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.

Adaptive stochastic resonance method for weak signal detection based on particle swarm optimization

In order to solve the parameter adjustment problems of adaptive stochastic resonance system in the areas of weak signal detection,this article presents a new method to enhance the detection efficiency and availability in the system of two-dimensional Duffing based on particle swarm optimization.First,the influence of different parameters on the detection performance is analyzed respectively.The correlation between parameter adjustment and stochastic resonance effect is also discussed and converted to the problem of multi-parameter optimization.Second,the experiments including typical system and sea clutter data are conducted to verify the effect of the proposed method.Results show that the proposed method is highly effective to detect weak signal from chaotic background,and enhance the output SNR greatly.

Novel Woods-Saxon stochastic resonance system for weak signal detection

We propose a joint exponential function and Woods–Saxon stochastic resonance(EWSSR)model.Because change of a single parameter in the classical stochastic resonance model may cause a great change in the shape of the potential function,it is difficult to obtain the optimal output signal-to-noise ratio by adjusting one parameter.In the novel system,the influence of different parameters on the shape of the potential function has its own emphasis,making it easier for us to adjust the shape of the potential function.The system can obtain different widths of the potential well or barrier height by adjusting one of these parameters,so that the system can match different types of input signals adaptively.By adjusting the system parameters,the potential function model can be transformed between the bistable model and the monostable model.The potential function of EWSSR has richer shapes and geometric characteristics.The effects of parameters,such as the height of the barrier and the width of the potential well,on SNR are studied,and a set of relatively optimal parameters are determined.Moreover,the EWSSR model is compared with other classical stochastic resonance models.Numerical experiments show that the proposed EWSSR model has higher SNR and better noise immunity than other classical stochastic resonance models.Simultaneously,the EWSSR model is applied to the detection of actual bearing fault signals,and the detection effect is also superior to other models.

Adaptive Bistable Stochastic Resonance Based Weak Signal Reception in Additive Laplacian Noise

Weak signal reception is a very important and challenging problem for communication systems especially in the presence of non-Gaussian noise,and in which case the performance of optimal linear correlated receiver degrades dramatically.Aiming at this,a novel uncorrelated reception scheme based on adaptive bistable stochastic resonance(ABSR)for a weak signal in additive Laplacian noise is investigated.By analyzing the key issue that the quantitative cooperative resonance matching relationship between the characteristics of the noisy signal and the nonlinear bistable system,an analytical expression of the bistable system parameters is derived.On this basis,by means of bistable system parameters self-adaptive adjustment,the counterintuitive stochastic resonance(SR)phenomenon can be easily generated at which the random noise is changed into a benefit to assist signal transmission.Finally,it is demonstrated that approximately 8dB bit error ratio(BER)performance improvement for the ABSR-based uncorrelated receiver when compared with the traditional uncorrelated receiver at low signal to noise ratio(SNR)conditions varying from-30dB to-5dB.

Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism.We propose a novel composite multistable stochastic-resonance(NCMSR)model combining the Gaussian potential model and an improved bistable model.Compared with the traditional multistable stochastic resonance method,all the parameters in the novel model have no symmetry,the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters.The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation,the NCMSR model has a higher utilization of noise.Taking the output signal-to-noise ratio as the index,weak periodic signal is detected based on the NCMSR model in Gaussian noise andαnoise environment respectively,and the detection effect is good.The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race.The outstanding advantages of this method in weak signal detection are verified,which provides a theoretical basis for industrial practical applications.

Re-scaling and adaptive stochastic resonance as a tool for weak GNSS signal acquisition

Weak global navigation satellite system（GNSS） signal acquisition has been a limitation for high sensitivity GPS receivers. This paper modifies the traditional acquisition algorithms and proposes a new weak GNSS signal acquisition method using re-scaling and adaptive stochastic resonance（SR）. The adoption of classical SR is limited to low-frequency and periodic signals. Given that GNSS signal frequency is high and that the periodic feature of the GNSS signal is affected by the Doppler frequency shift, classical SR methods cannot be directly used to acquire GNSS signals. Therefore, the re-scaling technique is used in our study to expand its usage to high-frequency signals and adaptive control technique is used to gradually determine the Doppler shift effect in GNSS signal buried in strong noises. The effectiveness of our proposed method was verified by the simulations on GPS L1 signals. The simulation results indicate that the new algorithm based on SR can reach-181 d BW sensitivity with a very short data length of 1 ms.

