Array Of Oscillators Research Articles

A Novel Spiking Graph Attention Network for Intelligent Fault Diagnosis of Planetary Gearboxes

As an essential component in the power transmission system of rotating machinery, planetary gearboxes are often subjected to extreme operating conditions, including heavy loads and low speeds, which can cause key components to fail over time. Early planetary gearbox fault features are weak, coupled with the impact of strong noise in the industrial field, which brings great challenges to the accurate identification and diagnosis of planetary gearbox faults. To address these issues, we propose a novel spiking graph attention network (Spiking-GAT) for intelligent fault diagnosis of planetary gearboxes, which realizes synchronous extraction of temporal and spatial features of the original signal, to accurately identify the fault category and severity of planetary gearbox. Firstly, a graph data construction method based on chaos theory is proposed. A multi-phase coupled chaotic oscillator array based on Duffing (MP-COAD) is established to reconstruct the original signal, and the K-nearest neighbor classifier (KNN) is used to construct the reconstructed signal as graph data. Secondly, a novel Spiking GAT intelligent fault diagnosis framework has been developed, which provides an adaptive spiking coding approach for graph data and deep mining and extraction of spatial-temporal features to accurately identify the health status of planetary gearboxes. Finally, the experimental and industrial fault simulation test rigs of the planetary gearbox are designed, and three cases are studied to verify the accuracy and stability of Spiking-GAT. The results show that the classification accuracy of Spiking-GAT reaches 100% on the datasets of the two test rigs, and has excellent noise robustness.

Driven-dissipative topological phases in parametric resonator arrays

We study the phenomena of topological amplification in arrays of parametric oscillators. We find two phases of topological amplification, both with directional transport and exponential gain with the number of sites, and one of them featuring squeezing. We also find a topologically trivial phase with zero-energy modes which produces amplification but lacks the robust topological protection of the others. We characterize the resilience to disorder of the different phases and their stability, gain, and noise-to-signal ratio. Finally, we discuss their experimental implementation with state-of-the-art techniques.

Discrete Breathers of Nonlinear Dimer Lattices: Bridging the Anti-continuous and Continuous Limits

In this work, we study the dynamics of an infinite array of nonlinear dimer oscillators which are linearly coupled as in the classical model of Su, Schrieffer and Heeger (SSH). The ratio of in-cell and out-of-cell couplings of the SSH model defines distinct $\textit{phases}$: topologically trivial and topologically non-trivial. We first consider the case of weak out-of-cell coupling, corresponding to the topologically trivial regime for linear SSH; for any prescribed isolated dimer frequency, $\omega_b$, which satisfies non-resonance and non-degeneracy assumptions, we prove that there are discrete breather solutions for sufficiently small values of the out-of-cell coupling parameter. These states are $2\pi/\omega_b$- periodic in time and exponentially localized in space. We then study the global continuation with respect to this coupling parameter. We first consider the case where $\omega_b$, the seeding discrete breather frequency, is in the (coupling dependent) phonon gap of the underlying linear infinite array. As the coupling is increased, the phonon gap decreases in width and tends to a point (at which the topological transition for linear SSH occurs). In this limit, the spatial scale of the discrete breather grows and its amplitude decreases, indicating the weakly nonlinear long wave regime. Asymptotic analysis shows that in this regime the discrete breather envelope is determined by a vector gap soliton of the limiting envelope equations. We use the envelope theory to describe discrete breathers for SSH- coupling parameters corresponding to topologically trivial and, by exploiting an emergent symmetry, topologically nontrivial regimes, when the spectral gap is small. Our asymptotic theory shows excellent agreement with extensive numerical simulations over a wide range of parameters.

A Weak Reverse Coupling Cascaded Injection-Locked VCO Array for Beam Scanning in Phased Arrays

We propose a novel phase shifter for beam scanning in phased arrays using a cascaded injection-locked voltage-controlled oscillator (VCO) array with weak reverse coupling. We analyze the phase noise performance of a multi-signal injection-locked oscillator and establish a phase output model for the array, studying the effects of forward and reverse injection ratios on phase and phase noise at each stage. By decoupling and cascade locking VCO array elements through controlled injection ratios, we design a 2.45 GHz one-dimensional linear array of four VCOs that achieves a continuous fixed phase difference between adjacent oscillators from −180∘ to 180∘, enabling electronic tuning of phase shift and beam scanning. Finally, the beam scanning of the antenna array is realized by using the VCO array. Our theoretical and experimental results demonstrate the effectiveness of our proposed approach.

