Stochastic resonance in FitzHugh–Nagumo system with time-delayed feedback

2008 ◽  
Vol 372 (32) ◽  
pp. 5299-5304 ◽  
Author(s):  
Dan Wu ◽  
Shiqun Zhu
Keyword(s):  
Stochastic Resonance ◽  
Delayed Feedback ◽  
Time Delayed Feedback

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

Enhanced Rotating Machine Fault Diagnosis Based on Time-Delayed Feedback Stochastic Resonance

2015 ◽  
Vol 137 (5) ◽  
Author(s):  
Siliang Lu ◽  
Qingbo He ◽  
Haibin Zhang ◽  
Fanrang Kong
Keyword(s):  
Fault Diagnosis ◽  
Signal Detection ◽  
Stochastic Resonance ◽  
Delayed Feedback ◽  
Weak Signal ◽  
Noise Interference ◽  
Rotating Machine ◽  
Machine Fault Diagnosis ◽  
Machine Fault ◽  
Time Delayed Feedback

The fault-induced impulses with uneven amplitudes and durations are always accompanied with amplitude modulation and (or) frequency modulation, which leads to that the acquired vibration/acoustic signals for rotating machine fault diagnosis always present nonlinear and nonstationary properties. Such an effect affects precise fault detection, especially when the impulses are submerged in heavy background noise. To address this issue, a nonstationary weak signal detection strategy is proposed based on a time-delayed feedback stochastic resonance (TFSR) model. The TFSR is a long-memory system that can utilize historical information to enhance the signal periodicity in the feedback process, and such an effect is beneficial to periodic signal detection. By selecting the proper parameters including time delay, feedback intensity, and calculation step in the regime of TFSR, the weak signal, the noise, and the potential can be matched with each other to an extreme, and consequently a regular output waveform with low-noise interference can be obtained with the assistant of the distinct band-pass filtering effect. Simulation study and experimental verification are performed to evaluate the effectiveness and superiority of the proposed TFSR method in comparison with a traditional stochastic resonance (SR) method. The proposed method is suitable for detecting signals with strong nonlinear and nonstationary properties and (or) being subjected to heavy multiscale noise interference.

Asymmetric stochastic resonance under non-Gaussian colored noise and time-delayed feedback

2020 ◽  
Vol 29 (5) ◽  
pp. 050501 ◽  
Author(s):  
Ting-Ting Shi ◽  
Xue-Mei Xu ◽  
Ke-Hui Sun ◽  
Yi-Peng Ding ◽  
Guo-Wei Huang
Keyword(s):  
Stochastic Resonance ◽  
Colored Noise ◽  
Delayed Feedback ◽  
Gaussian Colored Noise ◽  
Non Gaussian ◽  
Time Delayed Feedback

Stochastic resonance in deformable potential with time-delayed feedback

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200234 ◽  
Author(s):  
Y. J. Wadop Ngouongo ◽  
M. Djolieu Funaye ◽  
G. Djuidjé Kenmoé ◽  
T. C. Kofané
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Brownian Particle ◽  
Delayed Feedback ◽  
Memory Effects ◽  
Loop Area ◽  
Feedback Strength ◽  
Hysteresis Loop Area ◽  
Time Delayed Feedback ◽  
With Memory

This paper reports the stochastic resonance (SR) phenomenon with memory effects for a Brownian particle in a potential whose shape is subjected to deformation. We model the deformation in the system by the Remoissenet–Peyrard potential and the memory effects by the time-delayed feedback. The question of the possible influence of time-delayed feedback on the occurrence of SR is then of our interest. We examine numerically the effect of feedback strength as well as time delay on SR phenomenon in terms of hysteresis loop area. It is found that time-delayed feedback has a significant effect on SR and can induce double resonances in the system. We show that the properties of SR are varying, depending on interdependence between feedback strength, time delay and shape parameter. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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