具有随机参数的线性振荡器的随机共振

研究了噪声作用下的具有随机参数的过阻尼线性振荡器的随机共振现象.基于线性系统理论,得到了系统输出幅度增益的精确表达式.研究表明,输出幅度的增益是噪声强度和激励信号频率的非单调函数.而且,适当的噪声强度和振荡器参数可以使有噪声情况下的输出幅度增益大于无噪声时的输出幅度增益.讨论了噪声的强度和振荡器参数对输出幅度增益的影响.     

Atangana-Baleanu分数阶双稳系统的随机共振现象

针对基于常用分数阶微积分对随机共振现象的研究存在奇异性的问题,提出了基于Atangana-Baleanu分数阶微积分的双稳系统随机共振现象的研究方法。首先,根据Atangana-Baleanu分数阶微积分的定义构造了用于描述随机共振系统的Langevin方程;其次,通过改进的Oustaloup算法对其近似化求解;最后,编写仿真程序,利用控制单一变量法研究参数变化对随机共振的影响。仿真结果表明:噪声强度一定时改变分数阶求导阶次,分数阶求导阶次与输出信号的功率谱值呈非线性关系且存在一个最佳分数阶求导阶次使系统产生随机共振;分数阶求导阶次一定时改变噪声强度,噪声强度与输出信号的功率谱值呈非线性关系且存在一个最佳噪声强度使系统产生随机共振。     

非线性分数阶双稳系统逻辑随机共振的研究

在整数阶逻辑随机共振的郎之万方程基础上构建了分数阶情况下的郎之万方程。对该方程描述的非线性分数阶双稳系统进行了仿真验证,分析分数阶阶次和系统参数的改变对逻辑随机共振现象的影响。结果表明当分数阶阶次小于临界值时,即使没有外加高斯白噪声或微弱周期信号也能观察到逻辑随机共振现象;当分数阶阶次大于临界值时,需要外加高斯白噪声或微弱周期信号才能实现逻辑随机共振,选择合适的噪声强度、微弱周期信号振幅、频率等可以提高逻辑输出的成功率。     

随机参数诱导交流积分器中的随机共振研究

研究了具有随机参数的交流积分器中的随机共振现象。基于线性系统理论,得到了系统输出信噪比的表达式。研究发现,输出信噪比是噪声强度、噪声相关率以及系统参数的非单调函数。信噪比随着激励信号频率的增大而增大,随着信号直流分量的增大而减小。     

双稳态施密特触发电路在OU噪声驱动下的逻辑随机共振

噪声能够帮助非线性系统产生反常的有序行为的现象吸引了人们的广泛关注.我们以一个双稳态的施密特触发电路作为模型系统,用OU(Ornstein-Uhlenbeck)噪声驱动,利用噪声进行逻辑计算,实现了逻辑门的模拟运算.同时研究了噪声强度、噪声相关时间下的逻辑随机共振,并且探讨了系统的弛豫性质对逻辑随机共振的影响.结果表明,色噪声驱动下的双稳态系统中的逻辑随机共振现象同样存在.     

自适应多尺度噪声调节二阶随机共振增强方法EI北大核心CSCD

经典双稳态随机共振系统通过各种参数地调节可实现噪声、周期信号及非线性双稳态系统的最佳匹配从而实现随机共振,促使系统输出的微弱周期分量得到了一定的噪声能量而达到增强的效果,从而有效检测出微弱的周期分量,但噪声能量利用有限,系统响应中仍存在一定的噪声能量。二阶随机共振增强的系统模型,借助“双重积分”实现噪声的重复利用,将噪声进行二次利用,有效促进高频噪声能量进一步转移到低频区域,有效提高输出响应的信噪比。考虑到多尺度带限噪声对随机共振的影响,并基于随机共振特殊低通滤波器的数学本质,提出了以协同信噪比(collaborative signal to noise ratio,CSNR)为目标函数,基于Paul小波的自适应多尺度噪声调节二阶随机共振增强方法,充分利用了小波的多分辨时频分析能力,将输入信号和噪声划分到不同频带,实现了不同频带信号和噪声强度大小的控制,以进一步改善随机共振检测效果。数值仿真、实验数据及工程实际应用均验证了该方法的有效性。     