Synchronization of the Self-Oscillations of the Magnetic Vortices in Exchange-Coupled Ferromagnetic Disks

The low-frequency (gyrotropic) self-oscillations of the magnetic vortices in interacting ferromagnetic disks, which are caused by a spin-polarized current, are studied by numerical simulation. Various magnetization oscillation modes depending on the configuration of the magnetic state of the system are considered. The influence of the pumping current nonuniformity on the phase difference of the vortex gyration in neighboring disks is investigated. The overlap of the disks is shown to increase the interaction between the vortices and, hence, to decrease the dephasing of the vortex core oscillations. The prospects of using overlapping disks to ensure phase synchronization of arrays of spin-transfer vortex oscillators are discussed.

Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators

AbstractThe stochastic response of a multi‐degree‐of‐freedom nonlinear dynamical system is determined based on the recently developed Wiener path integral (WPI) technique. The system can be construed as a representative model of electrostatically coupled arrays of micromechanical oscillators, and relates to an experiment performed by Buks and Roukes. Compared to alternative modeling and solution treatments in the literature, the paper exhibits the following novelties. First, typically adopted linear, or higher‐order polynomial, approximations of the nonlinear electrostatic forces are circumvented. Second, for the first time, stochastic modeling is employed by considering a random excitation component representing the effect of diverse noise sources on the system dynamics. Third, the resulting high‐dimensional, nonlinear system of coupled stochastic differential equations governing the dynamics of the micromechanical array is solved based on the WPI technique for determining the response joint probability density function. Comparisons with pertinent Monte Carlo simulation data demonstrate a quite high degree of accuracy and computational efficiency exhibited by the WPI technique. Further, it is shown that the proposed model can capture, at least in a qualitative manner, the salient aspects of the frequency domain response of the associated experimental setup.

Travelling chimeras in oscillator lattices with advective-diffusive coupling.

We consider a one-dimensional array of phase oscillators coupled via an auxiliary complex field. While in the seminal chimera studies by Kumamoto and Battogtokh only diffusion of the field was considered, we include advection which makes the coupling left-right asymmetric. Chimera starts to move and we demonstrate that a weakly turbulent moving pattern appears. It possesses a relatively large synchronous domain where the phases are nearly equal, and a more disordered domain where the local driving field is small. For a dense system with a large number of oscillators, there are strong local correlations in the disordered domain, which at most places looks like a smooth phase profile. We find also exact regular travelling wave chimera-like solutions of different complexity, but only some of them are stable. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.

Asymmetric spiral chimeras on a spheric surface of nonlocally coupled phase oscillators.

The spiral chimera state shows a remarkable spatiotemporal pattern in a two-dimensional array of oscillators for which the coherent spiral arms coexist with incoherent cores. In this work, we report on an asymmetric spiral chimera having incoherent cores of different sizes on the spherical surface of identical phase oscillators with nonlocal coupling. This asymmetric spiral chimera exhibits a strongly symmetry-broken state in the sense that not only the coherent and incoherent domains coexist, but also their incoherent cores are nonidentical, although the underlying coupling structure is symmetric. On the basis of analyses along the Ott-Antonsen invariant manifold, the bifurcation conditions of asymmetric spiral chimeras are derived, which reveals that the asymmetric spiral chimera state emerges via a supercritical symmetry-breaking bifurcation from the symmetric spiral chimera. For the coupling function composed of two Legendre modes, rigorous stability analyses are carried out to present a complete stability diagram for different types of spiral chimeras, including the stationary symmetric and asymmetric spiral chimeras as well as breathing asymmetric spiral chimera. For the general coupling scheme the asymmetric spiral chimera occurs as a result of competition between the odd and even Legendre modes of the coupling function. Our theoretical findings are verified by using extensive numerical simulations of the model system.

Prediction of chimera in coupled map networks by means of deep learning

Chimera states are Spatio-temporal patterns in coupled oscillator arrays, in which incoherent domains coexist with coherent ones. To characterize chimeras, however, is a nontrivial problem since it is difficult to distinguish between coherent domains and incoherent domains. A useful tool for this task is machine learning, in particular deep learning techniques like reservoir computing and multilayer perceptrons. In this work we use these quantifiers in order to identify chimera states in logistic map lattices with non-local coupling. We compare our results from machine learning techniques with more conventional characterizations, such as Lyapunov exponents and a local order parameter.

