Frequency Jumps Research Articles

A robust time scale for space applications using the student’s t-distribution

Abstract In this article, the principles of robust estimation are applied to the standard basic time scale equation to obtain a new method of assigning weights to clocks. Specifically, the Student's t-distribution is introduced as a new statistical model for an ensemble of clocks that are experiencing phase jumps, frequency jumps or anomalies in their measurement links. The proposed robust time scale is designed to mitigate the effects of these anomalies without necessarily identifying them, but through applying a method of robust estimation for the parameters of a Student's t-distribution. The proposed time scale algorithm using the Student's t-distribution (ATST) is shown to achieve comparable robustness to phase jumps, frequency jumps, and anomalies in the measurements with respect to the AT1 oracle time scale. The AT1 oracle is a special realization of the AT1 time scale which corrects all anomalies by having prior knowledge of their occurrences. The similar performance of ATST and AT1 oracle suggests that the ATST algorithm is efficient for obtaining robustness with no prior knowledge or detection of the occurrences of anomalies.

Anomaly detection for atomic clocks using unsupervised machine learning algorithms

Atomic clocks are the most accurate timekeeping instruments in the world and play a crucial role in numerous applications, notably in satellite navigation. Nonetheless, the accuracy of these clock signals is subject to anomalies, highlighting the importance of anomaly characterization and detection. In our study, we identify three types of anomalies in the phase data of atomic clocks—outliers, phase jumps and inflection points, and also frequency jumps in the frequency data, which corresponds to the inflection points. The novelty of our work lies in the application of machine learning methods for atomic clock anomaly detection (AD), as opposed to traditional algorithms. We introduce a variety of unsupervised AD and change point detection (CPD) algorithms from the realms of statistics and machine learning, propose a customized thresholding function for AD, and evaluate AD and CPD algorithms on both synthetic and real-world atomic clock data. Our experiments reveal that the subsequence local outlier factor algorithm achieves excellent performance in detecting outliers and phase jumps, but struggles with inflection points. Crucially, we found that the application of a CPD algorithm specifically for detecting the frequency jumps in frequency data substantially improves performance. Our study adopts unsupervised machine learning methods for AD provides robust detection strategies, thereby contributing an expanded understanding of the use of machine learning for clock data monitoring.

Self-induced non-synchronous resonance phenomena and stability in reduced aero-elastic system

The paper is aimed at the parametric dynamic analysis of the two degrees of freedom (DoF) phenomenological model of aero-elastic interaction between a friction-damped flexible mounted body and a flowing fluid. A coupled system of a linear structure oscillator and the van der Pol based wake oscillator is introduced. Firstly, the complex eigenvalue problem is used for the comprehensive analysis of frequency lock-in, veering and crossing areas from the structural mode stability point of view. Further, an in-depth analysis of the fully nonlinear model based on the numerical continuation method is presented. The analysis focuses on non-synchronous vibration in the resonance areas. Attention is paid to the investigation of transition mechanisms to frequency lock-in and frequency veering in the structural response. In experimental studies, the amplitude and frequency jumps are observed. Here, we show that the origin of these jump phenomena results from the mutual coexistence of two stable solutions, which form a hysteresis region, which can be found in experimentally gained data. Moreover, the influence of structure friction-damping on nonlinear response is evaluated. The proposed phenomenological model is validated concerning two different experimental-based investigations.

State estimation of variable frequency power grid of multi-electric aircraft based on adaptive enhanced complex-coefficient filter

The power grid of a multi-electric aircraft is a typical isolated island microgrid with a wide frequency range from 360 to 800 Hz. The dynamic performance of the traditional constant-frequency power grid synchronization method is insufficient in the variable frequency power grid of the multi-electric aircraft. An adaptive enhanced complex-coefficient filter-based phase locked loop (AECCF-PLL) is designed for the variable frequency power grid by integrating an adaptive module into the enhanced complex-coefficient filter-based phase locked loop to accurately estimate the state of variable frequency power grid. The relationship between the transfer function and the step response is analyzed. The relationship between the model parameters and the frequency is derived, and the frequency adaptive module is established to meet the requirements for stability and rapidity in the state estimation of the variable frequency power grid. The experimental results show that the proposed AECCF-PLL can achieve the rapid and stable estimation of the state of the variable frequency power grid when there are disturbances such as large or small frequency jumps, harmonics and slopes.