相关偏置信号调制噪声和加性噪声驱动线性系统随机共振

研究了偏置信号调制噪声和加性噪声驱动线性系统的随机共振现象。根据线性系统理论,得到了系统输出信噪比的精确表达式。研究结果表明：系统输出信噪比是系统衰减常数、调制信号偏置参数、信号调制噪声强度和加性噪声强度的非单调函数。同时,系统输出信噪比随两种噪声的相关强度成非单调关系。     

噪声扰动下RLC串联谐振电路随机共振的数值研究

采用四阶Runge-Kutta算法,以信噪比增益和谱功率放大率为随机共振测度指标,研究了电容参数和激励信号均受高斯白噪声扰动时RLC串联谐振电路的随机共振现象。研究表明,欠阻尼RLC串联谐振电路在适当的电路参数、激励信号频率和噪声参数条件下,信噪比增益和谱功率放大率是噪声强度和输入信号频率的非单调函数,且其值均大于1,电路中存在随机共振现象;而在临界阻尼或过阻尼情况下尽管信噪比增益在一定条件下也是噪声强度和输入信号频率的非单调函数,但谱功率放大率取值小于1,电路发生了随机共振现象,改善了信噪比,信号能量却并未得到加强。这一结论使得将欠阻尼RLC串联谐振电路应用于微弱信号检测成为可能。     

信号调制白噪声作用下线性系统的随机共振

研究了信号调制白噪声作用下的二阶过阻尼线性系统中的随机共振现象.基于线性系统理论和相关删去法方法,得到了系统平均输出幅度增益的精确表达式.研究表明:输出幅度增益是噪声强度,系统阻尼系数和系统固有频率,以及激励信号频率的非单调函数,适当的噪声强度和系统参数可以使噪声情况下的输出幅度增益大于无噪声时的输出幅度增益.     

《二值噪声作用下线性系统的随机共振》

研究了二值噪声用下的二阶过阻尼线性系统的随机共振现象。基于线性系统理论和相关删去法方法,得到了系统平均输出幅度增益的精确表达式。研究表明：输出幅度增益是噪声的强度和相关时间、系统阻尼系数,以及激励信号的频率的非单调函数;另外,适当的噪声参数和系统参数可以使噪声情况下的输出幅度增益大于无噪声时的输出幅度增益。     

含分数阶导数项的随机Duffing振子的稳态响应分析

本文对一个含有分数阶导数项阻尼的、Gaussian白噪声激励下的Duffing振子进行了稳态响应分析。首先,基于能量平衡理论,运用等效线性化方法,计算等效系统的线性阻尼及自然频率,建立统计意义下的等效线性化系统。然后,利用平均法建立随机Ito方程,得到随机响应的Markovian近似;给出描述振子振幅概率密度函数演化的Fokker-Planck方程,并得到它的稳态解。进一步,对于含有响应振幅的等效线性系统,借助由Laplace变换得到的转换函数,得到原系统的条件功率谱密度,结合振幅的稳态概率密度作为权重函数,给出原系统功率谱密度的估计,以及响应的统计量的估计。数值模拟的结果说明所提出的功率谱密度的近似解析表达式是可靠的,它甚至适用于Duffing振子具有强非线性回复力的情形,因为它可以较好的表现出功率谱密度共振频谱加宽及多峰现象的出现。     

分数阶双稳系统随机共振现象研究及FPGA实现

相比整数阶微积分,分数阶对一些具有记忆依赖性以及空间相关性的复杂系统的描述更简明与贴合.利用分数阶微积分的这一优点并结合广义郎之万方程阻尼具有幂律衰减特性,选择合理的核函数,将整数阶郎之万方程推广至分数阶.以此为理论基础,提出了一种分数阶双稳态随机共振系统的FPGA实现方法.对该系统进行了仿真实验验证,仿真结果表明:在...     

