幂函数型单势阱随机振动系统的广义随机共振

将线性随机振动系统中通常的简谐势阱推广为更一般的幂函数型势阱,得到幂函数型单势阱非线性随机振动系统.利用随机情形下的二阶Runge-Kutta算法研究了噪声强度、势阱参数和周期激励参数对系统稳态响应的一阶矩振幅和系统响应的稳态方差的影响.对决定势阱形状的势阱参数之一b历经b2,b2以及相当于简谐势阱的b=2等全部情况的研究表明:随噪声强度D的变化,系统稳态响应的一阶矩振幅可以在b2时出现非单调变化,即发生广义随机共振现象,而对通常的b=2简谐势阱以及b2的情况,则无该现象发生;随势阱参数的变化,系统稳态响应的一阶矩振幅以及系统响应的稳态方差也可以发生非单调变化.     

Calculation of pressure reflection ratio

For oscillators with non-linear damping, excited by white noise, an approximation to the stationary joint density function of the displacement and velocity response is derived. This involves reducing the basic two-dimensional Fokker-Planck equation for the transition density function to a one-dimensional equation relating to the energy envelope of the response. Results obtained from this approximation are compared with other theoretical predictions, and also with digital simulation results, in typical cases.     

A critical evaluation of closure methods via two simple dynamic systems

Two simple dynamic systems with cubic nonlinearity and additive Gaussian white noise are used to assess the performance and the usefulness of closure methods in nonlinear random vibration. One of the systems has a single potential well while the other has two potential wells. It is shown that the performance of closure methods is determined by the structure of the moment equations rather than the way in which these equations are closed. For the system with one potential well, any closure method is satisfactory. For the system with two potential wells, closure methods can be inaccurate irrespective of the closure level. It is also shown that moment equations can be augmented with moment inequalities to solve approximately the infinite hierarchy of moment equations.     

Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.     

Non-stationary random response of a finite cable

Numerous problems of current concern involve the designs of aerodynamic systems which either travel at high speeds or contain structural elements which are excited by moving pressure fluctuations. In a number of recent papers responses of dynamic systems to random excitation have been considered. The appropriate theory for calculating the mean square response of linear systems to both stationary and non-stationary random excitation is well known [1–7]. In this paper, the mean square response of a finite cable to non-stationary random excitation is considered. The non-stationary random excitation is of the form s(t) = e(t)α(t), where e(t) is a well defined envelope function and α (t) is the Guassian, narrow band, stationary part of the excitation which has zero mean. Both the unit step and rectangular step functions are used for the envelope function, and both white noise and noise with an exponentially decaying harmonic correlation function are used to prescribe the statistical property of the excitation. The results obtained are shown to be a complete expression for the mean square response when checked for accuracy by reduction to expressions previously obtained by Lyon [4]. It is felt that these results will aid the design of both linear and two-dimensional aerodynamic systems excited by random pressure fluctuations.     

"Green" noise in quasistationary stochastic systems

We consider the behavior of stochastic systems driven by noise with a zero value of spectral density at zero frequency ("green" noise). For this purpose we propose the version of the Krylov-Bogoliubov averaging method to study the systems which are not stationary in the case of an external white noise. We use the ergodicity of a nonlinear random function in the method, and obtain equations for any approximation of the theory. In particular, it is shown in the first approximation that there is an effective potential to describe the averaged motion of the system. We consider a phase-locked loop as an example and show that metastable states are possible. The lifetime of these states essentially increases if the form of a green noise spectrum becomes sharper in the low-frequency region. The high stability of the system driven by green noise is confirmed by numerical simulation. It is important that the theoretical result obtained by the averaging method and the one obtained in the simulation coincide with sufficient accuracy. In conclusion, we discuss some of the unsolved green noise problems. (c) 2001 American Institute of Physics.     

Features of the moment functions of an oscillator with parametric instability due to dichotomous noise with Erlang distribution functions

We study stability of the periodic solutions of a linear undamped oscillator with frequency modulated by dichotomous noise whose statistic is determined by the Erlang distribution. It is shown that the amplitudes of harmonic oscillations of such an oscillator increase with time at different rates determined by the ratio of the oscillator eigenfrequency to the characteristic frequency of dichotomous noise. To solve the problem, we use a finite system of closed equations with respect to the moment functions, which was obtained without assumption on the quasi-Gaussianity and delta-correlatedness of the studied process.     

New Type of Brownian Motion

We consider an oscillator with a random mass for which the particles of the surrounding medium adhere to the oscillator for some random time after the collision (Brownian motion with adhesion for a harmonically bound particle). This is another form of a stochastic oscillator, different from oscillator usually studied that is subject to a random force or having random frequency or random damping. Calculation of the first two stationary moments shows that for white multiplicative noise of week strength the second moment coincides with that of usual Brownian motion, but for symmetric dichotomous noise, the second moment may appear the same type of the “energetic” instability, which exists for white noise random frequency or damping coefficient.     