Wideband Low Phase-Noise Signal Generation Using Coaxial Resonator in Cascaded Phase Locked Loop

The generation of high-quality wideband frequency sweeps presents a significant challenge, particularly in modern telecommunication, radar, and measurement systems where miniaturization is paramount. While phase-locked loops (PLLs) have become the dominant technique for signal generation, their application in broadband sweeps necessitates fractional-N operation. This, in turn, degrades phase noise and introduces unwanted spurs. This paper proposes a novel approach for broadband signal generation. By cascading two PLLs and utilizing a coaxial resonator, we achieve a high-performance oscillator that operates without the excessive fractional spurs, maintaining their level below −80 dBc across the entire frequency band. The prototype demonstrates non-degraded phase noise performance, reaching −102 dBc/Hz at 100 kHz offset and −121 dBc/Hz at 1 MHz offset for signals at 10 GHz. Despite significant frequency jumps, our design achieves lock times below 41 µs. These results, supported by theoretical analysis, validate the proposed method’s effectiveness in generating low-noise broadband frequency sweeps, ideal for local oscillator applications.

Insight into the effect of strain on Li-ion diffusivity and conductivity in Li3OCl anti-perovskite solid-state electrolyte: A perspective from AIMD simulations

Utilizing first-principle calculations, this study elucidated the underlying mechanism of elastic strains affecting the Li-ion diffusivity and conductivity in Li3OCl anti-perovskite solid-state electrolyte. Strain was shown to modulate the Li-ion vibrational amplitude, attempt frequency and adjacent site jumps, as revealed by ab initio molecular dynamics (AIMD) simulation post-processing. Additionally, analysis of lattice dynamics and phonon behavior under various strain conditions demonstrated that tensile strains soften the lattice and lower the phonon band center frequency, thereby diminishing the energy barriers impeding ion transport. Further, we have systematically investigated strain-induced distortions of the coordination environment via continuous symmetry measures (CSM), assessing the variations at initial and saddle sites along the Li-ion migration routes. And the study of bonding variability under strain provided a deeper understanding of strain-induced conducting behavior. These results underscore insights into the fundamental mechanisms governing ionic transport in Li3OCl anti-perovskite under elastic strain, highlighting the potential of strain engineering as a promising avenue for optimizing the performance of solid-state electrolytes in energy storage applications.

Synthetic Meta-Signal Observations: The Beidou Case.

A Global Navigation Satellite System (GNSS) meta-signal is obtained when two or more side-band components from different frequencies are jointly processed as a single entity. This requires advanced signal processing techniques able to cope with the subcarrier, generated by the interaction of the side-band components, and handle possibly multi-peaked ambiguous correlation functions. An alternative approach to meta-signal processing is to reconstruct meta-signal observations using side-band measurements. Meta-signal high-accuracy pseudoranges can be reconstructed from the side-band code and carrier observations. The success of the reconstruction depends on several factors, including the frequency separation of the side-band components and the presence of measurement biases. The Beidou Navigation Satellite System (BDS), with its second- and third-generation signals, provides a wide range of components with various frequency separations. In this paper, we experimentally investigate the performance and limitations of the measurement reconstruction approach using Beidou observations. When the B1I and B1C components are considered, their reduced frequency separation leads to unambiguous measurements fully exploiting the potential of meta-signals. For larger frequency separations, jumps and discontinuities are observed in the position domain, which is a major limiting factor of this type of approach.

Frequency jumps and subharmonic components in calls of female Odorrana tormota differentially affect the vocal behaviors of male frogs

Studies have demonstrated that the sounds of animals from many taxa with nonlinear phenomena (NLP)—caused by nonlinear characteristics of vocal organ dynamics that lead to nonlinear vocal phenomena—can influence the behavior of receivers. However, the specific functions of different NLP components have received less attention. In most frog species, females produce few or no vocalizations; in contrast, female Odorrana tormota exhibit a diverse range of calls that are rich in NLP components. Previous field playbacks have shown that the female calls can elicit responses from male frogs. Therefore, we conducted a phonotaxis experiment to investigate the differential effects of different NLP calls by female O. tormota on the vocal behavior of male frogs. The results revealed that calls with subharmonics elicited a greater number of short calls and answering calls from male frogs compared to calls with frequency jumps. However, calls with frequency jumps triggered more staccato calls from males than calls with subharmonics. Additionally, during the phonotaxis experiments, we recorded the initial vocalizations of males in response to playbacks of female calls. The majority of males first produced short calls. Under calls with frequency jumps, most of male frogs approaching within 10 cm of the loudspeaker produced staccato calls instead of “meow” calls or short calls. While under calls with subharmonics, most male frogs preferred to produced short calls. Our findings demonstrate that frequency jumps and subharmonic components in the calls of female O. tormota have different effects on male vocal behaviors. The current study lays a foundation for a further understanding of the function of anuran NLP components.

