三稳系统的动态响应及随机共振

以平衡点参数p, q构造出一类对称三稳势函数, 进而提出微弱信号和噪声共同驱动的三稳系统模型. 深入研究并总结参数p, q对势垒高度ΔU₁, ΔU₂及两势垒高度差的影响. 从定常输入的角度提出了系统稳态解曲线的概念, 并进一步研究低频谐波信号输入时系统的输出动态响应. 引入噪声, 三稳系统在合适的参数条件下实现随机共振, 从稳态解曲线的角度分析了噪声诱导的三稳系统随机共振机理. 最后研究了阻尼比k和平衡点参数p, q对系统随机共振的影响.     

Implication of two-coupled tri-stable stochastic resonance in weak signal detection

Stochastic resonance(SR) has been proved to be an effective approach to extract weak signals overwhelmed in noise.However, the detection effect of current SR models is still unsatisfactory. Here, a coupled tri-stable stochastic resonance(CTSSR) model is proposed to further increase the output signal-to-noise ratio(SNR) and improve the detection effect of SR. The effects of parameters a, b, c, and r in the proposed resonance system on the SNR are studied, by which we determine a set of parameters that is relatively optimal to implement a comparison with other classical SR models.Numerical experiment results indicate that this proposed model performs better in weak signal detection applications than the classical ones with merits of higher output SNR and better anti-noise capability.     

Stochastic resonance in an asymmetric bistable system driven by multiplicative and additive Gaussian noise and its application in bearing fault detection

The phenomenon of stochastic resonance (SR) in a new asymmetric bistable model is investigated. Firstly, a new asymmetric bistable model with an asymmetric term is proposed based on traditional bistable model and the influence of system parameters on the asymmetric bistable potential function is studied. Secondly, the signal-to-noise ratio (SNR) as the index of evaluating the model are researched. Thirdly, Applying the two-state theory and the adiabatic approximation theory, the analytical expressions of SNR is derived for the asymmetric bistable system driven by a periodic signal, unrelated multiplicative and additive Gaussian noise. Finally, the asymmetric bistable stochastic resonance (ABSR) is applied to the bearing fault detection and compared with classical bistable stochastic resonance (CBSR) and classical tri-stable stochastic resonance (CTSR). The numerical computations results show that:(1) the curve of SNR as a function of the additive Gaussian noise and multiplicative Gaussian noise first increased and then decreased with the different influence of the parameters a, b, r and A; This demonstrates that the phenomenon of SR can be induced by system parameters; (2) by parameter compensation method, the ABSR performs better in bearing fault detection than the CBSR and CTSR with merits of higher output SNR, better anti-noise and frequency response capability.     

A multiscale noise tuning stochastic resonance for fault diagnosis in rolling element bearings

Condition monitoring of rotating machinery is important to extend the mechanical system's reliability and operational life. However, in many cases, useful information is often overwhelmed by strong background noise and the defect frequency is difficult to be extracted. Stochastic resonance (SR) is used as a noise-assisted tool to amplify weak signals in nonlinear systems, which can detect weak signals of interest submerged in the noise. The multiscale noise tuning SR (MSTSR), which is originally based on discrete wavelet transform (DWT), has been applied to identify the fault characteristics and has also increased the signal-to-noise ratio (SNR) improvement of SR. Therefore, a novel tri-stable SR method with multiscale noise tuning (MST) is proposed to extract fault signatures for fault diagnosis of rotating machinery. The wavelet packets transform (WPT) based MST can obtain better denoising effect and higher SNR of resonance output compared with the traditional SR method. Thus the proposed method is well-suited for enhancement of rotating machine fault identification, whose effectiveness has been verified by means of practical vibration signals carrying fault information from bearings. Finally, it can be concluded that the proposed method has practical value in engineering.     

Weak signal detection based on underdamped stochastic resonance with an exponential bistable potential

Stochastic resonance (SR) is a vital approach to detect weak signals submerged in strong background noise, which is useful for mechanical fault diagnosis. The underdamped bistable SR (UBSR) is a kind of the most used SR, however, their potential structures are deficient to match with the complicated and diverse mechanical vibration signals and their parameters are selected subjectively which probably resulting in poor performance of UBSR. To overcome these shortcomings, this paper proposes an underdamped SR with exponential potential (UESR) which is generalized by using a harmonic model and a Gaussian potential (GP) model. The dynamics in UESR system is evaluated by the signal-to-noise ratio (SNR) which represents the effectiveness of noise utilization. Then, the effects of system parameters on system performance are investigated by output SNR versus noise intensity D for different parameters. Finally, the proposed method is used to process bearing experimental data and further perform bearing fault diagnosis. The experimental results demonstrate that a larger output SNR and higher spectrum peaks at fault characteristic frequencies can be obtained by the proposed method compared with the UBSR method, which confirm the effectiveness of the proposed method.     