A Study of Marginal Oscillator Behavior

In a magnetic resonance spectrometer, a marginal oscillator is used as a transducer to convert a minute change in the tank coil resistance into a change in the amplitude of oscillation. Thus one can define a conversion gain as the ratio of the fractional change in the amplitude of oscillation to the fractional change in the tank coil resistance. Since the change in the tank coil resistance is made periodic at a low frequency to facilitate phase-sensitive detection, a study of the transient behavior of the oscillator becomes important. In this paper, the conversion gain, bandwidth, and noise associated with the oscillator are studied as functions of the circuit parameters, utilizing a piecewise linear characteristic for the active device. Unlike the studies carried out by other authors making use of a polynomial expansion for the nonlinear characteristic, the piecewise linear characteristic has been chosen because it is more amenable to synthesis. The sensitivity of the amplitude of oscillation to the variation of the characteristics of the active device has also been evaluated, and the relationship between the stability requirement of the device characteristics and the conversion gain has been established.     

First passage failure of SDOF nonlinear oscillator with lightly fractional derivative damping under real noise excitations

The first passage failure of single-degree-of-freedom (SDOF) nonlinear oscillator with lightly fractional derivative damping under real noise excitations is investigated in this paper. First, the system state is approximately represented by one-dimensional time-homogeneous diffusive Markov process of amplitude through stochastic averaging. Then, the backward Kolmogorov equation governing the conditional reliability function and the Pontryagin equation governing the conditional mean of first passage time are established from the averaged Itô equation for Hamiltonian. The conditional reliability function, the conditional probability density and mean of the first passage time are obtained by solving these equations together with suitable initial condition and boundary conditions. Finally, two examples are worked out in detail and the analytical solutions are checked by those from the Monte Carlo simulation of original systems.     

Tsallis Distribution-Based Fractional Derivative Method for Lamb Wave Signal Recovery

A new fractional derivative method based on the Tsallis distribution function is developed to recover the Lamb wave signals from the noisy Lamb wave signals. After the fractional derivative of the amplitude spectrum of the noisy Lamb signal at different derivative orders, the quartic polynomial function between the peak amplitude and the derivative order as well as that between the peak frequency and the derivative order is proposed based on the Tsallis distribution function. Then, the characteristic parameters of the amplitude spectrum are deduced by using the proposed polynomial relationship. Finally, the noise-free Lamb wave signal is recovered based on the characteristic parameters. Simulated results indicate that the Lamb wave signals can be recovered in the case of the white noise, the transient noise and the sine wave signal. Experimental results confirm the validity of the method. Consequently, the developed method can recover the Lamb wave signals effectively.     

One-port noise model of a crystal oscillator

This paper presents a one-port noise model of a crystal oscillator combined with equivalent impedances of a resonator and linearized feedback amplifier. Based on the noise conversion technique, we translate the thermal additive and flicker noise of both the resonator and amplifier into the oscillator signal amplitude and phase. The generic transformation coefficients for the noise are derived, and the power spectral density (psd) function of the oscillator signal phase is analyzed in detail. The remarkable property of the model is demonstrated by determining the separate contribution of each noise source to the oscillator performance. Some important rules for shaping the phase psd are noted. The consistency with Leeson's model also is reported.     

Frequency Multiplication Effects on Oscillator Instability

The effects which frequency multiplication produces on the power spectral density of an oscillator is examined as a function of the multiplication ratio and the power spectral density of the phase noise process. In addition, the power spectral density (PSD) of the multiplied-up oscillation is interconnected with the frequency standard L(f). It is explicitly demonstrated how errors are introduced when one attempts to define the rms fractional frequency deviation ?f(?)/f0 and the Allan variance ?2y(?) using the measurement of L(f). Finally, the genesis of spectral spreading of the PSD due to frequency multiplication is demonstrated in such a way that this interesting and important phenomena can be grasped by the practicing engineer.     

On the 1/f frequency noise in ultra-stable quartz oscillators

The frequency flicker of an oscillator, which appears as a 1/f3 line in the phase noise spectral density, and as a floor on the Allan deviation plot, originates from two basic phenomena, namely, (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology.     

Stochastic response of fractionally damped beams

This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system.Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional derivative order. Finally, the fractional derivative term introduces in the system dynamics both effective damping and effective stiffness frequency dependent terms.