Conventional Stochastic Resonance Research Articles

Fault diagnosis of rolling bearing based on the three-dimensional coupled periodic potential-induced stochastic resonance

Abstract Conventional bistable and monostable stochastic resonance (SR) methods exhibit certain limitations in their capacity to enhance and extract incipient characteristics. Firstly, the inherent potential function structure, characterized by a singular stable-state paradigm, proves inadequate in accommodating the heterogeneous and multifaceted condition monitoring signals. Secondly, the interconnected dynamic characteristics of the mechanical signals remain unaccounted for. Furthermore, conventional SR methods persist in utilizing a fixed constant as the critical system parameter, thereby neglecting the synergistic interaction among monitoring signals, potential function structures, and scale factors. Owing to the rich dynamic characteristics of the three-dimensional multi-stable coupled periodic potential SR system, it demonstrates superior noise utilization compared to monostable and bistable systems. In view of this, the present formulates a three-dimensional spatial model employing a coupled periodic potential model with nonlinear coupling. Subsequently, a pioneering method for diagnosing rolling bearing faults is introduced, utilizing the framework of three-dimensional multi-stable coupled periodic potential-induced SR. Simulation and experimental results illustrate that this approach effectively enhances and extracts the subtle fault characteristics of rolling bearings, ensuring a clear distinction between the spectral peak at the bearing fault characteristic frequency and the spectral peak originating from the interference noise.

Thermally driven single-electron stochastic resonance

Stochastic resonance (SR) in a single-electron system is expected to allow information to be correctly carried and processed by single electrons in the presence of thermal fluctuations. Here, we comprehensively study thermally driven single-electron SR. The response of the system to a weak voltage signal is formulated by considering the single-electron tunneling rate, instead of the Kramers’ rate generally used in conventional SR models. The model indicates that the response of the system is maximized at finite temperature and that the peak position is determined by the charging energy. This model quantitatively reproduces the results of a single-electron device simulator. Single-electron SR is also demonstrated using a GaAs-based single-electron system that integrates a quantum dot and a high-sensitivity charge detector. The developed model will contribute to our understanding of single-electron SR and will facilitate accurate prediction, design, and control of single-electron systems.

A New Dynamical Method for Bearing Fault Diagnosis Based on Optimal Regulation of Resonant Behaviors in a Fluctuating-Mass-Induced Linear Oscillator.

Stochastic resonance (SR), a typical randomness-assisted signal processing method, has been extensively studied in bearing fault diagnosis to enhance the feature of periodic signal. In this study, we cast off the basic constraint of nonlinearity, extend it to a new type of generalized SR (GSR) in linear Langevin system, and propose the fluctuating-mass induced linear oscillator (FMLO). Then, by generalized scale transformation (GST), it is improved to be more suitable for exacting high-frequency fault features. Moreover, by analyzing the system stationary response, we find that the synergy of the linear system, internal random regulation and external excitement can conduct a rich variety of non-monotonic behaviors, such as bona-fide SR, conventional SR, GSR, and stochastic inhibition (SI). Based on the numerical implementation, it is found that these behaviors play an important role in adaptively optimizing system parameters to maximally improve the performance and identification ability of weak high-frequency signal in strong background noise. Finally, the experimental data are further performed to verify the effectiveness and superiority in comparison with traditional dynamical methods. The results show that the proposed GST-FMLO system performs the best in the bearing fault diagnoses of inner race, outer race and rolling element. Particularly, by amplifying the characteristic harmonics, the low harmonics become extremely weak compared to the characteristic. Additionally, the efficiency is increased by more than 5 times, which is significantly better than the nonlinear dynamical methods, and has the great potential for online fault diagnosis.

Cooperative mechanism of resonant behaviors in a fluctuating-mass generalized Langevin system with generalized Mittag–Leffler memory kernel

In this study, we investigate the resonant behaviors in the fluctuating-mass generalized Langevin equation (GLE) with generalized Mittag–Leffler (M–L) memory kernel. By using the stochastic averaging method and Laplace transform, we obtain the exact expression of the first-order moment of system steady response, based on which we analyze the dynamical mechanism of the various non-monotonic phenomena. Based on tbe numerical results, we further discuss the dependence on various parameters systematically and study the interplay and cooperation between the generalized M–L memory kernel and trichotomous noise in terms of output amplitude amplification. The results reveal the coexistence of non-monotonic phenomena in the proposed system, such as bona fide stochastic resonance (SR), conventional SR and wide-sense SR. We even observe the stochastic multi-resonance (SMR) behaviors with five or six peaks in the evolution of output amplitude amplification varying with the driving frequency. It is worth emphasizing that quintuple-peak and sextuple-peak bona fide SR phenomena had never been observed in the previous literatures. Thus, these results will provide more extensive support for manipulating the resonant behaviors through system parameter control in the potential applications.

