software, with the aim of enabling the investigation of complex harvesters, providing more insights to direct researchers to more proof and optimized designs that tackle broadband and energy density problems found in simple harvesters.

Least-squares reverse time migration of simultaneous sources with deep-learning-based denoising

Least-squares reverse time migration (LSRTM) is currently one of the most advanced migration imaging techniques in the field of geophysics. It uses least-squares inversion to fit the observed data, resulting in high-resolution imaging results with more accurate amplitudes and better illumination compensation than conventional reverse time migration (RTM). However, noise in the observed data and the Born approximation forward operator can result in high-wavenumber artifacts in the final imaging results. Moreover, iteratively solving LSRTM leads to one or two orders of computational cost higher than conventional RTM, making it challenging to apply extensively in industrial applications. Simultaneous source acquisition technology can reduce the computational cost of LSRTM by reducing the number of wavefield simulations. However, this technique also can cause high-wavenumber crosstalk artifacts in the migration results. To effectively remove the high-wavenumber artifacts caused by these issues, simultaneous source and deep learning are combined to speed up LSRTM as well as suppress high-wavenumber artifacts. A deep residual neural network (DR-Unet) is trained with synthetic samples, which are generated by adding field noise to synthesized noise-free migration images. Then, the trained DR-Unet is applied on the gradient of LSRTM to remove high-wavenumber artifacts in each iteration. Compared to directly applying DR-Unet denoising to LSRTM results, embedding DR-Unet denoising into the inversion process can better preserve weak reflectors and improve denoising effects. Finally, the proposed LSRTM method is tested on two synthetic data sets and a land data set. The tests demonstrate that the proposed method can effectively remove high-wavenumber artifacts, improve imaging results, and accelerate convergence speed.

Optical vector-eigenmode decomposition for few-mode fibers through deep learning networks

For the optical vector-eigenmode (VE) decomposition, we introduce a novel deep learning-based optical-mode decomposition (OMD) technique for accurate retrieval of near-field beams generated from few-mode fiber (FMF) channel, in which this residual network (Resnet) scheme could obtain complete and accurate amplitude and phase coefficients from the near-field beams. For the case of 3 intra-module modes in the FMF, the correlation coefficient of the OMD reaches 0.9808, while the modal weight error and modal phase error are as low as 0.0287 and 0.0331, respectively. And for the case of 10 inter-module modes in the FMF, the correlation coefficient of the OMD achieves 0.9878, while the mode weight error and mode phase error are recorded down to 0.0071 and 0.0205, respectively. Moreover, the noise-added near-field beams show a good robustness of the OMD based on deep learning. Finally, we also investigate the relationship between modal differences and correlation coefficients, revealing the nature of VE-based OMD functions.

Spatial Selection-Based Intelligent N-OFDM Signal Processing in Wireless Communication Systems

The method of joint processing of pulses and OFDM (N-OFDM) signals is proposed. The corresponding analytical relations for the lower Cramer-Rao boundary on the dispersion of OFDM (N-OFDM) signals amplitude ratings in the presence of sources of pulsed radiation are obtained. Using mathematical modeling properties and limitations of the demodulation method of OFDM (N-OFDM) signals in the background of impulse signals in the integrated radar and telecommunication systems are established. It is determined that the use of the angular distance between the pulsed and OFDM signals sources at a value that is not less than 0.75 widths of the secondary beam of the digital antenna array pattern does not affect the accuracy of the OFDM signal amplitudes. The same applies to the active interferences.

Multipoint leak localization for pipelines via acoustic wave amplitude ratio

Pipeline leak localization is significant for maintaining the regular operation of pipelines. This paper proposes a multipoint leak localization method for pipelines via the acoustic wave amplitude ratio, which addresses the issue of the traditional time delay estimation method (TDE) not being able to locate multiple leaks simultaneously. Firstly, a multipoint leak localization method for pipelines is established without time delay estimation and acoustic velocity. This method merely needs to determine the amplitude of the leakage acoustic wave propagating to both ends of the pipeline to achieve leakage localization. Secondly, the improved empirical wavelet transform (IEWT) method denoises the leakage acoustic wave, which can obtain an accurate acoustic amplitude to reduce the localization error. Finally, the trouble that the mutation factor and crossover probability cannot be adaptively selected in the differential evolution (DE) algorithm is improved, and the improved differential evolution (IDE) algorithm is used to solve the objective function to obtain the position of each leakage point. Field experiments show that the multipoint leak localization method proposed in this paper has perfect accuracy, and the minimum localization error is 11 m.