A Frequency and Angle Feedforward Estimator for Unbalanced and Distorted Three-Phase Electric Grids

This work presents an open-loop frequency estimator able to deal with typical disturbances, yet exhibiting fast dynamics. The proposal is tested and compared experimentally against the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">orthogonal voltage decomposition</i> OVD approach, which is considered the state-of-the-art open-loop frequency estimator and the recently proposed AFPLL. The results verify that the proposed approach operates correctly under unbalancing, harmonics, noise, and interharmonics, and after frequency, phase, and amplitude jumps, while exhibiting settling times about <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {25\%}$</tex-math></inline-formula> better than the OVD, and a similar execution time. Furthermore, the proposed technique has a performance comparable to advanced <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">frequency-locked loops</i> , it is easy to tune, and thus, it could be seamlessly applied in typical synchronization tasks where PLLs are usually employed.

Nonlinear features in whistles produced by the short-beaked common dolphin (Delphinus delphis) off southeastern Brazil.

Animal vocalizations have nonlinear characteristics responsible for features such as subharmonics, frequency jumps, biphonation, and deterministic chaos. This study describes the whistle repertoire of a short-beaked common dolphin (Delphinus delphis) group at Brazilian coast and quantifies the nonlinear features of these whistles. Dolphins were recorded for a total of 67 min around Cabo Frio, Brazil. We identify 10 basic categories of whistle, with 75 different types, classified according to their contour shape. Most (45) of these 75 types had not been reported previously for the species. The duration of the whistles ranged from 0.04 to 3.67 s, with frequencies of 3.05-29.75 kHz. Overall, the whistle repertoire presented here has one of the widest frequency ranges and greatest level of frequency modulation recorded in any study of D. delphis. All the nonlinear features sought during the study were confirmed, with at least one feature occurring in 38.4% of the whistles. The frequency jump was the most common feature (29.75% of the whistles) and the nonlinear time series analyses confirmed the deterministic chaos in the chaotic-like segments. These results indicate that nonlinearities are a relevant characteristic of these whistles, and that are important in acoustic communication.

Integral‐type half‐tangent phase‐locked loop for more electric aircraft grids

AbstractIn this paper, an integral‐type half‐tangent phase‐locked loop (IHTan‐PLL) is proposed for the varying‐frequency AC grids of more electric aircraft (MEA). First, the performance of the synchronous reference frame phase‐locked loop (SRF‐PLL) and half‐tangent phase‐locked loop (HTan‐PLL) is discussed from a large‐signal viewpoint. When the frequency changes largely, the SRF‐PLL has many oscillations and endures a rather long transient process. The HTan‐PLL can address the large frequency jumps. However, for the varying‐frequency AC grids with harmonic disturbances, the HTan‐PLL still has oscillations in estimating the frequency when the frequency jumps largely. To enhance the performance of the SRF‐PLL and HTan‐PLL, the IHTan‐PLL is developed for the varying‐frequency AC grids with harmonic disturbances. The IHTan‐PLL performs better than the SRF‐PLL and HTan‐PLL in addressing the large frequency jumps. Specifically, under any large frequency changes, the IHTan‐PLL still converges to the equilibrium point (0,0), and no oscillations emerge. In addition, the IHTan‐PLL has better steady‐state accuracy in estimating the frequency than the SRF‐PLL and HTan‐PLL. The experimental results also demonstrate the superior performance of the proposed IHTan‐PLL.

Frequency jumps in excised larynges in anechoic conditions: A pilot study

Sudden fundamental frequency jumps between chest and falsetto registers are among the least understood phenomena occurring in human voice. Such jumps are recognized as bifurcation events and have been assumed to result from nonlinear-dynamic properties of the vocal folds interacting with acoustic resonances of the vocal tract and of the subglottal tract (ST). Here, we explored an anechoic (resonance-free) ST and investigated these frequency jumps in five excised human larynges, without a supraglottal vocal tract, under two conditions: (a) anechoic and (b) subglottally resonant. When smoothly elongating the vocal folds, we observed consistent jumps in anechoic conditions, proving that subglottal and supraglottal vocal tract resonances are not necessary for the jumps to arise. The presence of a resonant ST did not result in more numerous jumps compared to anechoic conditions, indicating that the inherent nonlinear-dynamic properties of the larynges were the primary cause for the jumps. Nevertheless, the resonant ST slightly altered the initial and terminating frequencies of the jumps, suggesting that the role of the interaction of the vocal fold oscillations with subglottal acoustics should not be neglected. These experimental findings should be considered when validating mathematical models simulating the nonlinear-dynamic behavior of the human vocal apparatus.

