Stochastic resonance in an asymmetric bistable system driven by coloured noises

The phenomenon of stochastic resonance is investigated in an asymmetric bistable system with coloured noises. The approximate Fokker Planck equation is derived based on the Novikov theorem and the Fox approach. By applying the two-state theory, the expression of the signal-to-noise ratio is obtained in the adiabatic limit. The effects of the noise parameters on signal-to-ratio are discussed. It is found that the stochastic resonance phenomena appear in most cases and disappear in some special cases.

Stochastic Resonance in an Asymmetric Mono-stable System Subject to Two Periodic Forces and Multiplicative and Additive Noise

在易于二外部周期的力量、趋于增加的一个不对称的单稳态的系统和添加剂噪音的随机的回声(SR ) 的现象被调查。为基本、更高的泛音的 signal-to-noise 比率(SNR ) 是紧张的一个非单调的函数，这被显示出趋于增加并且添加剂噪音，以及系统参数。而且，为基本泛音的 SNR 随系统不对称现象的增加减少，当为更高的泛音的 SNR 是 non-monotonically 表现时，系统不对称现象变化。

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

Based on adiabatic approximation theory,in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise.The analytical expressions of the mean first-passage time(MFPT)and output signal-to-noise ratio(SNR)are derived by using a path integral approach,unified colored-noise approximation(UCNA),and small delay approximation.The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed.Moreover,three types of asymmetric potential function characteristics are thoroughly discussed.And they are well-depth asymmetry(DASR),well-width asymmetry(WASR),and synchronous action of welldepth and well-width asymmetry(DWASR),respectively.The conclusion of this paper is that the time-delayed feedback can suppress SR,however,the non-Gaussian noise deviation parameter has the opposite effect.Moreover,the correlation time plays a significant role in improving SNR,and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance.Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance,in which no matter whether these signals have low frequency or high frequency,accompanied by strong or weak noise.

Stochastic Resonance in a Harmonic Oscillator Fluctuating Intrinsic Frequency by Asymmetric Dichotomous Noise

The stochastic resonance phenomenon in a harmonic oscillator with fluctuating intrinsic frequency by asymmetric dichotomous noise is investigated in this paper. By using the random average method and Shapiro- Loginov formula, the exact solution of the average output amplitude gain （OAG） is obtained. Numerical results show that OAG depends non-monotonically on the noise characteristics： intensity, correlation time and asymmetry. The maximum OAG can be achieved by tuning the noise asymmetry and or the noise correlation time.

Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system

This study investigates the dynamical behaviors of nearest neighbor asymmetric coupled systems in a confined space.First, the study derivative analytical stability and synchronization conditions for the asymmetrically coupled system in an unconfined space, which are then validated through numerical simulations. Simulation results show that asymmetric coupling has a significant impact on synchronization conditions. Moreover, it is observed that irrespective of whether the system is confined, an increase in coupling asymmetry leads to a hastened synchronization pace. Additionally, the study examines the effects of boundaries on the system's collective behaviors via numerical experiments. The presence of boundaries ensures the system's stability and synchronization, and reducing these boundaries can expedite the synchronization process and amplify its effects. Finally, the study reveals that the system's output amplitude exhibits stochastic resonance as the confined boundary size increases.

Stochastic resonance in a monostable system driven by square-wave signal and dichotomous noise

This paper investigates the stochastic resonance in a monostable system driven by square-wave signal, asymmetric dichotomous noise as well as by multiplicative and additive white noise. By the use of the properties of the dichotomous noise, it obtains the expressions of the signal-to-noise ratio under the adiabatic approximation condition. It finds that the signal-to-noise ratio is a non-monotonic function of the asymmetry of the dichotomous noise, and which varies non- monotonously with the intensity of the multiplicative and additive noise as well as the system parameters. Moreover, the signal-to-noise ratio depends on the correlation rate and intensity of the dichotomous noise.

Experiment and application of parameter-induced stochastic resonance in an over-damped random linear system

This paper investigates the parameter-induced stochastic resonance using experimental methods in an over-damped random linear system with asymmetric dichotomous noise. Non-monotonic dependence of signal-to-noise ratio on the system parameter is observed. Several potential applications of parameter-induced stochastic resonance are given in circuits.