水声波导中包络线谱强度数值预报

为了预报声呐远距离检测包络线谱的性能,本文分析在辐射噪声传播过程中包络线谱强度衰减的原因及提出在水声波导中包络线谱强度的数值预报方法。依据周期性局部平稳过程对舰船辐射噪声建模,推导出无噪声干扰及有噪声干扰下的包络线谱强度的数学表达式,获得了包络线谱强度传播衰减的规律,在水声波导中包络线谱声级传播规律与平稳谱一致,但包络线谱高出连续谱的强度的衰减取决于随信噪比变化的调幅深度修正因子。包络线谱强度数值预报方法如下:先利用传播衰减的数值方法例如用简正波方法波数积分方法PE方法等求出平稳辐射噪声的传播衰减,再求信噪比,最后依据调幅深度修正因子获得包络线谱强度降低的分贝数,预报出在水声波导中任意一点包络线谱信号高度。该理论和数值预报方法具有创新性,实用,简单,适合工程应用。      

Transduction of a bistable inductive generator driven by white and exponentially correlated Gaussian noise

In this theoretical study, the response of an inductive power generator with a bistable symmetric potential to stationary random environmental excitations is investigated. Both white and Ornstein-Uhlenbeck-type excitations are considered. In the white noise limit, the stationary Fokker-Plank-Kolmagorov equation is solved for the exact joint probability density function (PDF) of the response. The PDF is then used to obtain analytical expressions for the response statistics. It is shown that the expected value of the generator's output power is independent of the potential shape leading to the conclusion that under white noise excitations, bistabilities in the potential do not provide any enhancement over the traditional linear resonant generators which have a single-well potential. In the case of Ornstein-Uhlenbeck (exponentially correlated) noise, an approximate expression for the mean power of the generator which depends on the potential shape, the generator's design parameters and the noise bandwidth and intensity is obtained. It is shown that there exists an optimal potential shape which maximizes the output power. This optimal shape guarantees an optimal escapement frequency between the potential wells which remains constant even as the noise intensity is varied.     

具有固有频率涨落的记忆阻尼线性系统的随机共振

研究了在内噪声、外噪声(固有频率涨落噪声)及周期激励信号共同作用下具有指数型记忆阻尼的广义Langevin方程的共振行为.首先将其转化为等价的三维马尔可夫线性系统,再利用Shapiro-Loginov公式和Laplace变换导出系统响应一阶矩和稳态响应振幅的解析表达式.研究发现,当系统参数满足Routh-Hurwitz稳定条件时,稳态响应振幅随周期激励信号频率、记忆阻尼及外噪声参数的变化存在"真正"随机共振、传统随机共振和广义随机共振,且随机共振随着系统记忆时间的增加而减弱.数值模拟计算结果表明系统响应功率谱与理论结果相符.     

随机系统的概率密度函数形状调节

针对受高斯白噪声激励的非线性随机系统,提出了使状态响应的概率密度函数形状跟踪期望形状的调节方法.首先,确立了非线性随机系统的多项式反馈机制,同时对系统中的非线性部分进行多项式展开;然后,以Fokker-Planck-Kolmogorov方程为工具,导出了与控制增益相关的各阶矩递推方程,并根据跟踪问题的要求,构造了矩逼近优化问题,用梯度搜索法求解该优化问题,获得了调节函数;再依据特征函数与概率密度函数构成Fourier对的关系,对状态响应的概率密度函数进行重构;最后,通过两个例子仿真,验证了本文方法的有效性.     

Role of attention in overshoot: frequency certainty versus uncertainty

Overshoot, the elevation in the threshold for a brief signal that comes on close to masker onset, was measured with signal frequency certain (same frequency on every trial) or uncertain (randomized over trials). In broadband noise, thresholds were higher 2 ms after masker onset than 200 ms later, by 9 dB with frequency certainty, by 6-7 dB with uncertainty. In narrowband noise centered on the signal frequency, thresholds at 2 ms were not elevated with certainty, but were elevated 4-5 dB with uncertainty. Thus, frequency uncertainty leads to less overshoot in broadband noise, to more overshoot in narrowband noise. Reduced overshoot in broadband noise may come about because the masker, given its many frequencies, disrupts focusing at onset as much under certainty as uncertainty. Once the initial disruption dissipates, threshold is lower with certainty so overshoot is greater. In contrast, a narrowband noise with frequencies only near the signal does not disrupt focusing when the signal frequency is known beforehand, so overshoot is absent. When frequency is uncertain, the narrowband noise serves to focus attention on the signal frequency; as this requires time, detection near noise onset is poorer than later on, so overshoot is present.     