A new method for weak fault feature extraction based on piecewise mixed stochastic resonance

In a continuous bistable system, when the input signal is continuously increased, the output signal tends to be stable and no longer increases. At this time, the weak signal under strong background noise is difficult to be extracted, which means saturation occurs. Aiming at the saturation characteristics of stochastic resonance (SR), the proposed piecewise nonlinear bistable system (PNBSR) model has achieved certain results. However, the potential barrier in the middle of the PNBSR method still completely uses the potential function of classical bistable stochastic resonance (CBSR). There is no fundamental solution to the fourth-order limitation. This paper explores an improved piecewise mixed stochastic resonance (PMSR) potential model. The fourth-order potential function that restricts particle motion in CBSR is improved to a piecewise second-order potential function. This potential function subverts the shape of the traditional potential function and presents a symmetrical double-hook shape. Based on PMSR model, this paper uses particle swarm optimization (PSO) to select system parameters and elaborates the characteristics of the potential function curve in detail. Under the same conditions, the output signal-to-noise ratio (SNR) curve of the improved system is generally higher than that of the CBSR and PNBSR systems. Experiments on bearings and gears show that the proposed method can accurately extract weak fault features, and the effect is better than the PNBSR method.     

A weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance

Aiming at detecting the weak signal in a strong noise background, an enhanced weak signal detection method based on adaptive parameter-induced tri-stable stochastic resonance is proposed. Firstly, because the system can switch among the monostable, bistable and tri-stable state, the potential function characteristic of tri-stable systems is studied by analyzing the potential function curves with different system parameters. And the dynamic characteristics of system parameters on the depth of the potential well is analyzed. The ranges of R and the system parameters are determined, which is essential for ensuring the system is tri-stable state. Secondly, the range of R is used as the constraint condition and the average output signal-to-noise ratio is used as the fitness function of the adaptive algorithm. The system parameters a, b, c are optimized by the differential evolution particle swarm optimization (DEPSO) method to obtain the best output effect. Finally, the proposed adaptive parameter-induced tri-stable stochastic resonance method is adopted to detect the mixed multiple high-frequency weak signal. The detection results are compared with that of adaptive bistable stochastic resonance. At the meanwhile, the method is also applied to detect the fault signal of single crystal furnace. Both the simulation analysis and experiment results show that the proposed method can effectively improve the output signal-to-noise ratio and detect multi-frequency weak signal in the strong noise background.     

Stochastic Resonance in a Linear Fractional Langevin Equation

The fractional Langevin equation is derived from the generalized Langevin equation driven by the additive fractional Gaussian noise. We investigate the stochastic resonance (SR) phenomenon in the underdamped linear fractional Langevin equation under the external periodic force and multiplicative symmetric dichotomous noise. Applying the Shapiro-Loginov formula and the Laplace transform technique, we obtain the exact expressions of the amplitude and signal-to-noise ratio (SNR) of the system. By studying the impacts of the driving frequency and the noise parameters, we find the non-monotonic behaviors of the output amplitude and SNR. The results indicate that the bona fide SR, conventional SR and the wide sense of SR phenomena occur in the proposed linear fractional system.     

Weak fault feature extraction method based on compound tri-stable stochastic resonance

In the presence of strong background noise, in view of the difficulty in extracting weak fault features, a new compound tri-stable stochastic resonance (CTSR) model is proposed by combining the Gaussian Potential model and the mixed bi-stable model. Compared with the traditional tri-stable stochastic resonance (TTSR) method, all parameters of CTSR model have no coupling characteristics. Therefore, the output signal-to-noise ratio (SNR) can be easily optimized by adjusting the system parameters. The CTSR model retains the advantages of constraint and continuity of the Gaussian Potential model, and has a higher utilization rate of noise. Finally, through bearing and engineering experiments, the outstanding advantages of the proposed method in feature extraction of weak faults are verified.     

