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.     

级联双稳系统的随机共振特性

研究了两个双稳系统级联的随机共振特性，由于第一级双稳系统的作用是将白噪声转变为色噪声，因此它是整个级联系统中最重要的环节，以后各级系统近似按洛伦兹分布将噪声能量不断向低频区域集中，从而减弱高频抖动，突出波形的基本轮廓.频谱中信号谱峰随噪声强度的变化规律表明，级联双稳系统只在有限的低频范围内，通过一定量的噪声强度来增强信号频率处的谱峰高度，如果前一级系统未达到随机共振状态，那么其后一级并不能对前一级的输出进行“优化”而形成随机共振.级联双稳系统级数的增加，会使噪声能量集中的低频区域变窄，信号谱峰易被压缩和受到噪声干扰.虽然可以用二次采样方法进行改善，但其改善程度有限.因此对于信号检测而言，使用单级双稳系统即可. 关键词： 级联双稳系统 随机共振 频谱 噪声     

The correlation between stochastic resonance and theaverage phase-synchronization time of a bistable system driven bycolour-correlated noises

This paper investigates the correlation between stochastic resonance (SR) and the average phase-synchronization time which is between the input signal and the output signal in a bistable system driven by colour-correlated noises. The results show that the output signal-to-noise ratio can reach a maximum with the increase of the average phase-synchronization time, which may be helpful for understanding the principle of SR from the point of synchronization; however, SR and the maximum of the average phase-synchronization time appear at different optimal noise level, moreover, the effects on them of additive and multiplicative noise are different.     

Stochastic resonance in parabolic—bistable potential system with an additive colour noise

We propose a new model (parabolic bistable system) with a colour noise source. In the presence of periodic input signal, we investigate the output signal to-noise ratio and the power spectral density of output signal, in which the self-correlation time may be an arbitrary value with no restriction. We find that the curves of signal-to-noise ratio versus the noise intensity D exhibits a bell-shape behaviour. The peak height increases with the increasing value of amplitude A_0 of the input signal. However, the position of peak does not shift. Moreover, the signal-to-noise ratio is insensitive to the modulation frequency Ω, which completely differs from result of Ref.[6]. The power spectral density also has similar behaviour.     

由加性和乘性噪声驱动的非对称双稳系统的随机共振

根据信噪比理论，研究了由乘性和加性白噪声以及周期矩形信号共同作用的非对称双稳系统的随机共振。推导出了信噪比的解析表达式，并且该表达式适用于任意的信号振幅。数值分析表明乘性噪声强度D和加性噪声强度α对信噪比的影响是不同的：对应于任意的一个非对称系数r的值，SNR-α 曲线比SNR-D曲线更容易出现随机共振。即当系统的双阱不是很不对称的时候，改变加性噪声比改变乘性噪声更容易产生随机共振。此外，势井的非对称性能够减小信噪比。     

滤波器与随机共振结合检测微弱信号

基于双稳随机共振系统及滤波器的不同特性,本文提出了一种将两者结合起来检测微弱周期信号的方法,先用自适应前置滤波器对输入的弱周期信号及噪声进行滤波,再使其通过双稳随机共振系统,进而检测出弱信号。对比只有双稳随机共振的系统,仿真结果表明此时的输出信号中待测信号频谱幅度得到了很大的提高,且周围的干扰信号也得到了明显的削弱,即两者的结合使用可以更好的检测出微弱信号,这对强噪声背景下的信号检测有很强的实用性。     

Signal detection for frequency-shift keying via short-time stochastic resonance

A series of short-time stochastic resonance (SR) phenomena, realized in a bistable receiver, can be utilized to detect a train of information represented by signals that adopt frequency-shift keying (FSK). It is demonstrated that the values of noise intensity at resonance regions are close for adjacent periodic signals with an appropriate frequency separation. This establishes the possibility of decoding subthreshold or slightly suprathreshold M-ary FSK signals in bistable receivers. Furthermore, the mechanism of FSK signal detection via short-time SR effects is elucidated in terms of the receiver response speed. This phenomenon provides a possible mechanism for information processing in a bistable device operating in nonstationary noisy environments, where even the inputs appear over a short timescale or have a frequency shift.     

