基于耦合Duffing振子的局部放电信号检测方法研究

以双向环形耦合Duffing振子系统为对象, 研究脉冲信号激励下耦合振子间动力学行为变化特征时, 发现其与单向环形耦合Duffing振子系统类似, 在一定的参数条件下, 脉冲信号能引起其中一个振子与其他振子运动轨迹间出现短暂失同步的现象即瞬态同步突变现象. 基于这种现象, 提出了一种微弱脉冲信号检测的新方法, 用于检测强噪声背景中的局部放电脉冲信号. 实验测试表明, 利用本文方法对不同放电电极的局部放电脉冲信号进行检测时, 在低信噪比条件下可取得良好的检测效果, 进而扩展了现有的Duffing振子对非周期信号的检测范围及应用领域. 关键词： 耦合Duffing 振子 微弱信号检测 瞬态同步突变 局部放电脉冲信号     

Duffing振子系统周期解的唯一性与精确周期信号的获取方法

研究Duffing振子系统的周期解的唯一性与精确周期信号的获取方法.应用定性分析方法,获得了一类Duffing振子系统具有唯一周期解的必要条件,同时也得到了一类更广泛的非线性周期系统的周期解的唯一性.在一定条件下,给出了Duffing振子系统精确周期信号的获取方法。     

脉冲激励下环形耦合Duffing振子间的瞬态同步突变现象

研究非周期信号激励下Duffing振子动力学行为变化特征时,发现处于倍周期分岔的环形耦合Duffing振子系统,在一定的参数条件下,脉冲信号能引起其中一个振子与其他振子运动轨迹间出现短暂失同步的现象即瞬态同步突变现象.利用这种现象可以快速检测出强噪声背景中的微弱脉冲信号,从而扩展了现有的Duffing振子对非周期信号的检测范围及应用领域. 关键词： 瞬态同步突变 微弱信号检测 脉冲信号 Duffing振子     

一种基于广义Duffing振子的水中弱目标检测方法

海洋环境中,在水下目标的线谱频率未知或者目标辐射噪声的连续谱很弱时,很难实现水中弱目标的准确检测,本文提出基于广义Duffing振子检测系统的水下目标辐射噪声检测方法.通过对传统周期扰动的Duffing振子信号检测系统的分析和推广,提出了一种可输入非周期、非平稳信号的广义Duffing振子检测系统,可检测输入的无先验信息目标信号.为实现广义Duffing振子系统运动状态的精确、有效判断,提出了一种相空间图形的离散分布列计算方法,通过类网格函数实现了利用统计复杂度对系统输出的嵌入式表征,从而实现了无先验信息时的水中弱目标的嵌入式检测.相同条件下与传统检测方法仿真对比可知,本文提出的方法可以检测到更低信噪比下的目标,并能满足水中检测实时性要求.     

基于强耦合Duffing振子的微弱脉冲信号检测与参数估计

耦合Duffing振子在检测强噪声中的微弱脉冲信号时具有可检测信噪比低等优点,但目前检测模型还存在系统性能与初始状态有关、只能工作在倍周期分岔状态等缺陷.为此本文构建了一种能克服上述缺点的新的微弱脉冲信号检测模型,通过对两个Duffing振子同时施加较大的恢复力和阻尼力耦合,可使振子间产生广义的"阱内失同步"现象,基于这种现象可实现微弱脉冲信号的检测与恢复.以信噪比改善和波形相似度为衡量指标,研究了周期策动力幅值与周期、耦合系数、计算步长、阻尼系数等参量对模型信号检测与波形恢复效果的影响.对方波、双指数脉冲和高斯导数脉冲进行检测和恢复的实验结果表明,本文所构建的模型能够在较低信噪比条件下有效地检测并恢复出高斯白噪声背景中的微弱脉冲信号,进而改善了现有的Duffing振子对非周期脉冲信号的检测能力并扩展了其应用领域.     

环形耦合Duffing振子间的同步突变

以环形耦合Duffing振子系统为研究对象,分析了耦合振子间的同步演化过程.发现在弱耦合条件下,如果所有振子受到同一周期策动力的驱动,那么系统在经历倍周期分岔、混沌态、大尺度周期态的相变时,各振子的运动轨迹之间将出现由同步到不同步再到同步的两次突变现象.利用其中任何一次同步突变现象可以实现系统相变的快速判别,并由此补充了利用倍周期分岔与混沌态的这一相变对微弱周期信号进行检测的方法. 关键词： Duffing振子 同步突变 相变 微弱信号检测     