Non-linear finite-amplitude oscillations of the large beam arrays oscillating in viscous fluids

Over the past decade, several studies have been conducted on a single and multiple oscillating thin cantilever beams in an unbounded viscous fluid. With an increase in the applications of large array oscillators in a fluid environment for fields like medicine, biology, and energy harvesting devices, it is crucial to understand the nature of the surrounding fluid dynamics. In this present study, we perform a two-dimensional computational fluid dynamics (CFD) analysis of an array of beams oscillating in an unbounded viscous fluid. The two-dimensional Navier Stokes and continuity equations are solved to investigate the hydrodynamic forces exerted on the array members from interaction with the fluid environment. A complex hydrodynamic function is proposed here to represent the distributed hydrodynamic loading experienced by the oscillating beams. Results suggest that there is an increase in viscous damping with an increase in the size of the array. In addition, the nonlinearities become dominant when an array of beams is subjected to large amplitude oscillations. The number of beams in an array determines the overall hydrodynamics and the array effect. CFD analysis can predict the non-linearities unlike boundary integral method (BIM) approach, which is limited for low amplitudes. The results from the full Navier–Stokes simulations compared favorably with results using the BIM for the time-harmonic linearized Stokes equations.

Beam Steering and Signal Amplification Through Feedforward Networks. Part I: Transmission

Conventional and modern methods for beam steering in antennas and radar systems have one goal in common: to manipulate the phase shift between oscillating components, so that the direction of a radiating intensity pattern can be controlled. Typical components include arrays of nonlinear oscillators connected in a chain configuration. Modern methods for beam steering take advantage of the inherent nonlinearities of the individual components and of the collective dynamics of the array of oscillators to successfully manipulate phase shift. None of those methods include, however, signal amplification. In this manuscript, we introduce a novel array configuration: a feedforward network, which allows, simultaneously, for beam steering and signal amplification capabilities. We show that the amplitudes of certain bifurcating solutions in a feedforward network of nonlinear oscillators exhibit growth rates that are significantly larger than in other type of networks that operate near the onset of a Hopf bifurcation. Those branches of oscillations have the potential to lead to significant signal amplification of a radiating beam.

A 0.68–0.72-THz 2-D Scalable Radiator Array With –3-dBm Radiated Power and 27.3-dBm EIRP in 65-nm CMOS

A novel and compact 2-D scalable architecture of coupled harmonic oscillator array is proposed for high-power radiation beyond 600 GHz. The compact and symmetric scalable unit cell comprises two oscillators with two slot antennas radiating the third-harmonic power. Each unit cell is horizontally coupled out-of-phase and vertically in-phase with adjacent cells at the fundamental frequency. Therefore, coherent radiation and power combining are achieved at the third harmonic. A <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4\times4$ </tex-math></inline-formula> array prototype (32 radiating elements) is designed and fabricated in a 65-nm CMOS technology. An elliptical Teflon lens is attached at the backside of the chip for a highly directive beam. An effective isotropic radiated power (EIRP) of 27.3 dBm and an output power of −3 dBm are measured at 694-GHz with 754-mW power consumption under 1.2-V supply voltage, implying a dc-to-terahertz (THz) efficiency of 0.066%. The core design occupies a chip area of 0.61 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and the entire chip area is 0.97 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , leading to a 0.52-mW/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> area efficiency. The peak EIRP of 27.8 dBm and the radiated power of −2.4 dBm are measured at 699 GHz under 1.3-V supply voltage. A frequency tuning range of 5.26% from 679.4 to 716.1 GHz is measured by varying bias and supply voltages. The measured phase noise at 1-MHz offset is −73 dBc/Hz at 694 GHz. To the best of our knowledge, the designed array has the highest radiated power, radiated power per area, EIRP, frequency tuning range, and dc-to-THz efficiency among silicon-based scalable coherent radiator arrays operating beyond 600 GHz.

Modal Analysis for Localization of Harmonic Oscillations in Nonlinear Oscillator Arrays

Abstract When a nonlinear oscillator array is harmonically excited, specific oscillators in the array may oscillate with large amplitudes. This is known as the localization phenomenon; however, the reason for localization has not been clarified thus far. Thus, the aim of this study is to elucidate the reason for localization in nonlinear oscillator arrays. We theoretically investigated the behavior of a nonlinear oscillator array, which consists of N Duffing oscillators connected by linear springs under external and harmonic forces. The equations of motion in physical coordinates are transformed into modal equations of motion, which reveal that the array forms an autoparametric system in the modal coordinates when it consists of identical oscillators. The first mode of vibration is directly excited by the external force, whereas the remaining modes are indirectly excited by the nonlinear terms coupled with the first mode. The approximate solutions of the harmonic oscillations were obtained using van der Pol's method. The frequency response curves (FRCs) for both the physical and modal coordinates for N = 2 and 3 are presented. Localization can occur when multiple modes are excited simultaneously. Furthermore, the effects of imperfections in the restoring forces on the responses of the two-Duffing-oscillator array are examined.