具有非线性阻尼涨落的线性谐振子的随机共振

较之于线性噪声, 非线性噪声更广泛地存在于实际系统中, 但其研究远不能满足实际情况的需要. 针对作为非线性阻尼涨落噪声基本构成成分的二次阻尼涨落噪声, 本文考虑了周期信号与之共同作用下的线性谐振子, 关注这类具有基本意义的阻尼涨落噪声的非线性对系统共振行为的影响. 利用Shapiro-Loginov公式和Laplace变换推导了系统稳态响应振幅的解析表达式, 并分析了稳态响应振幅的共振行为, 且以数值仿真验证了理论分析的有效性. 研究发现: 系统稳态响应振幅关于非线性阻尼涨落噪声系数具有非单调依赖关系, 特别是非线性阻尼涨落噪声比线性阻尼涨落噪声更有助于增强系统对外部周期信号的响应程度; 而且, 非线性阻尼涨落噪声比线性阻尼涨落噪声使得稳态响应振幅关于噪声强度具有更为丰富的共振行为; 同时, 二次阻尼涨落噪声使得稳态响应振幅关于系统频率出现真正的共振现象; 而在这些现象和性质中, 非线性噪声项的非线性性质对共振行为起着关键的作用. 显然, 以二次阻尼涨落作为基本形式引入的非线性阻尼涨落噪声, 可以有助于提高微弱周期信号检测的灵敏度和实现对周期信号的频率估计.     

Spectro-temporal envelope changes caused by temporal fine structure modification

The study of speech from which the temporal fine structure (TFS) has been removed has become an important research area. Common procedures for removing TFS include noise and tone vocoders. In the noise vocoder, bands of noise are modulated by the envelope of the speech within each band, and in the tone vocoder the carrier is a sinusoid at the center of each frequency band. Five different procedures for removing TFS are evaluated in this paper: the noise vocoder, a low-noise noise approach in which the noise envelope is replaced by the speech envelope in each frequency band, phase randomization within each band, the tone vocoder, and sinusoidal modeling with random phase. The effects of TFS modification on the speech envelope are evaluated using an index based on the envelope time-frequency modulation. The results show that for all of the TFS techniques implemented in this study, there is a substantial loss in the accuracy of reproduction of the envelope time-frequency modulation. The tone vocoder gives the best accuracy, followed by the procedure that replaces the noise envelope with the speech envelope in each band.     

Coherence depression in stochastic excitable systems with two-frequency forcing

We study the response of two generic neuron models, the leaky integrate-and-fire (LIF) model and the leaky integrate-and-fire model with dynamic threshold (LIFDT) (i.e., with memory) to a stimulus consisting of two sinusoidal drives with incommensurate frequency, an amplitude modulation ("envelope") noise and a relatively weak additive noise. Spectral and coherence analysis of responses to such naturalistic stimuli reveals how the LIFDT model exhibits better correlation between modulation and spike train even in the presence of both noises. However, a resonance-induced synchrony, occurring when the beat frequency between the sinusoids is close to the intrinsic neuronal firing rate, decreases the coherence in the dynamic threshold case. Under suprathreshold conditions, the modulation noise simultaneously decreases the linear spectral coherence between the spikes and the whole stimulus, as well as between spikes and the stimulus envelope. Our study shows that the coefficient of variation of the envelope fluctuations is positively correlated with the degree of coherence depression. As the coherence function quantifies the linear information transmission, our findings indicate that under certain conditions, a transmission loss results when an excitable system with adaptive properties encodes a beat with frequency in the vicinity of its mean firing rate.     

Moments and Mean First—Passage Time of Parabolic—Bistable Potential System Driven by Colored Noise

A parabolic-bistable potential system driven by colored noise is studied.The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived.Furthermore,the mean first-passage time is calculated by the use of two approximate methods,respectively.It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity;(ii) a minimum occurs on the curve of the second-order moment of the system vs.noise intensity at the point DΓ=0.025;(iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time τ,while the conventional steepest descent approximation leads to poor results.     

Stochastic resonance of a damped oscillator with frequency fluctuation driven by a periodic external force

<正>Considering a damped linear oscillator model subjected to a white noise with an inherent angular frequency and a periodic external driving force,we derive the analytic expression of the first moment of output response,and study the stochastic resonance phenomenon in a system.The results show that the output response of this system behaves as a simple harmonic vibration,of which the frequency is the same as the external driving frequency,and the variations of amplitude with the driving frequency and the inherent frequency present a bona fide stochastic resonance.     

External non-white noise: Theory and experiment

We consider a system under the influence of an external gaussian noise with a flat spectrum and finite cut-off frequency. The stationery properties of the system are studied as a function of the correlation time of the noise. Theoretical predictions based on an expansion in powers of the correlation time are corroborated by experimental measurements on an electric circuit with a digital noise generator. The two main qualitative properties experimentally observed which can not be explained in a white noise limit theory are: (i) appearance of relative extrema of the stationery distribution for high noise intensity when the correlation time is not too small; (ii) dependence on the noise characteristics of the position of the maximum of the stationary distribution for low noise intensity.     

Local methods for constructing stationary distribution functions of systems of stochastic differential Langevin-type equations: Noise influence on simple bifurcation

The influence is considered of two additive correlated noise effects on a two-dimensional quadratic-nonlinear system describing the behavior of two hydrodynamic modes. Using the method of Gaussian approximation, local characteristics of the distribution function are calculated, which are used to construct the global distribution function with the aid of the method of fraction-rational approximations. It is shown that for a system at whose bifurcation point the asymptotic stability is lost, in an expanded space of parameters (bifurcation parameter in the absence of noise plus noise parameters) there appears an instability zone within which the stationary distribution function does not exist. The effect of noise correlation on the stationary characteristics of the system is studied.