Sparse Identification of Nonlinear Duffing Oscillator From Measurement Data

In this paper we aim to apply an adaptation of the recently developed technique of sparse identification of nonlinear dynamical systems on a Duffing experimental setup with cubic feedback of the output. The Duffing oscillator described by nonlinear differential equation which demonstrates chaotic behavior and bifurcations, has received considerable attention in recent years as it arises in many real-world engineering applications. Therefore its identification is of interest for numerous practical problems. To adopt the existing identification method to this application, the optimization process which identifies the most important terms of the model has been modified. In addition, the impact of changing the amount of regularization parameter on the mean square error of the fit has been studied. Selection of the true model is done via balancing complexity and accuracy using Pareto front analysis. This study provides considerable insight into the employment of sparse identification method on the real-world setups and the results show that the developed algorithm is capable of finding the true nonlinear model of the considered application including a nonlinear friction term.Comment: 6 pages, 8 figures, conference pape

Single-shot Readout of a Superconducting Qubit using a Josephson Parametric Oscillator

We propose and demonstrate a new read-out technique for a superconducting qubit by dispersively coupling it to a Josephson parametric oscillator. We employ a tunable quarter-wavelength superconducting resonator and modulate its resonant frequency at twice its value with an amplitude surpassing the threshold for parametric instability. We map the qubit states onto two distinct states of classical parametric oscillation: one oscillating state, with $185\pm15$ photons in the resonator, and one with zero oscillation amplitude. This high contrast obviates a following quantum-limited amplifier. We demonstrate proof-of-principle, single-shot readout performance, and present an error budget indicating that this method can surpass the fidelity threshold required for quantum computing.Comment: 11 pages, 5 figure

Generating Giant and Tunable Nonlinearity in a Macroscopic Mechanical Resonator from Chemical Bonding Force

Nonlinearity in macroscopic mechanical system plays a crucial role in a wide variety of applications, including signal transduction and processing, synchronization, and building logical devices. However, it is difficult to generate nonlinearity due to the fact that macroscopic mechanical systems follow the Hooke's law and response linearly to external force, unless strong drive is used. Here we propose and experimentally realize a record-high nonlinear response in macroscopic mechanical system by exploring the anharmonicity in deforming a single chemical bond. We then demonstrate the tunability of nonlinear response by precisely controlling the chemical bonding interaction, and realize a cubic elastic constant of \mathversion{bold}$2 \times 10^{18}~{\rm N}/{\rm m^3}$, many orders of magnitude larger in strength than reported previously. This enables us to observe vibrational bistate transitions of the resonator driven by the weak Brownian thermal noise at 6~K. This method can be flexibly applied to a variety of mechanical systems to improve nonlinear responses, and can be used, with further improvements, to explore macroscopic quantum mechanics

Weak Signal Detection Technology Based on Holmes Duffing Oscillator

AbstractIn this paper, the principle and application of weak signal detection based on Holmes Duffing oscillator is introduced. The relationship between the state equation of Duffing oscillator and the control of signal by scanning is analyzed and the signal is detected. The simulation and design the circuit of weak signal detection are researched based on Duffing oscillator. Control experiments are carried out on the circuit with sine signal of different frequencies. We achieve the purpose of detecting weak period signal from noise background by scanning. This study is a useful exploration in Chaos control using engineering signal detection

A new method for detecting line spectrum of ship-radiated noise based on a new double duffing oscillator differential system

34-43In order to detect line spectrum of ship-radiated noise under the ocean background noise and improve the method of detecting duffing oscillator intermittent chaos, a method of detecting intermittent chaos based on variable step size dual duffing oscillator differential system is proposed. Based on the duffing oscillator, two independent and incompletely coupled duffing oscillators can be differentiated based on the differential principle by using the proposed method, which reduces the computational complexity and makes the timing diagram more intuitive. In order to further improve the detection efficiency and reduce the computational complexity of the system, the author put forward that a sequence of solving steps can be built by using only one duffing oscillator and the method of detecting the unknown frequency signal can be achieved by changing the step size of the system. Simulation results show that compared with the conventional duffing oscillator detection method, the proposed method has improved the SNR (signal-to-noise ratio) by at least 10.6 dB. Comparing with duffing system chaotic oscillator column and double duffing system chaotic oscillator column detection method, the proposed method is most effective in detecting line spectrum of ship-radiated noise