Exact Solution of a Time-Dependent Quantum Harmonic Oscillator with Two Frequency Jumps via the Lewis-Riesenfeld Dynamical Invariant Method.

Harmonic oscillators with multiple abrupt jumps in their frequencies have been investigated by several authors during the last decades. We investigate the dynamics of a quantum harmonic oscillator with initial frequency ω0, which undergoes a sudden jump to a frequency ω1 and, after a certain time interval, suddenly returns to its initial frequency. Using the Lewis−Riesenfeld method of dynamical invariants, we present expressions for the mean energy value, the mean number of excitations, and the transition probabilities, considering the initial state different from the fundamental. We show that the mean energy of the oscillator, after the jumps, is equal or greater than the one before the jumps, even when ω1<ω0. We also show that, for particular values of the time interval between the jumps, the oscillator returns to the same initial state.

Mirror Clock: A Strategy for Identifying Atomic Clock Frequency Jumps.

Atomic clock frequency jumps directly influence the accuracy and reliability of timekeeping systems. The necessary corrections are typically implemented by postprocessing mutual comparison data between multiple atomic clocks based on the overly strict assumption that these atomic clocks are independent of each other. This paper describes the concept of a mirror clock, which enables atomic clock frequency jumps to be identified in real time without any assumptions. By comparing whether the real measured data and a corresponding mirror clock prediction fall within a confidence interval determined by the uncertainty of past physical clock data, atomic clock frequency jumps can be effectively identified and corrected. The results of several experiments using three hydrogen masers verify that the precision and recall of simultaneous jump identification reach 96.41% and 73.49%, respectively.

The roles of rigid splitter plates in flow-induced vibration of a circular cylinder

While it is known that rigid splitter plates play significant roles in flow control, the exact roles of them in flow-induced vibration (FIV) have not been systematically investigated. This has motivated the present work to experimentally investigate the FIV of a cylinder equipped with an upstream rigid splitter plate (USP), a downstream plate (DSP), and symmetrically arranged splitter plates in a water tunnel with Reynolds number of 1100–7700. The length of the plate is in a range of L* = 0–3.6 (L*=L/D, L is the plate length, D is the cylinder diameter). The response characteristics, vortex evolution, fluid force, and pressure fields are thoroughly analyzed. Both USP and DSP can succeed in oscillation mitigation and drag reduction. However, dramatic galloping is observed for DSP with L* = 0.4–3.2. The low-pressure region forms near the downstream plate is beneficial to trigger galloping. For USP, only vortex-induced vibration is found, and the transition of response branches corresponds to the variation in oscillation frequency and phase jumps in total transverse force and vortex force. However, the vortex mode transition from 2S to 2P disappears with long plate length. Flow visualization reveals that the upstream vortex induced by USP alters the downstream vortex shedding. Furthermore, a high-pressure region forms near the tip of USP, yielding an obstructive force that suppresses the growth of oscillation. With the combination of USP and DSP, weak galloping is excited in a narrow range of L* = 1.0–1.8, and the linear increase is also broken due to the existence of USP.

High pressure Raman study of LiClO4

Lithium perchlorate (LiClO4), as one of the new high-energy oxidizers, is chosen for high pressure Raman research to gain a better understanding of the structure and stability, which is very important for the performance of an explosive. Raman spectra of LiClO4 crystal have been measured from ambient to 25.07 GPa with diamond anvil cells (DACs) at room temperature to investigate the structural stability of this system. Raman vibrational modes of LiClO4 crystal at ambient pressure were resolved comprehensively on the basis of our experimental and calculated results. Upon increase of pressure on LiClO4 crystal sample to 1.96 GPa, it was found that the LiClO4 crystal exhibited a pressure-induced first-order phase transformation behavior. The occurrence of a second phase transformation of LiClO4 crystal induced by pressure was observed at about 5.09 GPa. Both phase transformations were demonstrated based on the detailed spectroscopic analysis of the variations in the number of lattice modes, splitting of Raman bands and frequency jumps of the Raman vibrational modes of LiClO4 crystal.