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     

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     

Resonance behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise

The stochastic resonance (SR) behavior for an underdamped bistable system driven by square-wave signal and multiplicative noise is investigated. Under the adiabatic approximation condition, the expression for the system output signal-to-noise ratio (SNR) is obtained. The analysis results show that stochastic multi-resonance phenomenon occurs when the SNR varies with the intensities of the multiplicative and additive noise. SR phenomenon can be observed on the curves of the SNR versus the system bias, versus the amplitude of the dichotomous noise and versus the amplitude of the square-wave signal. Moreover, the SNR varies non-monotonously with the variety of other system parameters.     

Optimum adaptive array stochastic resonance in noisy grayscale image restoration

Considering the widespread noise interference in the two-dimensional (2D) image transmission processing, we proposed an optimal adaptive bistable array stochastic resonance (SR)-based grayscale image restoration enhancement method under low peak signal-to-noise ratio (PSNR) environments. In this method, the Hilbert scanning is adopted to reduce the dimension of the original grayscale image. The 2D image signal is converted into a one-dimensional (1D) binary pulse amplitude modulation (BPAM) signal. Meanwhile, we use the adaptive bistable array SR module to enhance the 1D low SNR BPAM signal. In order to obtain the restored image, we transform the enhanced BPAM signal into a 2D grayscale image signal. Simulation results show that the proposed method significantly outperforms the classical image restoration methods (i.e., mean filter, Wiener filter and median filter) both on the grayscale level and the PSNR of the restored image, particularly in a low PSNR scenario. Larger array size brings better image restoration effect.     

Adaptive bistable stochastic resonance and its application in mechanical fault feature extraction

Stochastic resonance (SR) is an important approach to detect weak vibration signals from heavy background noise. In order to increase the calculation speed and improve the weak feature detection performance, a new bistable model has been built. With this model, an adaptive and fast SR method based on dyadic wavelet transform and least square system parameters solving is proposed in this paper. By adding the second-order differential item into the traditional bistable model, noise utilization can be increased and the quality of SR output signal can be improved. The iteration algorithm for implementing the adaptive SR is given. Compared with the traditional adaptive SR method, this algorithm does not need to set up the searching range and searching step size of the system parameters, but only requires a few iterations. The proposed method, discrete wavelet transform and the traditional adaptive SR method are applied to analyzing simulated vibration signals and extracting the fault feature of a rotor system. The contrastive results verify the superiority of the proposed method, and it can be effectively applied to weak mechanical fault feature extraction.     

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.     

Stochastic resonance in an under-damped bistable system driven by harmonic mixing signal

Stochastic resonance(SR) is studied in an under-damped bistable system driven by the harmonic mixing signal and Gaussian white noise. Using the linear response theory(LRT), the expressions of the spectral amplification at fundamental and higher-order harmonic are obtained. The effects of damping coefficient, noise intensity, signal amplitude, and frequency on spectral amplifications are explored. Meanwhile, the power spectral density(PSD) and signal-to-noise ratio(SNR) are calculated to quantify SR and verify the theoretical results. The SNRs at the first and second harmonics exhibit a minimum first and a maximum later with increasing noise intensity. That is, both of the noise-induced suppression and resonance can be observed by choosing proper system parameters. Especially, when the ratio of the second harmonic amplitude to the fundamental one takes a large value, the SNR at the fundamental harmonic is a monotonic function of noise intensity and the SR phenomenon disappears.     