Effect of Asymmetry in a Bistable System Subject to Multiplicative Colored Noise

By the method of the stochastic energetics,we investigate the stochastic resonance (SR) phenomenon of anoverdamped Brown particle in an asymmetric bistable potential,driven by external periodical signal and multiplicativenoise.The expressions have been obtained for the quasi-steady-state probability distribution function.It is found thatthe input energy (IE) pumped into the system by the external driving shows an SR-like behavior as a function of thenoise strength,whereas the IE turns to be a monotonic function of the correlation time of the noise.The effect ofpotential asymmetry is also studied on SR and IE.

非饱和非对称二维随机共振系统的优化及在高速铁路轴承故障诊断中的应用

针对传统双稳杜芬随机共振SR的输出饱和及噪声能量转换不足的问题,引入张角系数控制下的线性分段势阱函数,以抑制SR系统的输出饱和现象,采用非对称势阱函数扩大布朗粒子在单边势阱内的振荡范围,以增加SR输出幅值。结合非线性SR系统最佳耦合方式,构建非饱和-非对称二维SR系统,该系统的4个三维势阱的动力学特性丰富,势阱宽且陡峭度低,布朗粒子的振荡范围较大。采用多尺度简化粒子群优化算法,对构建的非饱和-非对称的二维SR系统进行多参数同步优化,进一步提高粒子在势阱内迁移向上的运动能量。仿真试验与高速铁路轴箱轴承的故障试验结果表明:所提出的优化耦合SR系统,能够显著增强特征信号幅值,提高噪声的利用率,在轴承早期损伤检测中具有突出优势。

Lévy噪声和高斯白噪声共同激励的非对称三稳系统的随机共振

将Lévy噪声和高斯白噪声引入非对称三稳系统模型中,采用数值方法计算不同参数下系统的信噪比,分析噪声参数、系统参数以及信号振幅对系统随机共振现象的影响机制.研究结果表明,较大的稳定性指标、偏斜参数、3次刚度系数以及信号振幅会抑制随机共振现象的发生,而较大的非对称参数则会促进随机共振现象的发生.特别地,当信噪比作为加性噪声强度的函数时,较大的5次刚度系数不易于出现随机共振现象,而当信噪比作为乘性噪声强度的函数时,情况则相反,即5次刚度系数越大越容易发生随机共振现象.

α稳定噪声下时滞非对称单稳系统的随机共振

将α稳定噪声与单稳系统相结合,分别研究了不同α稳定噪声环境下的无时滞项和有时滞项的非对称单稳系统的随机共振。利用数值仿真说明了在无时滞项和有时滞项的非对称单稳系统中均存在随机共振现象,并讨论了α稳定噪声特征指数α(0<α≤2)、对称参数β(-1≤β≤1)、单稳系统参数a、乘性噪声放大系数D、非对称系数r及时滞量τ对系统信噪比增益的影响。

分段线性非对称系统在故障检测中的研究

随机共振具有能够提取轴承故障特征频率和将噪声能量转为信号能量的优点。针对对称分段线性模型性能不够理想的问题,提出了一种非对称分段线性随机共振系统模型,并采用遗传算法对模型参数进行优化选取。在假定模型具有两个稳态的情况下,对该模型进行了解析关系分析与输出信噪比(SNR)的公式推导。同时在模型的公式分析与数值仿真两方面与对称双稳态分段线性随机共振系统进行对比分析,证明该系统的优越性。而后将该模型应用于轴承故障检测当中,采用自适应遗传算法对系统各参数进行协同寻优,对称系统内外圈故障信号检测中故障频率处的幅度值分别为50.79与13.03,非对称系统为391.8与189.3。结果显示该模型具有优良的检测效果,证明该模型在故障检测当中具有巨大潜力。

两种不同类型噪声驱动下的非对称双稳系统的随机共振

研究了由色关联的乘性色噪声和加性白噪声联合激励下的非对称双稳系统的随机共振现象,运用两态模型理论和统一色噪声近似理论,在绝热近似条件下得到了信噪比的表达式。信噪比是乘性色噪声强度,加性白噪声强度,噪声耦合强度,乘性噪声自关联时间和噪声互关联时间的非单调函数,所以在该双稳系统中产生了随机共振。在系统的偏度不是太大的情况下调节加性白噪声强度比调节乘性色噪声强度更容易控制随机共振,并且以信噪比作为噪声之间耦合强度的函数时可以观察到二次随机共振现象。

非对称三值噪声激励下一类线性系统的随机共振现象

研究了一类具有外部周期信号的线性系统在乘性非对称三值噪声激励下呈现随机共振现象的情况.采用Shapiro-Loginov公式,计算出系统输出信号振幅的精确表达式.通过平面及三维图示分析,系统观察出两类广义的随机共振现象.也就是系统在某些参数下,输出信号振幅随着三值噪声强度及其非对称度的变化显现出非单调依赖性.