Inverse stochastic resonance in Hodgkin–Huxley neural system driven by Gaussian and non-Gaussian colored noises

Inverse stochastic resonance (ISR) is the phenomenon of the response of neuron to noise, which is opposite to the conventional stochastic resonance. In this paper, the ISR phenomena induced by Gaussian and non-Gaussian colored noises are studied in the cases of single Hodgkin–Huxley (HH) neuron and HH neural network, respectively. It is found that the mean firing rate of electrical activities depends on the Gaussian or non-Gaussian colored noises which can induce the phenomenon of ISR. The ISR phenomenon induced by Gaussian colored noise is most obvious under the conditions of low external current, low reciprocal correlation rate and low noise level. The ISR in neural network is more pronounced and lasts longer than the duration of a single neuron. However, the ISR phenomenon induced by non-Gaussian colored noise is apparent under low noise correlation time or low departure from Gaussian noise, and the ISR phenomena show different duration ranges under different parameter values. Furthermore, the transition of mean firing rate is more gradual, the ISR lasts longer, and the ISR phenomenon is more pronounced under the non-Gaussian colored noise. The ISR is a common phenomenon in neurodynamics; our results might provide novel insights into the ISR phenomena observed in biological experiments.

Stability and Stochastic Resonance for a Time-Delayed Cancer Development System Subjected to Noises and Multiplicative Periodic Signal

In this paper, the stability and the phenomenon of stochastic resonance (SR) for a stochastic time-delayed cancer development system that is induced by the multiplicative periodic signal, the multiplicative and the additive noises are investigated. By using the fast descent method, small time delay method and the two-state theory, the expressions of the steady state probability distribution function and the signal-to-noise ratio (SNR) are obtained. Numerical results reflect that the multiplicative and additive noise always restrain the diffusion of the cancer cells. Whereas, the time delay can not only control the spread of the tumor cells, but also suppress the extinction of cancer cells. Meanwhile, the conventional SR occurs in the tumor cell growth model under the excitation of different noises and time delay. In conclusion, the multiplicative noise always plays a critical role in restraining SR, a smaller additive noise can stimulate the SR, but the larger additive noise can weaken the SR and SNR. In particular, the time delay displays relatively complicated effects on the SR phenomenon of the system. It plays different roles in motivating or suppressing SR under the different conditions of parameters.

An adaptive stochastic resonance method based on grey wolf optimizer algorithm and its application to machinery fault diagnosis

Stochastic resonance (SR) is widely used as an enhanced signal detection method in machinery fault diagnosis. However, the system parameters have significant effects on the output results, which makes it difficult for SR method to achieve satisfactory analysis results. To solve this problem and improve the performance of SR method, this paper proposes an adaptive SR method based on grey wolf optimizer (GWO) algorithm for machinery fault diagnosis. Firstly, the SR system parameters are optimized by the GWO algorithm using a redefined signal-to-noise ratio (SNR) as optimization objective function. Then, the optimal SR output matching the input signal can be adaptively obtained using the optimized parameters. The proposed method is validated on a simulated signal detection and a rolling element bearing test bench, and then applied to the gear fault diagnosis of electric locomotive. Compared with the conventional fixed-parameter SR method, the adaptive SR method based on genetic algorithm (GA-SR) as well as the well-known fast kurtogram method, the proposed method can achieve a greater accuracy. The results indicated that the proposed method has great practical values in engineering.

Chaotic Resonance in Coupled Inferior Olive Neurons with the Llinás Approach Neuron Model.

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron's characteristics, but it was not as easy for SR.

Weak impulsive signals detection based on step-varying asymmetric stochastic resonance

Rotating machinery response is often characterized by the presence of periodic impulses modulated by high-frequency components. The fault information is often hidden in its envelope signal which is unilateral when demodulated. Conventional stochastic resonance with a symmetric potential cannot always contain the signal’s original features especially the asymmetry. In this article, a step-varying asymmetric stochastic resonance system for impulsive signal denoising and recovery as well as the rotating machine fault diagnosis is proposed to further improve the impulsive signal-to-noise ratio. In the method, the asymmetry of step-varying asymmetric stochastic resonance can match the unilateral impulsive signal well to generate an optimal dynamic system by selecting proper system parameters and degree of asymmetry. Systems with different simulated or experimental signals are also studied to verify its effectiveness and availability. Results indicate that the step-varying asymmetric stochastic resonance performs much better in detection of impulsive signal than the conventional stochastic resonance with merits of good frequency response, anti-noise capability, adaptability to asymmetric signal and original waveform preserving.