Nonlinear damping in mechanical resonators based on graphene and carbon nanotubes

Carbon nanotubes and graphene allow fabricating outstanding nanomechanical resonators. They hold promise for various scientific and technological applications, including sensing of mass, force, and charge, as well as the study of quantum phenomena at the mesoscopic scale. Here, we have discovered that the dynamics of nanotube and graphene resonators is in fact highly exotic. We propose an unprecedented scenario where mechanical dissipation is entirely determined by nonlinear damping. As a striking consequence, the quality factor Q strongly depends on the amplitude of the motion. This scenario is radically different from that of other resonators, whose dissipation is dominated by a linear damping term. We believe that the difference stems from the reduced dimensionality of carbon nanotubes and graphene. Besides, we exploit the nonlinear nature of the damping to improve the figure of merit of nanotube/graphene resonators.Comment: main text with 4 figures, supplementary informatio

Chaotic receivers for optical communication systems

El objetivo de esta tesis concierne al estudio de sistemas de detección de señales enmascaradas en entornos ruidosos. En concreto para escenarios hibridos de comunicaciones wireless que conectan con redes ópticas. Se propone la implementación de un sistema caótico como alternativa a los métodos de detección deterministas. Este sistema estará basado en un receptor Duffing no lineal de segundo orden. Se pretende implementar y caracterizar un receptor caótico para la detección de señales binarias (ASK, PSK y FSK). Además, se propondrá una modificación del sistema de recepción caótico Duffing con respecto a su implementación convencional. Con objeto de evaluar el rendimiento en términos de Bit Error Ratio (BER) y relación señal a ruido (SNR), se presentarán diferentes métodos para la decisión de símbolos. Estos métodos habrán de estar implementados a continuación de nuestro receptor caótico y junto con este último, compondrán el receptor de nuestro sistema. Una vez implementado el receptor, se llevarán a cabo una serie de simulaciones con objeto de comparar el rendimiento del sistema de recepción caótico Duffing frente a los métodos de demodulación estandar. Finalmente, se realizará un montaje óptico en el laboratorio para escenarios de radio sobre fibra a fin de demostrar experimentalmente los resultados obtenidos en las simulaciones. Este estudio se centrará en analizar aquella simulación que anteriormente hubiese resultado más ventajosa con respecto a los métodos de demodulación estandar

Approach to health monitoring and assessment of rolling bearing

A bearing is the most common and vital element in the majority of rotating machinery. Condition monitoring and performance assessment of rolling bearing have recently attracted significant attention. This paper proposes a set of methodologies to realize the efficient health monitoring and assessment of rolling bearing. Considering the difficulties and disadvantages in detecting the fault signal of rolling bearing with background noise, this paper presents a method based on the Duffing oscillator and Hu’s moment invariant for health monitoring. The proposed method mainly combines the chaotic oscillator and moment invariant, fully utilizing the sensitivity of the former to detect the fault signal and taking the latter as a quantitative index for fault identification without the need for a qualitative artificial judgment on the Duffing oscillator phase trajectory map. To provide the optimal performance of Hu’s moment invariant in automatic recognition for the phase trajectory map, the influencing principle of different oscillator parameters was analyzed. Therefore, the health state of rolling bearing can be automatically monitored by quantitatively identifying the transition state of the phase trajectory map. A health assessment model was established to evaluate the health state of bearings. Wavelet packet transform was used to extract the features (approximate entropy) of bearing vibration signal, which were input into the self-organizing map (SOM) network. The health state of rolling bearings was then assessed using the SOM network and confidence values. A case study on health monitoring and assessment for rolling bearing was conducted to demonstrate the effectiveness and accuracy of the proposed methods