Combined action of time-delay and colored cross-associated multiplicative and additive noises on stability and stochastic resonance for a stochastic metapopulation system

In this paper, the transition between the stable state of a big density and theextinction state and stochastic resonance (SR) for a time-delayed metapopulation systemdisturbed by colored cross-correlated noises are investigated. By applying the fastdescent method, the small time-delay approximation and McNamara and Wiesenfeld’s SRtheory, we investigate the impacts of time-delay, the multiplicative, additive noises andcolored cross-correlated noise on the SNR and the shift between the two states of thesystem. Numerical results show that the multiplicative, additive noises and time-delay canall speed up the transition from the stable state to the extinction state, while thecorrelation noise and its correlation time can slow down the extinction process of thepopulation system. With respect to SNR, the multiplicative noise always weakens the SReffect, while noise correlation time plays a dual role in motivating the SR phenomenon.Meanwhile, time-delay mainly plays a negative role in stimulating the SR phenomenon.Conversely, it could motivate the SR effect to increase the strength of thecross-correlation noise in the SNR-β plot, while the increase of additive noiseintensity will firstly excite SR, and then suppress the SR effect.     

Stochastic resonance in two kinds of asymmetric nonlinear systems with time-delayed feedback and subject to additive colored noise

This paper attempts to investigate the stochastic resonance (SR) behaviors in two kinds of asymmetric nonlinear systems with time-delayed feedback driven by additive colored noise by virtue of two-state theory, small time delay approximation, path integral approach, and unified colored-noise approximation, where asymmetric nonlinear systems include asymmetric well depth and asymmetric well width alone. The characteristics of SR in two kinds of asymmetric systems are different for different asymmetric ratios and correlated times of additive colored noise. For asymmetric well width, optimal noise intensity is independent of asymmetric ratio and correlated time, whereas for asymmetric well depth it is closely related with asymmetric ratio and correlated time. However, optimal noise intensity is closely related with feedback intensity, and time-delay for two kinds of asymmetries. Even there exists the optimal feedback intensity, time delay and correlated time to make output SNR maximum. Above clues are helpful to achieve weak signal detection under strong background noise.     

Turbo译码算法的分岔与控制

Turbo码在信道编码中通过迭代译码的方式可以较好的逼近香农限.本文以其译码算法中的迭代次数作为时间轴，译码输出作为状态变量，信噪比SNR及信息比特数N作为系统参数建立动力学模型，研究Turbo译码输出与迭代次数之间的关系.通过大量计算机仿真和理论分析发现随着信噪比SNR由小到大，译码算法先后经历了不确定不动点、奇异区和清晰不动点三个阶段，其中在由不确定不动点过渡到奇异区时发生了分岔现象.通过改变信息比特数N的方法得到了离散时间动力学中的切分岔、倍周期分岔和Neimark-Sacker分岔 .在奇异区内观察到倍周期、准周期、周期三、混沌等不同的相空间轨迹.奇异区的出现给Turbo码在低信噪比下的应用带来了一定困难，本文通过延迟反馈控制的方法将相空间轨道稳定到不动点上，仿真结果表明，本算法可以使Turbo码在低信噪比奇异区内获得0.1—0.3 dB的增益. 关键词： Turbo译码算法 动力学 分岔 混沌 延迟反馈控制法     

光学双稳系统中的随机共振

运用绝热近似理论，研究了由加性噪声和乘性噪声及周期信号驱动的光学双稳系统的随机共振现象. 发现该模型中输出信噪比R～随着加性噪声强度D_a的变化曲线中会出现随机共振现象，而信噪比R～随着乘性噪声强度D_m的变化曲线是单调减小的，信噪比曲线中没有出现随机共振现象. 因此，加性噪声和乘性噪声对输出信噪比的影响是不同的. 关键词： 随机共振 信噪比 乘性噪声 加性噪声     

Improvement of signal-to-noise ratio by stochastic resonance in sigmoid function threshold systems, demonstrated using a CMOS inverter

Stochastic resonance (SR) has become a well-known phenomenon that can enhance weak periodic signals with the help of noise. SR is an interesting phenomenon when applied to signal processing. Although it has been proven that SR does not always improve the signal-to-noise ratio (SNR), in a strongly nonlinear system such as simple threshold system, SR does in fact improve SNR for noisy pulsed signals at appropriate noise strength. However, even in such cases, when noise is weak, the SNR is degraded. Since the noise strength cannot be known in advance, it is difficult to apply SR to real signal processing. In this paper, we focused on the shape of the threshold at which SR did not degrade the SNR when noise was weak. To achieve output change when noise was weak, we numerically analyzed a sigmoid function threshold system. When the slope around the threshold was appropriate, SNR did not degrade when noise was weak and instead was improved at suitable noise strength. We also demonstrated SNR improvement for noisy pulsed voltages using a CMOS inverter, a very common threshold device. The input-output property of a CMOS inverter resembles the sigmoid function. By inputting the noisy signal voltage to a CMOS inverter, we measured the input and output voltages and analyzed the SNRs. The results showed that SNR was effectively improved over a wide range of noise strengths.     