Stochastic resonance in a piecewise nonlinear model driven by multiplicative non-Gaussian noise and additive white noise

The phenomenon of stochastic resonance (SR) in a piecewise nonlinear model driven by a periodic signal and correlated noises for the cases of a multiplicative non-Gaussian noise and an additive Gaussian white noise is investigated. Applying the path integral approach, the unified colored noise approximation and the two-state model theory, the analytical expression of the signal-to-noise ratio (SNR) is derived. It is found that conventional stochastic resonance exists in this system. From numerical computations we obtain that: (i) As a function of the non-Gaussian noise intensity, the SNR is increased when the non-Gaussian noise deviation parameter q is increased. (ii) As a function of the Gaussian noise intensity, the SNR is decreased when q is increased. This demonstrates that the effect of the non-Gaussian noise on SNR is different from that of the Gaussian noise in this system. Moreover, we further discuss the effect of the correlation time of the non-Gaussian noise, cross-correlation strength, the amplitude and frequency of the periodic signal on SR.

Stochastic Resonance in an Underdamped System with Pinning Potential for Weak Signal Detection.

Stochastic resonance (SR) has been proved to be an effective approach for weak sensor signal detection. This study presents a new weak signal detection method based on a SR in an underdamped system, which consists of a pinning potential model. The model was firstly discovered from magnetic domain wall (DW) in ferromagnetic strips. We analyze the principle of the proposed underdamped pinning SR (UPSR) system, the detailed numerical simulation and system performance. We also propose the strategy of selecting the proper damping factor and other system parameters to match a weak signal, input noise and to generate the highest output signal-to-noise ratio (SNR). Finally, we have verified its effectiveness with both simulated and experimental input signals. Results indicate that the UPSR performs better in weak signal detection than the conventional SR (CSR) with merits of higher output SNR, better anti-noise and frequency response capability. Besides, the system can be designed accurately and efficiently owing to the sensibility of parameters and potential diversity. The features also weaken the limitation of small parameters on SR system.

Stochastic resonance and stability for a time-delayed cancer growth system subjected to multiplicative and additive noises

In the present paper, the steady-state properties of a time-delayed cancer growth system that is driven by a correlated multiplicative noise and an additive one are investigated. The numerical results show that the conventional stochastic resonance (SR) phenomenon occurs in the tumor cell growth model for different system parameter values. The results indicate that the additive noise strength always weakens the SR phenomenon, while the time delay mainly increases the SR phenomenon. On the other hand, it is shown that the effects of the strength of the multiplicative noise are different.

Stochastic resonance in a harmonic oscillator with fractional-order external and intrinsic dampings

In this paper, the phenomenon of stochastic resonance (SR) in a harmonic oscillator with fractional-order external and intrinsic dampings under the external periodic force is investigated. Applying the Shapiro–Loginov formula, fractional Shapiro–Loginov formula, generalized fractional Shapiro–Loginov formula and the Laplace transform technique, we obtain the analytic expressions of the first moment and the amplitude of the output signal. By studying the impacts of the driving frequency, system parameters and the noise parameters, we find the non-monotonic behaviors of the output amplitude. The results indicate that the bona fide SR, the generalized SR and the conventional SR phenomena occur in the proposed model. Furthermore, the numerical simulations are presented to verify the effectiveness of the analytic result.

Effect of Time Delay and Cross-Correlated Noises on Stochastic Resonance for a Metapopulation System with a Multiplicative Periodic Signal

In this paper, stochastic resonance (SR) in a time-delayed metapopulation system subjected to cross-correlated noises and a multiplicative signal is investigated. By using the fast descent method and the two-state theory, we obtain the expression of the signal-to-noise ratio (SNR). Numerical results show that the conventional SR phenomenon appears in the metapopulation model under different values of the system parameters. The results demonstrate that the strength of the correlation noise λ always plays a decisive role in motivating the SR phenomenon. On the other hand, for the case of λ ＞ 0, the intensities of the multiplicative and additive noises and the time delay can all weaken the effect of SR; for the case of λ ＜ 0, the multiplicative noise can restrain the effect of SR, the weak additive noise can excite the effect of SR, the time delay τ can produce different effects on the SNR under the conditions of different parameters.