Focused surface acoustic wave induced nano-oscillator based reservoir computing

We demonstrate using micromagnetic simulations that a nanomagnet array excited by surface acoustic waves (SAWs) can work as a reservoir. An input nanomagnet is excited with focused SAW and coupled to several nanomagnets, seven of which serve as output nanomagnets. To evaluate memory effect and computing capability, we study the short-term memory (STM) and parity check (PC) capacities, respectively. The SAW (4 GHz carrier frequency) amplitude is modulated to provide a sequence of sine and square waves of 100 MHz frequency. The responses of the selected output nanomagnets are processed by reading the envelope of their magnetization states, which is used to train the output weights using the regression method. For classification, a random sequence of 100 square and sine wave samples is used, of which 80% are used for training, and the rest are used for testing. We achieve 100% training and 100% testing accuracy. The average STM and PC are calculated to be ∼4.69 and ∼5.39 bits, respectively, which is indicative of the proposed acoustically driven nanomagnet oscillator array being well suited for physical reservoir computing applications. The energy dissipation is ∼2.5 times lower than a CMOS-based echo-state network. Furthermore, the reservoir is able to accurately predict Mackey-Glass time series up to several time steps ahead. Finally, the ability to use high frequency SAW makes the nanomagnet reservoir scalable to small dimensions, and the ability to modulate the envelope at a lower frequency (100 MHz) adds flexibility to encode different signals beyond the sine/square waves classification and Mackey-Glass predication tasks demonstrated here.

Metastructure with integrated internal oscillators of constant, linearly and nonlinearly varying natural frequency

This research focuses on the analysis of the model and performance of lightweight metastructures encompassing a distributed array of internal homogenous oscillators, integrated into the host structure to create a single-piece element. This metastructure performs longitudinal vibrations, whose axis is colinear with the direction of the transverse vibration of the internal oscillators. First, the mechanical models of the separate elements of the metastructure and the metastructure as a whole are created and considered. The first modal frequencies of longitudinal vibrations of the metastructure with blocked and free internal oscillators are tuned to the first modal frequency of transverse vibration of one internal oscillator, yielding the optimal number of internal oscillators for this to be achieved, which is a new result for the proposed design. This theoretical result is then checked experimentally with the metastructures produced by 3D printing technology, comprising a different number of internal oscillators, all of which have the same natural frequency. Besides validating the theoretical results, experimental investigations with blocked and freely vibrating internal oscillators of the constant natural frequency are used to explore other performance characteristics, such as the width of the regions where the reduced amplitude is achieved. Finally, based on the theoretical and additional numerical results, the internal oscillators are modified in two ways, which is an original approach: their natural frequency is increased linearly and nonlinearly along the metastructure in accordance with the previous new theoretical results. The benefits of such new redesigns for the multi-modal performance characteristics of the metastructure are discussed.

Boundary-free spin torque nano-oscillators based on ferrimagnetic skyrmions

Skyrmion-based spin torque nano-oscillators have great potential as microwave signal generators in communication technology. In this work, we propose a spin torque nano-oscillator based on ferrimagnetic skyrmions, where the current-induced force can be easily balanced by the controllable Magnus force due to the ferrimagnetic nature, resulting in a stable motion around the edge of the area with applied current. The direction of such a motion is switchable by tuning the ferrimagnet across the compensation point. The oscillation frequency is found to rely on the magnetization and can exceed 1.5 GHz around the angular momentum compensation point. In contrast to previous proposals based on ferromagnetic or antiferromagnetic skyrmions, our ferrimagnetic nano-oscillator does not require a shaped magnetic working layer, thus suggesting that the ferrimagnet could be a potential platform for building oscillator arrays and studying interaction between them.

Modeling the tonotopic map using a two-dimensional array of neural oscillators.

We present a model of a tonotopic map known as the Oscillatory Tonotopic Self-Organizing Map (OTSOM). It is a 2-dimensional, self-organizing array of Hopf oscillators, capable of performing a Fourier-like decomposition of the input signal. While the rows in the map encode the input phase, the columns encode frequency. Although Hopf oscillators exhibit resonance to a sinusoidal signal when there is a frequency match, there is no obvious way to also achieve phase tuning. We propose a simple method by which a pair of Hopf oscillators, unilaterally coupled through a coupling scheme termed as modified power coupling, can exhibit tuning to the phase offset of sinusoidal forcing input. The training of OTSOM is performed in 2 stages: while the frequency tuning is adapted in Stage 1, phase tuning is adapted in Stage 2. Earlier tonotopic map models have modeled frequency as an abstract parameter unconnected to any oscillation. By contrast, in OTSOM, frequency tuning emerges as a natural outcome of an underlying resonant process. The OTSOM model can possibly be regarded as an approximation of the tonotopic map found in the primary auditory cortices of mammals, particularly exemplified in the studies of echolocating bats.

