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 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.     

Double Gaussian potential stochastic resonance method and its application in centrifugal fan blade crack detection

Stochastic resonance (SR) has been extensively utilized in the field of weak fault signal detection for its characteristic of enhancing weak signals by transferring the noise energy. Aiming at solving the output saturation problem of the classical bistable stochastic resonance (CBSR) system, a double Gaussian potential stochastic resonance (DGSR) system is proposed. Moreover, the output signal-to-noise ratio (SNR) of the DGSR method is derived based on the adiabatic approximation theory to analyze the effect of system parameters on the DGSR method. At the same time, for the purpose of overcoming the drawback that the traditional SNR index needs to know the fault characteristic frequency (FCF), the weighted local signal-to-noise ratio (WLSNR) index is constructed. The DGSR with WLSNR can obtain optimal parameters adaptively, thereby establishing the DGSR system. Ultimately, a DGSR method is proposed and applied in centrifugal fan blade crack detection. Through simulations and experiments, the effectiveness and superiority of the DGSR method are verified.     

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.     

Characteristics of piecewise linear symmetric tri-stable stochastic resonance system and its application under different noises

Weak signal detection has become an important means of mechanical fault detections. In order to solve the problem of poor signal detection performance in classical tristable stochastic resonance system (CTSR), a novel unsaturated piecewise linear symmetric tristable stochastic resonance system (PLSTSR) is proposed. Firstly, by making the analysis and comparison of the output and input relationship between CTSR and PLSTSR, it is verified that the PLSTSR has good unsaturation characteristics. Then, on the basis of adiabatic approximation theory, the Kramers escape rate, the mean first-passage time (MFPT), and output signal-to-noise ratio (SNR) of PLSTSR are deduced, and the influences of different system parameters on them are studied. Combined with the adaptive genetic algorithm to synergistically optimize the system parameters, the PLSTSR and CTSR are used for numerically simulating the verification and detection of low-frequency, high-frequency, and multi-frequency signals. And the results show that the SNR and output amplitude of the PLSTSR are greatly improved compared with those of the CTSR, and the detection effect is better. Finally, the PLSTSR and CTSR are applied to the bearing fault detection under Gaussian white noise and Levy noise. The experimental results also show that the PLSTSR can obtain larger output amplitude and SNR, and can detect fault signals more easily, which proves that the system has better performance than other systems in bearing fault detection, and has good theoretical significance and practical value.     

α稳定噪声环境下多频微弱信号检测的参数诱导随机共振现象

本文将α稳定噪声与双稳随机共振系统相结合, 研究了不同α稳定噪声环境下高低频(均为多频)微弱信号检测的参数诱导随机共振现象, 探究了α稳定噪声的特征指数α(0 < α ≤ 2)和对称参数β (-1≤ β ≤ 1)及随机共振系统参数a, b对共振输出效应的作用规律. 研究结果表明, 在不同分布的α稳定噪声环境下, 通过调节系统参数a和b均可诱导随机共振来实现多个高、低频微弱信号的检测, 且存在多个a, b参数区间均可诱导随机共振, 这些区间不随α或β的变化而变化; 在高、低频微弱信号检测中, α或β对随机共振输出效应的作用规律相同. 本研究结果将有助于α稳定噪声环境下参数诱导随机共振现象中系统参数的合理选取, 进而可为实现基于随机共振的多频微弱信号检测方法的工程应用奠定基础. 关键词： 随机共振 α稳定噪声')" href="#">α稳定噪声 多频微弱信号检测 平均信噪比增益     

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.     

Analysis of weak signal detection based on tri-stable system under Levy noise

Stochastic resonance system is an effective method to extract weak signal.However,system output is directly influenced by system parameters.Aiming at this,the Levy noise is combined with a tri-stable stochastic resonance system.The average signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The characteristics of tri-stable stochastic resonance under Levy noise is analyzed in depth.First,the method of generating Levy noise,the effect of tri-stable system parameters on the potential function and corresponding potential force are presented in detail.Then,the effects of tri-stable system parameters w,a,b,and Levy noise intensity amplification factor D on the resonant output can be explored with different Levy noises.Finally,the tri-stable stochastic resonance system is applied to the bearing fault detection.Simulation results show that the stochastic resonance phenomenon can be induced by tuning the system parameters w,a,and b under different distributions of Levy noise,then the weak signal can be detected.The parameter intervals which can induce stochastic resonances are approximately equal.Moreover,by adjusting the intensity amplification factor D of Levy noise,the stochastic resonances can happen similarly.In bearing fault detection,the detection effect of the tri-stable stochastic resonance system is superior to the bistable stochastic resonance system.     

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。     

Improving the Stochastic Resonance in a Bistable System with the Bounded Noise Excitation

Journal of Statistical Physics - The stochastic resonance (SR) phenomenon is investigated in a typical bistable system that excited by the bounded noise and the weak low-frequency signal...     