A low-side-lobe folded transmitarray antenna based on metasurface with independent amplitude/phase control

In this paper, a low-side-lobe folded transmitarray antenna (LSLFTA) based on metasurface (MS) that can independently control amplitude and phase is proposed. An MS, composed of two vertically placed polarization gates, can realize the efficient reflection of y-polarized waves, efficient transmission of x-polarized waves, and independently control of phase and amplitude is designed for the top surface. A polarization conversion surface (PCS) using an open resonant ring that can efficiently achieve cross polarization conversion is presented. The feed antenna is placed on the center of the top surface to obtain an accurate electromagnetic amplitude distribution. To the best of our knowledge, our work is thus the first one to achieve low-side-lobe FTA. The LSLFTA operating at 14.5 GHz is fabricated and measured to verify the design. After adding amplitude modulation (Taylor distribution), the side lobe level (SLL) is 5.2 dB and 7.5 lower than that of only phase modulation in the yoz plane and xoz plane, respectively. The 3 dB gain bandwidth of the antenna is 19.4% (13.5∼16.4 GHz), and the maximum aperture efficiency is 25.8%. Our work is a promising candidate in the design of high-gain, low SLL, and low-profile antenna.

Finite-size effects in periodic coupled cluster calculations

We provide the first rigorous study of the finite-size error in the simplest and representative coupled cluster theory, namely the coupled cluster doubles (CCD) theory, for gapped periodic systems. Given exact Hartree-Fock orbitals and their corresponding orbital energies, we demonstrate that the correlation energy obtained from the approximate CCD method, after a finite number of fixed-point iterations over the amplitude equation, exhibits a finite-size error scaling as O(Nk−13). Here Nk is the number of discretization points in the Brillouin zone and characterizes the system size. Under additional assumptions ensuring the convergence of the fixed-point iterations, we demonstrate that the CCD correlation energy also exhibits a finite-size error scaling as O(Nk−13). Our analysis shows that the dominant error lies in the coupled cluster amplitude calculation, and the convergence of the finite-size error in energy calculation can be boosted to O(Nk−1) with accurate amplitudes. This also provides the first proof of the scaling of the finite-size error in the third order Møller-Plesset perturbation theory (MP3) for periodic systems.

Low-Level Radio-Frequency system integrated with feed-forward control and vector modulation

To provide a more accurate and stable Radio-Frequency (RF) signal in conditioning and processing test progress, it is necessary to design a Low-Level Radio-Frequency (LLRF) control system which can provide high precision RF driving signal based on meeting the amplitude and phase stabilization requirement. Through Feed-Forward operation, accurate phase adjustment and amplitude adjustment are realized inside the pulse, to realize the precision and automation of phase-inversion, amplitude stabilization, phase stabilization, and wave-form adaptation matching. An LLRF System integrated with feed-forward control and vector modulation output was designed and built, and the long-term working stability of the LLRF system was verified during a new 50MW S-band Klystron conditioning progress.

Quasi-periodic oscillation characteristics of a nonlinear energy sink system under harmonic excitation

Quasi-periodic oscillation characteristics of a nonlinear energy sink (NES) system under harmonic excitation are studied in this work. It is found that there exist uniformly distributed sidebands in frequency spectra of quasi-periodic oscillations. The traditional incremental harmonic balance (IHB) method and the IHB method with two time-scales are used to obtain accurate frequency components and amplitudes of periodic responses and two different quasi-periodic oscillations of the system, respectively, with variations of the external excitation frequency and amplitude. The two different quasi-periodic oscillation characteristics are analyzed; energy absorption of the NES system under different excitation frequencies and amplitudes is also analyzed. Stability of quasi-periodic solutions obtained from the IHB method with two time-scales is analyzed by the Floquet theory. Analytical results obtained from the traditional IHB method and the IHB method with two time-scales agree very well with those from numerical integration using the fourth-order Runge–Kutta method. Results show that the efficiency of energy absorption of a strongly quasi-periodic oscillation is greater than those of a periodic response and a weakly quasi-periodic oscillation.