Enhanced spin wave coupling between array of spin torque nano oscillators in magnonic crystal cavities

Spin wave coupling between nano contact spin torque nano oscllators in asymmetric and symmetric array of antidot MC cavities to obtain sustained spin wave oscillations using supercell plane wave method and micromagnetics is discussed. The SWs were excited by injecting a spin-polarized current into a single nano contact in a L3 magnonic crystal cavity(MCC) and radiate like an end-fire antenna. The SW oscillations are then coupled into one of the guided modes of a magnonic crystal waveguide (MCW). The MCC acts as a SW resonator and spin-torque injection as gain. Together they achieve sustainable oscillations in a manner analogous to the behavior of a laser cavity. The phase locking of arrays of cavities arranged symmetrically and asymmetrically on both sides of a MCW is also discussed. Spin waves are radiated like a broadside antenna. The PSD of the broadside case is 28 dB lower than that of the end-fire case. The obtained value from the micromagnetic simulation is used to find the corresponding point in the guided mode of MCW, and this occurs nearer to the edge of the Brillouin zone. We also investigated the point in dispersion where the maximum energy is coupled from MCC to MCW. The spectral characteristics of the broadside coupling were correlated with frequency pulling effects in the laser cavity. Asymmetric spin-torque excitations on either sides of the MCW cause odd frequency peaks in the PSD characteristics. This can be mitigated when we use MC cavities placed symmetrically on both sides of the MCW, and excite spin waves in each cavity. However, spin waves excited in an asymmetric array of cavities add in phase, yielding a power enhancement with an increase in the number of cavities. Spin waves excited in a symmetric array of cavities add out of phase and result in spin-wave decoherence with an increase in the number of cavities.

Towards Real-Time Monitoring of Thermal Peaks in Systems-on-Chip (SoC).

This paper presents a method to monitor the thermal peaks that are major concerns when designing Integrated Circuits (ICs) in various advanced technologies. The method aims at detecting the thermal peak in Systems on Chip (SoC) using arrays of oscillators distributed over the area of the chip. Measured frequencies are mapped to local temperatures that are used to produce a chip thermal mapping. Then, an indication of the local temperature of a single heat source is obtained in real-time using the Gradient Direction Sensor (GDS) technique. The proposed technique does not require external sensors, and it provides a real-time monitoring of thermal peaks. This work is performed with Field-Programmable Gate Array (FPGA), which acts as a System-on-Chip, and the detected heat source is validated with a thermal camera. A maximum error of 0.3 °C is reported between thermal camera and FPGA measurements.

A 0.47-THz Ring Scalable Coupled Oscillator–Radiator Array With Miniature Patch Antennas

This article integrates several techniques for large-scale, high power-efficiency, and area-efficiency terahertz (THz) radiators. First, we present a systematic design method to synthesize a high output power harmonic oscillator at a high fundamental to maximum oscillation frequency ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{\mathrm {osc}}/f_{\mathrm {max}})$ </tex-math></inline-formula> ratio by making a quantitative tradeoff between fundamental oscillation and harmonic output power. Then, a ring scalable coupled oscillator array topology is proposed for a flexible and compact layout. Patch antennas are preferred for large-scale radiator arrays, but the size is much larger than the commonly used slot antenna. Therefore, a miniature on-chip patch antenna is proposed for front-side radiation, whose compact size also helps make the design scalable in 2-D. A quartz superstrate is superimposed on the chip to improve the radiation efficiency. A 16-element ring-coupled oscillator–radiator array is designed and fabricated in a 0.8-mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> total area using a 65-nm CMOS process to verify the design methods. Maximum radiated power of −2.8 dBm is measured at 472 GHz. This design achieves an area efficiency of 0.66 mW/mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the highest among THz radiator arrays using on-chip patch antennas. It is even higher than most radiator arrays using slot antennas. This design also achieves the state-of-the-art dc-to-THz efficiency and frequency tuning range of 0.12% and 4.2%, respectively. The chip can be easily configured to feed a low-cost Teflon lens. A maximum effective isotropic radiated power (EIRP) of ~30 dBm is measured with a 12-mm diameter lens. The measured directivity is 33.7 dBi. At 472 GHz, the measured phase noise is −71.3 dBc/Hz at the 1-MHz offset.