Asymmetric delay feedback stochastic resonance detection method based on prior knowledge particle swarm optimization

For the adjustable parameters stochastic resonance system, the selection of the structural parameters plays a decisive role in the performance of the detection method. The vibration signal of rotating machinery is non-linear and unstable, and its weak fault characteristics are easily concealed by noise. Under strong background noise interference, the detection of fault features is particularly challenging. Therefore, a type of weak fault feature extraction method, named knowledge-based particle swarm optimization algorithm for asymptotic delayed feedback stochastic resonance (abbreviated as KPSO-ADFSR) is proposed. Through deduction under adiabatic approximation, we observe that both the asymmetric parameters, the length of delay and the feedback strength, impact the potential function. After adjusting the asymmetric parameters of the system, the output signal-to-noise ratio (SNR) is used as the fitness function, and the setting of the relationship between the noise intensity and barrier height is used as the prior knowledge of the particle swarm algorithm. Through this algorithm, the delay length and the feedback strength are optimized. This method achieves global optimization of system parameters in a short time; it overcomes the shortcomings of the traditional stochastic resonance method, which has a long convergence time and tends to easily fall into local optimization. It can effectively improve the detection of weak fault features. In the bearing rolling body pitting corrosion failure experiment and steel field engineering experiment, the proposed method could extract the characteristics of a weak fault more effectively than the traditional stochastic resonance method based on the standard particle swarm algorithm.     

基于振动共振的随机共振控制

分析了非线性双稳系统在高、低两种不同频率信号作用下的动力学特性，给出了高频信号参数与双稳系统输出信号的信噪比和功率谱放大率关系的解析表达式，提出了基于振动共振的随机共振控制方法.理论分析和数值仿真结果表明，通过调节高频信号的幅值或频率大小，能有效地控制双稳系统输出信号的信噪比和功率谱放大率.     

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.     

基于随机共振进行弱信号探测的实验研究

非线性随机共振系统可利用噪声增强微弱信号检测的能力,为强噪声背景下微弱信号的检测开创了新方法.基于随机共振的基本原理设计了硬件电路系统,并将其应用于检测单频和多频微弱信号;通过输入模拟工程实际的带噪信号,采样所得的输出信号的频谱分析结果表明,利用随机共振技术可从强噪声背景下有效地提取出单频和多频弱信号.多频弱信号的有效提取拓展了基于随机共振原理的弱信号检测技术的应用领域,结合数字滤波处理技术有效地消除了低频噪声对信号识别的影响.基于随机共振的弱信号检测技术在信息识别与信息处理方面具有巨大的潜在的应用价值.     

利用随机共振在强噪声下提取信息信号

已有利用随机共振在强噪声下提取单一频率信号的若干报道，但单一频率信号所携带的信息量为零.本实验研究表明：在调幅波和白噪声的协同作用下，非线性双稳系统的输出不仅可以呈现随机共振现象，而且经检波、滤波后能提取出调制信号(信息信号)；与直接经电子学系统检波、线性滤波后所提取的调制信号相比，前者所获调制信号的信噪比更高.给出了绝热近似条件下，调制信号信噪比的解析表达式. 关键词： 随机共振 信噪比 调制信号 噪声     

Stochastic resonance in multi-scale bistable array

This Letter explores a new mechanism of stochastic resonance (SR) that is induced by the multi-scale noise decomposed from the input signal, which is promising in signal detection and processing under heavy background noise. The input signal is firstly decomposed to multi-scale signals by orthogonal wavelet transform. Then, the approximate signal, which contains the driving signal, is processed by an uncoupled parallel bistable array with the detailed signal of each scale as the internal noise. At last, a SR mechanism combining the effects of colored noise and array SR is proposed. The simulation results show that a high quality output signal can be obtained by the new mechanism. The proposed model is more adaptive to input signal with high noise intensity than single bistable SR system, which can be seen from the signal-to-noise ratio curves and average noise intensity curves.     

二次采样随机共振频谱研究与应用初探

研究了双稳系统随机共振频谱的洛伦兹分布特征，得出在谱分布能量较集中的低频区才能产生可辨识的随机共振谱峰. 探讨了大参数信号双稳系统的二次采样随机共振的频谱特性. 以强噪声中弱信号的检测为实例，阐述了二次采样随机共振技术的具体应用. 关键词： 随机共振 二次采样随机共振 双稳系统 频谱     

大参数周期信号随机共振解析

通过调节双稳系统参数实现大参数频率范围内周期信号的随机共振, 在工程上具有重要意义. 推导了双稳系统参数的归一化变换, 利用归一化变换原理对大参数周期信号的随机共振进行了数值仿真, 阐明该原理适用于任意频率周期信号. 对大参数随机共振用电路模拟进行了实验验证, 揭示了通过调节双稳系统参数可以实现大参数频率范围内的随机共振. 分析了二次采样实现大参数周期信号随机共振的机理, 通过数值仿真与参数归一化变换方法进行了比较. 仿真结果表明, 在输入信号幅度变化的情况下, 二次采样方法易出现发散现象, 而归一化变换具有更好的稳定性与适应性.     

Signal-to-Noise Ratio in Bistable System Subject to Signal and Monochromatic Noise

Signal- to-noise ratio (SNR) of stochastic resonance under white noise is smaller than thatproduced by linear filter under the same condition. For bistable system acted by signal ofproper strength and equal-frequency (monochromatic) noise in certain range, the outputSNR can be greater than that of the linear system under the same condition. Therefore, itcan provide a method superior to linear filter of acquiring signal from noise.     

双稳系统随机共振的反馈控制

将双稳系统的输出反馈到输入端再作用于系统,提出了采用反馈来控制随机共振的方法.以典型双稳系统为对象,并以信噪比和功率谱放大率作为度量随机共振效应的可观察变量,分别研究了采用线性或非线性反馈函数所产生的随机共振现象.理论分析和数值仿真结果表明随机共振是可控制的.该方法特别适用于系统参数固定或难以改变的系统. 关键词： 双稳系统 随机共振 反馈控制 共振效应