Stochastic resonance in FizHugh-Nagumo model driven by multiplicative signal and non-Gaussian noise

The stochastic resonance phenomenon in FizHugh-Nagumo neural system induced by a multiplicative periodic signal and non-Gaussian noise is studied. Based on path integral approach and two-state theory, the Fokker–Planck equation and signal-to-noise ratio are derived. By analyzing the influence of different parameters in the optimization of signal-to-noise ratio, we observe that the conventional stochastic resonance and double stochastic resonance occur in FizHugh-Nagumo neural model under different values of system parameters. Furthermore, there is a critical value of non-Gaussian noise intensity D, above which the increase of D weakens the resonant effect and below which it enhances the resonant effect.

Stochastic resonance in an over-damped linear oscillator

For an over-damped linear system subjected to both parametric excitation of colored noise and external excitation of periodically modulated noise, and in the case that the cross-correlation intensity between noises is a time-periodic function, we study the stochastic resonance (SR) in this paper. Using the Shapiro—Loginov formula, we acquire the exact expressions of the first-order and the second-order moments. By the stochastic averaging method, we obtain the analytical expression of the output signal-to-noise ratio (SNR). Meanwhile, we discuss the evolutions of the SNR with the signal frequency, noise intensity, correlation rate of noise, time period, and modulation frequency. We find a new bona fide SR. The evolution of the SNR with the signal frequency presents periodic oscillation, which is not observed in a conventional linear system. We obtain the conventional SR of the SNR with the noise intensity and the correlation rate of noise. We also obtain the SR in a wide sense, in which the evolution of the SNR with time period modulation frequency presents periodic oscillation. We find that the time-periodic modulation of the cross-correlation intensity between noises diversifies the stochastic resonance phenomena and makes this system possess richer dynamic behaviors.

Stochastic Resonance for a Cancer Growth System Subjected to Correlated Multiplicative and Additive Noises

In the present paper, the phenomena of stochastic resonance (SR) for a stochastic cancer development system that is driven by correlated multiplicative and additive noises is investigated. By using the fast descent method and the two-state theory, the expression of the signal-to-noise ratio (SNR) is obtained. Numerical results show that conventional SR occurs in the cancer growth model under different values of the system parameters. If the correlation strength between the two noises is positive or negative, the effects of the addictive noise intensity, the multiplicative noise intensity, and the correlated noise strength on the SNR are different.

A Novel Parameter-Tuned Stochastic Resonator for Binary PAM Signal Processing at Low SNR

To improve the receiving performance of binary pulse amplitude modulated (BPAM) signal at low signal-to-noise ratio (SNR), a novel parameter-tuned stochastic resonator (PSR) is proposed. In this letter, we propose a new method for PSR which combines the conventional stochastic resonance (SR) approach based on classic adiabatic approximation theory with the non-conventional SR approach based on parameter tuned theory. Based on this method, we derive an analytical expression of the parameters of SR system. By tuning the parameters of SR system according to the proposed method, there exists a cooperative effect that the BPAM signal is enhanced by the background noise, and the PSR-based receiver is easy to be implemented. Simulation results demonstrate that the bit error ratio (BER) performance of the nonlinear PSR-based receiver is superior to the linear optimal receiver at low SNR.

Stochastic resonance in a piecewise nonlinear system driven by colored correlated additive and multiplicative colored noises

In this paper, we study the stochastic resonance in a piecewise nonlinear system driven by a periodic signal and colored noises, which is described by multiplicative and additive colored noises with colored cross-correlation. Using the two-state theory and the unified colored approximation, we can derive the analytical expressions of the steady-state probability density and the signal-to-noise ratio (SNR). Effects of colored noises and the periodic signal on SNR are presented. It is found that the conventional stochastic resonance and bona-fide stochastic resonance may exist in this system. Moreover, the value of the SNR peak decreases with increasing correlation time and correlation between the additive and multiplicative noises.

Stochastic resonance of a memorial-damped linear system with natural frequency fluctuation

The stochastic resonance is investigated in the generalized Langevin equation with exponential memory kernel subjected to the joint action of internal noise, external noise and external sinusoidal forcing. The system is converted into three-dimensional Markovian Langevin equations. Furthermore, using the Shapiro-Loginov formula and the Laplace transformation technique, the exact expressions of the first moment and the steady response amplitude are obtained. The research results show that with the variations of external sinusoidal force frequency and the parameters of memory kernel and external noise, the system presents bona-fide stochastic resonance, conventional stochastic resonance and stochastic resonance in a broad sense under the condition of Routh-Hurwitz stability. In addition, the stochastic resonance can be weakened as the memory time increases. Moreover, the numerical results of power spectrum of system are in agreement with the analytic results.