Multi-scale bistable stochastic resonance array: A novel weak signal detection method and application in machine fault diagnosis

Weak signal detection based on stochastic resonance （SR） can hardly succeed when noise intensity exceeds the optimal value of SR. This paper explores a novel parallel bistable SR array mechanism by decomposed multi-scale noises from input signal. A smoother output with lower noise is obtained from the combination of colored noise SR ellect and parallel bistable SR array. The influence of noise intensity and array size on the SR effect and output noise intensity is analyzed through numerical simu- lation. A signal detection method based on the new SR mechanism and normalized scale transform is proposed for the case of heavy background noise. Simulation is conducted to confirm the effectiveness of parameter tuning and amplitude tuning of normalized scale transform on the proposed SR model. The proposed method has three advantages： the input noise intensity of each unit is reduced by wavelet decomposition; the output noise level decreases due to array ensemble average; the SR effect of each unit is optimized by normalized scale transform for high frequency signal. Experiment on bearing inner and outer race fault diagnosis has verified the effectiveness and advantages of the proposed SR model in comparison with traditional SR method and kurlogram.

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 linear system driven by multiplicative noise and additive quadratic noise

In this paper the stochastic resonance （SR） is studied in an overdamped linear system driven by multiplicative noise and additive quadratic noise. The exact expressions are obtained for the first two moments and the correlation function by using linear response and the properties of the dichotomous noise. SR phenomenon exhibits in the linear system. There are three different forms of SR： the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the effect of the asymmetry of the multiplicative noise on the signal-to-noise ratio （SNR） is different from that of the additive noise and the effect of multiplicative noise and additive noise on SNR is different.

Stochastic resonance in an optical bistable system subjected to cross-correlated additive white noise and multiplicative colored noise

The stochastic resonance （SR） of an optical bistable system with cross-correlated additive white and multiplicative colored noises and periodic signal is studied using the unified colored noise approximation and the theory of signal-to-noise ratio （SNR）. Results show that cross-correlation intensity λ enforces the SR of the system. The position of the peak on the SNR-τ curves moves to the right direction along with the increase of λ （τ is the self-correlation time of the multiplicative colored noise）. We find the SR phenomenon in the SNR-D and SNR-Q curves （D and Q are the intensities of the additive and multiplicative noises, respectively）, but not in the SNR-λ curves.

Preliminary Application of Scale Transformation Stochastic Resonance in Dual-Sequence Frequency Hopping System

Aiming at the detection failure of strong noise interference in the dual channel of the dual-sequence frequency hopping(DSFH),the scale transformation stochastic resonance(STSR)is applied for the first time,and the output signal to noise ratio(SNR)is raised effectively,at the same time,the symbol reception is completed for DSFH at low input SNR.Firstly,the radio frequency(RF)and intermediate frequency(IF)signals are analyzed based on the super-heterodyne reception of DSFH;secondly,the equations of probability density function(PDF),output power spectrum and SNR of the STSR output are derived for the IF signal;finally,the algorithm of the optimal matching STSR is proposed with the optimal matching parameters.The simulation results show that the algorithm can effectively solve the detection failure,as the global output SNR of DSFH is strongly improved that the output SNR can reach-17.72 d B when the input SNR is-20 d B after the processing of the optimal matching STSR.

基于三稳态随机共振的ZPW-2000移频信号检测方法研究

针对ZPW-2000移频信号谐波干扰检测技术在抑制噪声时,不可避免损害有用信号的问题,提出三稳态随机共振系统,将部分噪声能量向移频信号能量转化,减少移频信号能量损失。首先,将移频信号的中心频率从较高频段搬移到较低频段,着重研究移频信号的有用频段。选取尺度变化系数为1 000,保证输入信号在尺度变化的过程中满足数值计算的稳定性,使尺度变换后的小参数信号满足绝热近似理论。其次,使用混沌麻雀算法(chaos sparrow search optimization algorithm, CSSOA)优化三稳态随机共振系统,得到输出信噪比(signal-to-noise ratios, SNR)最大时的系统参数a、b、c以及γ。然后,将搬移至低频区段的移频信号输入至优化后的三稳态随机共振系统,实现信号降噪。最后,对降噪信号采用复调制快速傅里叶算法(zoom fast fourier transformation, ZFFT)实现低频信号的检测。仿真结果表明:对比三稳态随机共振系统处理前后移频信号频谱图,显示频域特征增强,在降噪的同时不损害移频信号的能量;以-5 dB为步长将噪声注入至移频信号时,输出信噪比至少可提升16.54 dB;降噪后的信号通过ZFFT算法解调能够完成ZPW-2000移频信号低频信号的检测。对比经验模态分解算法、小波阈值算法等算法处理不同信噪比的含噪移频信号,验证混沌麻雀算法优化的三稳态随机共振系统输出信噪比较大,降噪效果较好,具有良好的抗干扰能力。研究结果为实现在抑制噪声的同时减少移频信号能量损失提供参考。