Detection of multi-frequency weak signals with adaptive stochastic resonance system

Aiming at the poor detection rate of multi-frequency weak signals under a strong background of noise, a novel method based on adaptive stochastic resonance (SR) theory is proposed in this paper. The optimal parameters can be obtained automatically via measurement by establishing an adaptive SR system model and using the reverse location method. After passing through the adaptive SR system, the spectrum values of all eight signals greatly improve, the largest spectrum value gain increases from 12.41 to 2033 when the frequency is 0.01?Hz, which is an improvement of a factor of 162.8, and the signal-to-noise ratio (SNR) gain of the whole system is 10.3134?dB. Under the condition of different input noise intensities and signal amplitudes, the mean SNR of the system increases from –13.1136 to –2.7614?dB, which is a 78.9% increase, and the largest SNR gain is 13.4702?dB when the noise intensity D?=?1.2 and signal amplitude A?=?0.11. Compared to the single optimal spectrum value, when defining multiple optimum spectrum values as the SNR criterion, the detection sensitivity is less than 0.35 when the input noise intensity is between 0.5 and 2.5, and the sensitivity value is 6.29 times higher when D?=?2.5. The system successfully realizes the adaptive detection of twelve weak signals, and the SNR gain is 7.9743?dB, which improves the channel capacity of signal detection. The experimental results demonstrate the high efficiency and strong applicability of the system, improving the signal processing efficiency and speed of signal transmission.     

Stochastic resonance in a single-well system with exponential potential driven by Levy noise

Noise and potential function are vital to stochastic resonance (SR). This paper attempts to broaden the research of the SR and explore a better potential function. Based on the absolute and exponential potentials, a generalized exponential type single-well potential function is constructed. Then the characteristics of the corresponding exponential type single-well SR (ESR) system driven by Levy noise is analyzed numerically. Firstly, the effects of the characteristic index α, symmetric parameter β and noise intensity D of Levy noise on the input signal to noise ratio (SNRi) are investigated. Then, the effects of system parameters a, b, r and noise intensity D on the resonant output is explored. Finally, the ESR system is applied to the fault characteristic extraction of rolling element bearings. The simulation results show that the SR phenomenon is able to be excited by tuning the parameters a, b, r and D under different values of α and β. The larger b (or a) widens the parameter interval of a (or b) which can induce SR. The ESR system is able to solve the problem that the traditional systems fail to achieve SR due to the improper selection of parameters. In bearing fault detection, the detection effect of the ESR system is superior to the bistable SR system.     

Entropic stochastic resonance in a confined asymmetrical bistable system with non-Gaussian noise

Particles moving in confined regions with bistable potential driven by weak signal and fluctuations may present a similar stochastic resonance (SR). This similar SR is called entropic stochastic resonance (ESR). The phenomenon of ESR in a confined asymmetrical bistable potential driven by a transverse periodic force is investigated when a non-Gaussian fluctuation is considered in the system. The left potential of the bistable system can be adjusted by introducing the asymmetrical ratio α. By the functional analysis and two-state theory, the approximate Signal-to-Noise ratio (SNR) is derived. It is found that there is a global maximum in the SNR curves when the asymmetrical ratio α and the noise intensity D are changed. It is also shown that the noise correlation time τ will suppress the ESR of the system and the departure q can obviously change the position of peak in the SNR. The above clues are helpful in achieving weak signal detection under irregular, small-scale systems.     

Stochastic resonance characteristic analysis of new potential function under Levy noise and bearing fault detection

Based on the output saturation of classcial bistable stochastic resonance (CBSR), a new type of piecewise nonlinear bistable stochastic resonance (PNBSR) system is constructed. The mean signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon. The laws for the resonant output of piecewise nonlinear bistable system governed by l, c, a, b and D of Levy noise are explored under different characteristic index α and symmetry parameter β of Levy noise. The results show that the output of PNBSR system has increased 4?dB by comparing with the output signal-to-noise ratio of CBSR system. And the stochastic resonance phenomenon can be induced by adjusting the piecewise nonlinear system's parameters under any α or β of Levy noise. The interval of the parameters of system which induces good stochastic resonance is roughly the same. And the output signal waveform of resonance is very similar to the input signal waveform, which has some reference value for the signal recovery. Moreover, we can find the good stochastic resonance interval of the system parameters do not change with D of Levy noise under the different noise intensity D of Levy noise. On the basis of this, adjusting the intensity amplification factor D of Levy noise, which induces good stochastic resonance, and the interval does not change with α or β. At last, the piecewise nonlinear bistable system is applied to detect bearing fault signals, which achieves better performance compared with the classical bistable system.     

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.