Stochastic resonance in a parallel array of linear elements

This paper studies stochastic resonance (SR) phenomenon in a parallel array of linear elements with noise. Employing the signal-to-noise ratio (SNR) theory, it obtains the output SNR, and investigates the effects on the output SNR of the system with signal-independent noise and signal-dependent noise respectively. Numerical results show: the curve of the output SNR is monotone with signal-independent noise; whereas SR appears with signal-dependent noise. Moreover, the output SNR enhances rapidly with the increase of N which is the number of elements in this parallel array linear system. This result may provide smart array of simple linear sensors which are capable of acting as noise-aided amplifiers.     

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.     

基于自适应随机共振理论的太赫兹雷达信号检测方法

太赫兹雷达系统在差频信号频谱分析过程中,干扰噪声影响其测距能力.针对上述问题,提出基于自适应随机共振理论的太赫兹雷达信号检测方法,通过对含噪差频信号进行二次采样,利用自适应随机共振系统提取信号,进行尺度恢复完成测距计算.实验数据显示,不同测量距离时,相较于快速傅里叶变换法,输出信噪比的平均增益为9.684 d B,其中测量距离为1000 mm处,差频信号初始频谱值提高了64.1倍,系统信噪比增益为11.761 d B;相较于滤波法,在测量距离为1000 mm处信噪比增益最大,提高了70.56%;输入噪声强度为1—5 V之间时,输出信噪比曲线的曲率相对于滤波法降低了86.5%,其中噪声强度为5 V时信噪比增益最大,为14.018 d B.实验表明太赫兹雷达系统的测距能力大幅提高.     

偏置信号调制下色关联噪声驱动的线性系统的随机共振

研究了偏置信号调制下关联分段噪声驱动的过阻尼线性系统的随机共振现象，推导出了一阶矩、二阶矩和信噪比的解析表达式. 通过对信噪比曲线的分析，发现该系统中存在三种不同形式的随机共振：传统的随机共振、真正的随机共振和广义的随机共振. 此外，数值结果还表明，加性噪声能够减弱输出的信噪比，而噪声之间的互相关强度能够使输出的信噪比增强. 关键词： 随机共振 信噪比 偏置信号调制的噪声 分段噪声     

Dynamical complexity and stochastic resonance in an asymmetry bistable system with time delay

The dynamical complexity and stochastic resonance (SR) of a time-delayed asymmetric bistable system are studied. Firstly, The effective potential function and steady-state probability density function are deduced based on Born-Oppenheimer approximation theory, and we find that the asymmetric item and time-delayed feedback item can both affect the curve of these two functions, especially the asymmetric item can induce phase displacement. Secondly, the mean first-passage time (MFPT) which plays an important role in research on particles escape rate is derived and we obtain an approximate asymmetric item r which can maintain a steady MFPT. Finally, the influences of different parameters on SR are researched by signal-to-noise ratio (SNR). The analytic expression of SNR is derived and three dimensional graphs and contour maps of SNR with different parameters are obtained. The results indicate that time delay τ and time delay strength e can enhance the SNR and the asymmetric item r has a non-monotone effect on SNR. Notably, adjusting time delay strength e is more sensitive than that of the time delay τ in controlling SR.     

Effect of inertia mass on the stochastic resonance driven by a multiplicative dichotomous noise

A stochastic system driven by dichotomous noise and periodic signal is investigated in the under-damped case.The exact expressions of output signal amplitude and signal-to-noise ratio(SNR) of the system are derived.Numerical results indicate that the inertial mass greatly affects the output signal amplitude and the SNR.Regardless of whether the noise is symmetric or asymmetric,the inertial mass can influence the phenomenon of stochastic resonance(SR) of the system,leading to two types of resonance phenomenon:one is coherence-resonance-like of the SNR with inertial mass,the other is the SR of the SNR with noise intensity.