基于随机共振的水下目标微弱回波信号增强检测

针对低信噪比下主动声呐探测水下目标的微弱回波信号检测难题,本文提出了一种基于随机共振的微弱回波信号增强检测方法。该方法通过建立频移变尺度随机共振系统,与输入高频微弱回波信号、随机噪声相匹配,实现微弱回波信号的共振增强;进而利用乘积谱与谱峭度构建目标回波亮点增强检测指标,有效提升微弱回波亮点的能量集中程度,抑制杂波及虚假成分干扰。仿真结果表明:在低信噪比下,随机共振系统输出信噪比增益可达5 dB以上,微弱目标回波亮点检测结果更加直观便捷,杂波干扰得到大幅抑制。海试数据处理结果进一步验证了所提方法的有效性和可靠性。

油气测井微弱信号检测方法分析

文章分析研究了油气测井中微弱信号识别检测方法,首先回顾了微弱信号检测的传统方法,指出传统方法在处理高噪声环境下的微弱信号时的局限性;其次,详细介绍了非线性系统理论中的混沌理论和随机共振理论;最后,探讨了这些先进理论在油气测井微弱信号检测中的具体应用。该研究对提升油气资源勘探和开发的效率和准确性具有重要的实践意义,为油气测井领域提供了一种新的微弱信号检测策略。

变尺度随机共振用于电机故障的监测诊断

以绝热近似小参数的随机共振理论为依据,提出变尺度随机共振的新方法,实现了大参数条件下的随机共振,进而达到从强噪声中检测出弱信号的目的。在大量可行的数值研究基础上,成功地将变尺度随机共振技术应用于电机故障的监测与诊断,证明了该方法在故障监测和预报方面是可行有效的。

强噪声背景中微弱信号检测的初步研究

为了提高信噪比,以往大都设法滤除噪声.根据随机共振理论,本文对用添加噪声来提高测量信号信噪比的方法进行了初步的尝试,并将此方法应用于强噪声背景中微弱信号的检测,得出了一些有意义的初步结果.

基于双稳类随机共振的信息检测

研究了小参数随机共振(SR)的响应幅值与信号频率和噪声强度的关系,并从噪声频谱的罗伦兹(Lorentz) 分布特性推出,只有在噪声能量集中的低频区域才能产生随机共振的论点。得出了二次采样大参数类随机共振的实现条件,即采样频率至少是信号频率的50倍并根据噪声强度选择二次采样频率。在大参数情况下,由双稳系统输入输出信噪比的分析,阐明了大参数类随机共振方法从强噪声中检测出弱信号的可行性。运用周期和非周期弱信号的检测实例,进一步证明了该方法的有效性和实用性。

基于调制随机共振的微弱信号检测研究

在工程信号处理过程中信号常超出随机共振绝热近似或线性响应理论的小参数要求而成为大参数信号。深入探讨非线性双稳系统随机共振发生机理和条件要求,将频率调制技术与随机共振理论相结合,提出用调制随机共振的方法实现随机共振理论在工程信号检测中的应用,进行了数值仿真分析证明其有效性,并将该方法应用于轴承内圈点蚀故障的检测。

检测地震勘探微弱同相轴的混沌振子算法

针对地震勘探资料湮没在随机噪声中的微弱同相轴问题提出基于混沌理论的混沌振子检测算法.利用修正的Duffing_Holmes方程建立检测微弱同相轴的混沌振子系统,之后经过对同相轴的扫描处理,构成新子波等时间间隔序列W(t),与此同时对随机噪声也进行相同的截断.截断的随机噪声在混沌振子系统中可以具有与周期信号相同的表现;经过大量仿真实验确定出满足通常地震勘探子波延续时间的使混沌振子检测子波不呈现周期相态的随机噪声截断时间范围.选用与松辽盆地T1、T2反射层类似的子波函数并构成待检微弱周期信号,经过MATLAB仿真试验成功地检测出该弱信号,信噪比达到约-10.3dB.

一种有效提取弱信号的新方法

A novel method for extracting weak signal based on the theory of stochastic resonance was proposed. It was implemented by using the cooperative effect of noise instead of adding noise to a weak signal. The previous studies show that several disadvantages exist in the adding noise method. Due to the fact that adding noise to the weak signal will decline the signal-noise-radio（SNR） of the input of the nonlinear system, it will lower the detection effect. Additionally, the resonance point is determined manually, and also obvious offset of the peak position may occur in the result analyzed. Here the novel method was applied to analyze the weak laser-Raman spectrum of a CCl4 sample （liquid in capillary） which was measured with SPEX-1403 laser-Raman-spectrometer from 250 cm-1 to 418 cm-1 on 5 mW （output power of laser）. The spectrum was analyzed with the novel method by varying the data to [-4\^13, 3\^50] and declining μ from 2.0 and compared with the result acquired by wavelet analysis. The results show that the novel method can greatly increase the SNR of input signal easily to detect the weak signal. With the deep research of the theory of stochastic resonance and improvement of the new method, it will probably become a power tool to analyze spectrum.