关联噪声驱动的非对称双稳系统的随机共振

运用统一色噪声近似理论和两态模型理论,研究了周期矩形信号和关联的乘性色噪声和加性白噪声驱动的非对称双稳系统的随机共振现象,得到了适合信号任意幅值的信噪比表达式.信噪比是乘性噪声强度、加性噪声强度、乘性噪声自关联时间、噪声耦合强度的非单调函数,所以该双稳系统中出现了随机共振.同时,调节加性噪声强度比调节乘性噪声强度更容易产生随机共振.势阱静态非对称性和噪声之间的耦合强度对信噪比的影响是不同的. 关键词： 非对称双稳系统 随机共振 信噪比 周期矩形信号     

基于量子粒子群算法的自适应随机共振方法研究

为提升随机共振理论在微弱信号检测领域中的实用性,以随机共振系统参数为研究对象,提出了基于量子粒子群算法的自适应随机共振方法.首先将自适应随机共振问题转化为多参数并行寻优问题,然后分别在Langevin系统和Duffing振子系统下进行仿真实验.在Langevin系统中,将量子粒子群算法和描点法进行了寻优结果对比;在Duffing振子系统中,Duffing振子系统的寻优结果则直接与Langevin系统的寻优结果进行了对比.实验结果表明:在寻优结果和寻优效率上,基于量子粒子群算法的自适应随机共振方法要明显高于描点法;在相同条件下,Duffing振子系统的寻优结果要优于Langevin系统的寻优结果;在两种系统下,输入信号信噪比越低就越能体现出量子粒子群算法的优越性.最后还对随机共振系统参数的寻优结果进行了规律性总结.     

基于扩展型Duffing振子的局部放电信号检测方法研究

目前, 小波阈值去噪法、数字滤波法、傅里叶频域变换法等常用的微弱信号检测方法所能达到的最低检测信噪比为-10 dB, 而双向环形耦合Duffing振子能达到的最低检测信噪比为-20 dB. 但是, 现场检测时常常会出现更低信噪比的放电脉冲信号, 因此现有检测方法就很难满足信号检测的实际需求. 为了有效解决该难题, 研究了一种扩展型Duffing振子的微弱脉冲信号检测的新方法. 该方法的主要思想是使用广义时间尺度变换, 将Duffing振子模型变换为扩展型Duffing振子模型, 有效扩展了微弱信号的频率检测范围. 仿真结果表明, 扩展型Duffing振子不仅具有良好的噪声免疫特性, 而且能有效检测到信噪比低至-40 dB的局部放电微弱脉冲信号, 进一步扩展了现有Duffing振子微弱信号检测方法的检测范围和应用领域.     

线性时滞反馈引起的周期性振动共振分析

研究了高频信号和微弱低频信号同时激励下线性时滞反馈对过阻尼双稳系统和Duffing振子系统中振动共振现象的影响. 解析分析和数值结果都表明, 系统对低频信号的响应幅值增益随时滞参数的变化同时呈现两种不同的周期性关系, 其周期分别为输入的高频信号和低频信号的周期. 数值结果还表明, 对不存在经典振动共振现象的单稳Duffing系统, 通过调节时滞参数也可以引发振动共振现象. 使用时滞反馈不仅可以有效地控制振动共振, 还可以进一步增强系统对微弱低频信号的响应. 关键词： 双稳系统 Duffing 系统 线性时滞反馈 振动共振     

Supernarrow spectral peaks near a kinetic phase transition in a driven nonlinear micromechanical oscillator

We measure the spectral densities of fluctuations of an underdamped nonlinear micromechanical oscillator. By applying a sufficiently large periodic excitation, two stable dynamical states are obtained within a particular range of driving frequency. White noise is injected into the excitation, allowing the system to overcome the activation barrier and switch between the two states. While the oscillator predominately resides in one of the two states for most frequencies, a narrow range of frequencies exist where the occupations of the two states are approximately equal. At these frequencies, the oscillator undergoes a kinetic phase transition that resembles the phase transition of thermal equilibrium systems. We observe a supernarrow peak in the spectral densities of fluctuations of the oscillator. This peak is centered at the excitation frequency and arises as a result of noise-induced transitions between the two dynamical states.     

耦合不连续系统同步转换过程中的多吸引子共存

本文研究了耦合不连续系统的同步转换过程中的动力学行为, 发现由混沌非同步到混沌同步的转换过程中特殊的多吸引子共存现象. 通过计算耦合不连续系统的同步序参量和最大李雅普诺夫指数随耦合强度的变化, 发现了较复杂的同步转换过程: 临界耦合强度之后出现周期非同步态(周期性窗口); 分析了系统周期态的迭代轨道,发现其具有两类不同的迭代轨道: 对称周期轨道和非对称周期轨道, 这两类周期吸引子和同步吸引子同时存在, 系统表现出对初值敏感的多吸引子共存现象. 分析表明, 耦合不连续系统中的周期轨道是由于局部动力学的不连续特性和耦合动力学相互作用的结果. 最后, 对耦合不连续系统的同步转换过程进行了详细的分析, 结果表明其同步呈现出较复杂的转换过程.     