Nonlinear characteristic analysis of gear rattle based on refined dynamic model

In order to explore the vibration response and the nonlinear behavior of gear rattle, a nonlinear dynamic model is developed in this paper considering the nonlinear oil film force, time-varying meshing stiffness, dragging torque and friction and gear backlash with time-varying characteristics. The time-varying meshing stiffness is calculated using the potential energy method. Considering the convolution and extrusion of the lubricant between the teeth, it is modeled as a nonlinear spring-damped element and a nonlinear oil film force is introduced. The drag torque is calculated numerically using fluid dynamics theory, friction principle, momentum conservation principle, and Bernoulli's principle. The model is verified by comparing the bench test results with the simulation results, and the parametric study is performed to investigate the nonlinear system characteristics by means of fast Fourier transform, Poincare map, and bifurcation diagram. The results show that as the excitation frequency increases, the system enters chaotic state under multiple frequency jumps. Excessive torque fluctuation may lead to severe rattling phenomenon of the gear pair and making the system enter a chaotic state; as the lubricant viscosity increases, the system shows periodic, bifurcation and chaotic behavior alternately, and when the viscosity is large enough, the high-frequency shock intensity decays more rapidly due to large drag torque, which is beneficial to reduce the percussion strength and prevent the system into chaos.

Nonlinear vocal phenomena affect human perceptions of distress, size and dominance in puppy whines.

While nonlinear phenomena (NLP) are widely reported in animal vocalizations, often causing perceptual harshness and roughness, their communicative function remains debated. Several hypotheses have been put forward: attention-grabbing, communication of distress, exaggeration of body size and dominance. Here, we use state-of-the-art sound synthesis to investigate how NLP affect the perception of puppy whines by human listeners. Listeners assessed the distress, size or dominance conveyed by synthetic puppy whines with manipulated NLP, including frequency jumps and varying proportions of subharmonics, sidebands and deterministic chaos. We found that the presence of chaos increased the puppy's perceived level of distress and that this effect held across a range of representative fundamental frequency (fo) levels. Adding sidebands and subharmonics also increased perceived distress among listeners who have extensive caregiving experience with pre-weaned puppies (e.g. breeders, veterinarians). Finally, we found that whines with added chaos, subharmonics or sidebands were associated with larger and more dominant puppies, although these biases were attenuated in experienced caregivers. Together, our results show that nonlinear phenomena in puppy whines can convey rich information to human listeners and therefore may be crucial for offspring survival during breeding of a domesticated species.

Vocalization of Bryde's whales (Balaenoptera edeni) in the Beibu Gulf, China

AbstractThe presence of Bryde's whales (Balaenoptera edeni) in the Beibu Gulf, China has been reported since 2016. In the current study, in situ Bryde's whale vocalizations were recorded. Bouts of frequency modulated repetitive and diversified calls were recorded. Repetitive calls were recorded when 1–3 whales were present within 2 km of the boat and were probably emitted by a single whale and functioned as contact calls. Repetitive calls were divided into biphonation downswept tonals and downswept tonals. Diversified calls were recorded when 4–7 whales were present within 2 km of the boat and were probably associated with acoustic exchanges between or among conspecifics. Diversified calls occasionally contained inflection points, frequency jumps, and break point features. The frequency band of Bryde's whale vocalizations overlapped highly with background noise. Most vocalizations in the current study were different than those previously reported for this species. Therefore, the findings of this study provide more information on the known acoustic repertoire of Bryde's whales and provide a basis for noninvasive monitoring of Bryde's whale with passive acoustic methods and for developing mitigation and conservation protocols to ensure their future viability.

Gravitational-wave glitches: Resonant islands and frequency jumps in nonintegrable extreme-mass-ratio inspirals

The detection of gravitational waves from extreme-mass-ratio inspirals with upcoming space-borne detectors will allow for unprecedented tests of general relativity in the strong-field regime. Aside from assessing whether black holes are unequivocally described by the Kerr metric, such detections may place constraints on the degree of spacetime symmetry. In particular, depending on exactly how a hypothetical departure from the Kerr metric manifests, the Carter symmetry, which implies the integrability of the geodesic equations, may be broken. Here, we examine the gravitational waveforms associated with nonintegrable extreme-mass-ratio inspirals involving a small-mass companion and a supermassive compact object of general relativity, namely the Manko-Novikov spacetime. We show that the waveforms display sudden frequency jumps when the companion transverses resonant islands. These findings demonstrate that such abrupt manifestations in the gravitational-wave frequencies are generic, have a genuine astrophysical origin, and function as a distinctive signature of chaotic phenomena in extreme-mass-ratio binaries.