Research and application of Stochastic Resonance in Quad-stable Potential System

2021 ◽  
Author(s):  
Li-Fang He ◽  
Qiu-Ling Liu ◽  
Tian-Qi Zhang
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Engineering Application ◽  
Reference Value ◽  
Passage Time ◽  
Signal To Noise ◽  
Stationary Probability Distribution ◽  
Potential System ◽  
Practical Engineering

Abstract To solve the problem of low weak signal enhancement performance in the quad-stable system, a new Quad-stable potential Stochastic Resonance (QSR) is proposed. Firstly, under the condition of adiabatic approximation theory, the Stationary Probability Distribution (SPD), the Mean First Passage Time (MFPT), the Work (W) and the power Spectrum Amplification Factor (SAF) are derived, and the impacts of system parameters on them are also deeply analyzed. Secondly, numerical simulations are performed to compare QSR with the Classical Tri-stable Stochastic Resonance (CTSR) by using the Genetic Algorithm (GA) and the fourth-order Runge-Kutta algorithm. It shows that the Signal-to-Noise Ratio (SNR) and Mean Signal-to-Noise Increase (MSNRI) of QSR are higher than CTSR, which indicates that QSR has superior noise immunity than CTSR. Finally, the two systems are applied in the detection on real bearing faults. The experimental results show that QSR is superior to CTSR, which provides a better theoretical significance and reference value for practical engineering application.

Piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance and its application in bearing fault diagnosis

2021 ◽  
pp. 2150280
Author(s):  
Gang Zhang ◽  
Chunlin Tan ◽  
Lifang He
Keyword(s):  
Theoretical Analysis ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Passage Time ◽  
Adaptive Genetic Algorithm ◽  
Exponential Potential ◽  
Steady State Probability ◽  
Bearing Fault ◽  
Practical Engineering

It is difficult to extract weak signals in strong noise background, therefore a piecewise asymmetric exponential potential under-damped bi-stable stochastic resonance (PAEUBSR) system is proposed. First, the theoretical analysis of the steady-state probability density (SPD), mean first passage time (MFPT) and output signal-to-noise ratio (SNR) are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on system performance is explored. Then the PAEUBSR system is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with the exponential potential over-damped symmetric bi-stable stochastic resonance (EOSBSR) system and the exponential potential under-damped symmetric bi-stable stochastic resonance (EUSBSR) system. Finally, the detection results on two sets of bearing fault data show that the PAEUBSR system has better effects on the enhancement and detection of bearing fault signals. This provides good theoretical support and application value for this system in subsequent theoretical analysis and practical engineering applications.

scholarly journals Rotating Elements Fault Diagnosis Method Based on Stochastic Resonance with Triple-well Potential System of Genetic Algorithm

2020 ◽  
Author(s):  
Liu ZiWen ◽  
Bao JinSong ◽  
Xiao Lei ◽  
Wang BoBo
Keyword(s):  
Genetic Algorithm ◽  
Fault Diagnosis ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Fitness Function ◽  
Engineering Application ◽  
Resonance Method ◽  
Rotating Body ◽  
Potential System ◽  
Diagnosis Method

Abstract In engineering applications, the fault signal of rotating elements is easily submerged in the background noise. In order to solve this problem, a rotating body fault diagnosis method based on stochastic resonance with triple-well potential system of genetic algorithm is proposed. In this method, the signal-to-noise ratio(SNR) of the Triple-well potential system is used as the fitness function of the genetic algorithm, and several parameters of the system are optimized at the same time, which effectively improves the feature extraction effect of the weak fault of the rotating body. The results of simulation and engineering experiments show that this method has better detection effect than bistable stochastic resonance method, and can effectively detect the fault signal submerged by noise, which has a good engineering application prospect.

Research and application of tristable stochastic resonance based on harmonic and pinning potential model

2022 ◽  
pp. 107754632110586
Author(s):  
Lifang He ◽  
Yilin Liu ◽  
Gang Zhang
Keyword(s):  
Stochastic Resonance ◽  
Potential Function ◽  
First Passage Time ◽  
Gaussian White Noise ◽  
Reference Value ◽  
Linear Response Theory ◽  
Passage Time ◽  
Two Dimensional ◽  
Dimensional Model ◽  
One Dimensional

In view of the unique potential barrier and complex potential function of the pining model, as well as the lack of researches on two-dimensional stochastic resonance, two new potential tristable models are proposed: one-dimensional tristable model and two-dimensional tristable model. The stochastic resonance mechanism and application of two potential systems under Gaussian white noise and weak external driving force are discussed and the differences and advantages of the two systems are analyzed in detail for the first time. First, the potential function and mean first passage time are analyzed. Second, according to the linear response theory, the probability flow method is used to calculate the spectral amplification. The effects of system parameters on spectral amplification of the two models are studied, and the two models are compared. Finally, the two models are applied to the detection of actual bearing fault signals together with the classical tristable system and the performance is compared. Both algorithms can detect fault signals effectively, but the two-dimensional model has better amplitude and difference, and the one-dimensional model has less interference burrs. The theoretical basis and reference value of the system are provided for further application in practical engineering testing.