Effect of multiplicative noise on parametric instabilities

We report a study on the effect of external multiplicative noise on parametric instabilities using two different experimental systems: an electronic RLC circuit, parametrically pumped with a voltage-variable capacitor, and surface waves generated by vertically vibrating a layer of fluid (the Faraday instability). Both systems are forced by the superposition of a sinusoidal and a noisy component. We study the statistical properties of the response of both systems to noisy parametric forcing and compare them with theoretical predictions. When the detuning from parametric resonance is such that the bifurcation in the absence of noise is supercritical, both systems behave in the same way under the influence of noise. We find that the effect of noise is twofold: on one hand, it triggers the instability before its deterministic onset under the form of oscillatory bursts; on the other hand, it inhibits the nonlinearly saturated oscillatory response above the deterministic onset. When the detuning is such that the bifurcation is subcritical, we find that the two systems behave differently. In the case of the electronic oscillator, noise mostly triggers random transitions between the two states of the bistable region that exists in the absence of noise, whereas in the surface wave experiment new states are created by noise and the bistable region is strongly enlarged.     

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

Synchronization in arrays of coupled self-induced friction oscillators

We investigate synchronization phenomena in systems of self-induced dry friction oscillators with kinematic excitation coupled by linear springs. Friction force is modelled according to exponential model. Initially, a single degree of freedom mass-spring system on a moving belt is considered to check the type of motion of the system (periodic, non-periodic). Then the system is coupled in chain of identical oscillators starting from two, up to four oscillators. A reference probe of two coupled oscillators is applied in order to detect synchronization thresholds for both periodic and non-periodic motion of the system. The master stability function is applied to predict the synchronization thresholds for longer chains of oscillators basing on two oscillator probe. It is shown that synchronization is possible both for three and four coupled oscillators under certain circumstances. Our results confirmed that this technique can be also applied for the systems with discontinuities.     

混沌振子系统周期解几何特征量分析与微弱周期信号的定量检测

提出了一种对微弱周期信号的定量检测方法.分析混沌振子系统在大尺度周期状态下的相对稳定输出时,发现了混沌振子系统输出周期解的平均面积是一个比较稳定的几何特征量.该几何特征量与待测信号幅值之间存在比较稳定的单调递增关系.在一定的参数条件下,几何特征量精度可达到10^-6V².利用混沌系统对随机噪声信号的免疫性和对微弱周期信号的敏感性,进一步建立了微弱周期信号的定量检测方法.仿真实验表明,随着待检测幅度的增加,在保证检测精度的同时,抗噪性能也随之增强. 关键词： 混沌振子系统 大尺度周期相态 周期解的几何特征量 微弱周期信号的定量检测     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.     

Spiral wave chimeras in populations of oscillators coupled to a slowly varying diffusive environment

Chimera states are firstly discovered in nonlocally coupled oscillator systems. Such a nonlocal coupling arises typically as oscillators are coupled via an external environment whose characteristic time scale τ is so small (i.e., τ → 0) that it could be eliminated adiabatically. Nevertheless, whether the chimera states still exist in the opposite situation (i.e., τ ≫ 1) is unknown. Here, by coupling large populations of Stuart−Landau oscillators to a diffusive environment, we demonstrate that spiral wave chimeras do exist in this oscillator-environment coupling system even when τ is very large. Various transitions such as from spiral wave chimeras to spiral waves or unstable spiral wave chimeras as functions of the system parameters are explored. A physical picture for explaining the formation of spiral wave chimeras is also provided. The existence of spiral wave chimeras is further confirmed in ensembles of FitzHugh−Nagumo oscillators with the similar oscillator-environment coupling mechanism. Our results provide an affirmative answer to the observation of spiral wave chimeras in populations of oscillators mediated via a slowly changing environment and give important hints to generate chimera patterns in both laboratory and realistic chemical or biological systems.     

超材料型周期管路声传播特性及低频宽带控制

船舶管路系统噪声的低频宽带控制是船舶设计和制造中亟待解决的关键问题之一。将超材料理论引入船舶管路系统的结构设计,构造了具有低频声波带隙的一维周期管路结构,并给出了周期管路声波带隙和声波透射系数的计算方法。计算结果表明,该周期管路同时存在声波布拉格带隙和局域共振带隙。在这两种带隙频率范围内,声波在系统中的传播将被衰减抑制。进一步发现,布拉格和局域共振带隙在一定条件会发生耦合,出现带隙耦合展宽现象,且两种带隙存在精确耦合条件。利用带隙耦合的展宽效应和低频设计,可实现声波在低频范围内的传播操控,从而达到船舶管路系统低频噪声宽带控制的目的。