RC串联电路的随机共振

研究了时间常数受非对称双值色噪声扰动的RC串联电路的随机共振现象。利用随机平均法和Shapiro-Loginov公式,得到了平均输出幅度增益的精确表达式。分析表明,平均输出幅度增益是噪声的强度、自相关率和非对称性参数的非单调函数,适当的噪声参数和系统参数可以使平均输出幅度增益取得最小值,输出幅度增益关于噪声非对称性和相关速率的函数的最小值不随信号频率的变化而变化。

分段非对称随机共振系统微弱信号检测

作为一种重要的信号处理方法,随机共振(SR)能够利用噪声能量增强微弱信号,有效降低噪声信号对特征提取的影响。针对分段对称系统模型随机共振幅值增益不够明显及噪声利用率较低等不足,提出一种分段非线性系统模型。该系统参数独立,易于调节,可通过调节参数诱导最佳随机共振。在双稳态模型下,推导了克莱默斯(Kramers)逃逸率和输出信噪比,同时在模型公式仿真和数值仿真两方面与分段对称系统进行对比分析,用于说明该方法的有效性。结果表明该方法能够有效地提取特征频率,具有良好的放大性能和抗噪声能力。最后将系统应用于不同型号的轴承故障检测,并用自适应智能算法最优化系统参数。结果显示,非对称系统的输出幅值分别为对称系统的8倍,3倍和6倍。数据表明,非对称系统能更有效地实现微弱特征检测与早期故障诊断。该研究进一步对系统在实际工程应用提供了理论指导与依据。

α稳定分布噪声下非对称三稳系统的随机共振特性分析

针对实际工程应用中系统的非对称性,将α稳定分布噪声与非对称三稳系统相结合,以平均信噪比增益(A-SNRI)为性能指标,分别探究了α稳定分布噪声的特征指数α和对称参数β取不同值时,系统参数a、b,刻画三稳系统非对称性的偏度r以及噪声强度放大系数D对非对称三稳系统随机共振输出的规律。研究结果表明:在α稳定分布噪声环境下,通过适当调节系统结构参数a、b和偏度r均可诱导随机共振,实现对微弱信号的检测,并且性能较好区间不随α或β的变化而改变;在研究噪声诱导的随机共振现象时,调节噪声强度放大系数D也可诱导随机共振,且共振效果较好的D区间也不随α或β的变化而变化。这些研究结论为α稳定分布噪声下非对称三稳系统共振中参数的合理选取提供了理论依据。

非对称双稳系统中乘性和加性噪声的随机共振

研究了具有相关乘性和加性噪声的非对称双稳系统中的随机共振现象.基于二态理论和绝热消去理论,得到了系统输出信噪比的解析表达式.发现信噪比是乘性噪声和加性噪声的强度、乘性和加性噪声强度的比值,以及乘性和加性噪声的关联强度和相关时间的非单调函数.另外,输出信噪比随系统的非对称性参数的变化而非单调变化.

基于二阶非对称随机共振的轴承故障特征提取

在强噪声背景下,针对故障信号特征提取困难这一问题,提出了二阶非对称随机共振方法.该方法首先以输出信噪比作为人群搜索算法的目标函数,然后对二阶非对称随机共振模型的参数同时优化,最后将优化的参数代入随机共振模型实现微弱特征信号的增强与提取.仿真和工程数据表明,二阶非对称随机共振方法能有效提取微弱特征信号,实现轴承故障诊断.同时,与传统随机共振方法相比,二阶非对称随机共振的滤波性能更加优越.

方波和非对称双值噪声作用下的熵随机共振研究

研究了在非对称双值噪声、白噪声和方波共同作用下受限系统中的熵随机共振现象。在绝热近似条件下，推导出了输出信噪比的表达式。分析表明，信噪比是非对称双值噪声的强度与非对称参数、白噪声强度，以及方波信号幅度的非单调函数。另外，信噪比随受限结构参数的变化而非单调变化。讨论了双值噪声的相关率对SNR的影响。