scholarly journals Stochastic resonance in periodically driven bistable systems subjected to anomalous diffusion

2021 ◽  
Vol 3 (4) ◽  
Author(s):  
F. Naha Nzoupe ◽  
Alain M. Dikandé
Keyword(s):  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Planck Equation ◽  
Relevant Information ◽  
Periodic Signal ◽  
Signal To Noise ◽  
Periodically Driven ◽  
Loop Area ◽  
Bistable Systems ◽  
Noise Ratio

AbstractThe occurrence of stochastic resonance in bistable systems undergoing anomalous diffusions, which arise from density-dependent fluctuations, is investigated with an emphasis on the analytical formulation of the problem as well as a possible analytical derivation of key quantifiers of stochastic resonance. The nonlinear Fokker–Planck equation describing the system dynamics, together with the corresponding Ito–Langevin equation, is formulated. In the linear response regime, analytical expressions of the spectral amplification, of the signal-to-noise ratio and of the hysteresis loop area are derived as quantifiers of stochastic resonance. These quantifiers are found to be strongly dependent on the parameters controlling the type of diffusion; in particular, the peak characterizing the signal-to-noise ratio occurs only in close ranges of parameters. Results introduce the relevant information that, taking into consideration the interactions of anomalous diffusive systems with a periodic signal, can provide a better understanding of the physics of stochastic resonance in bistable systems driven by periodic forces.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS

1994 ◽  
Vol 04 (02) ◽  
pp. 441-446 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Numerical Simulation ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Signal Distortion ◽  
Signal To Noise ◽  
Chua's Circuit ◽  
Noise Ratio ◽  
Modulated Signals

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).

EFFECT OF ASYMMETRY IN A BISTABLE SYSTEM WITH QUANTUM FLUCTUATIONS: STRONG FRICTION LIMIT

2011 ◽  
Vol 25 (32) ◽  
pp. 4331-4338
Author(s):  
CHUNHUA ZENG ◽  
AILING GONG ◽  
YUHUI LUO
Keyword(s):  
Signal To Noise Ratio ◽  
First Passage Time ◽  
Quantum Fluctuations ◽  
Quantum Effects ◽  
Passage Time ◽  
Bistable System ◽  
Original Position ◽  
Classical Counterpart ◽  
The Mean ◽  
Resonant Activation

In this paper, we study the effect of asymmetry of the potential in a bistable system with quantum fluctuations. Within the quantum Smoluchowski regime, the expressions for the mean first passage time (MFPT) and signal-to-noise ratio (SNR) of the system are obtained, respectively. Based on the MFPT and SNR, we consider both, the overdamped quantum case and its classical counterpart, the effects of the quantum fluctuations and the asymmetry of the potential on the MFPT and SNR are discussed. Our main results show that (i) the quantum fluctuations facilitate the particle to reach the destination from its original position, (ii) the resonant activation (RA) phenomena can be observed with varying asymmetry of the potential, and (iii) the quantum effects in an asymmetric bistable system about SNR are prominent for lower temperatures and smaller asymmetry of the potential. Moreover, the quantum effects enhance the stochastic resonance (SR) of the system.

Stochastic resonance and MFPT in an asymmetric bistable system driven by correlated multiplicative colored noise and additive white noise

2017 ◽  
Vol 31 (14) ◽  
pp. 1750113 ◽  
Author(s):  
Pei-Ming Shi ◽  
Qun Li ◽  
Dong-Ying Han
Keyword(s):  
White Noise ◽  
Stochastic Resonance ◽  
Colored Noise ◽  
First Passage Time ◽  
Passage Time ◽  
State Theory ◽  
Bistable System ◽  
Periodic Signal ◽  
Additive White Noise ◽  
Correlation Strength

This paper investigates a new asymmetric bistable model driven by correlated multiplicative colored noise and additive white noise. The mean first-passage time (MFPT) and the signal-to-noise ratio (SNR) as the indexes of evaluating the model are researched. Based on the two-state theory and the adiabatic approximation theory, the expressions of MFPT and SNR have been obtained for the asymmetric bistable system driven by a periodic signal, correlated multiplicative colored noise and additive noise. Simulation results show that it is easier to generate stochastic resonance (SR) to adjust the intensity of correlation strength [Formula: see text]. Meanwhile, the decrease of asymmetric coefficient [Formula: see text] and the increase of noise intensity are beneficial to realize the transition between the two steady states in the system. At the same time, the twice SR phenomena can be observed by adjusting additive white noise and correlation strength. The influence of asymmetry of potential function on the MFPTs in two different directions is different.

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