Stochastic Resonance in an Asymmetric Bistable System Subject to Frequency Mixing Periodic Force and Noise

2005 ◽  
Vol 22 (5) ◽  
pp. 1061-1064 ◽  
Author(s):  
Jin Yan-Fei ◽  
Xu Wei ◽  
Xu Meng
Keyword(s):  
Stochastic Resonance ◽  
Bistable System ◽  
Periodic Force ◽  
Frequency Mixing

Adaptive stochastic resonance in bistable system driven by noisy NLFM signal: phenomenon and application

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200239 ◽  
Author(s):  
Chen Yang ◽  
Jianhua Yang ◽  
Dengji Zhou ◽  
Shuai Zhang ◽  
Grzegorz Litak
Keyword(s):  
Stochastic Resonance ◽  
Bistable System ◽  
Nonlinear Frequency ◽  
Bearing Fault Diagnosis ◽  
Mode Function ◽  
Mode Decomposition ◽  
Stationary Signals ◽  
Fourier Transform Spectrum ◽  
Short Time ◽  
Sr Method

The stochastic resonance (SR) in a bistable system driven by nonlinear frequency modulation (NLFM) signal and strong noise is studied. Combined with empirical mode decomposition (EMD) and piecewise idea, an adaptive piecewise re-scaled SR method based on the optimal intrinsic mode function (IMF), is proposed to enhance the weak NLFM signal. At first, considering the advantages of EMD for dealing with non-stationary signals, the segmented NLFM signal is processed by EMD. Meanwhile, the cross-correlation coefficient is used as the measure to select the optimal IMF that contains the NLFM signal feature. Then, the spectral amplification gain indicator is proposed to realize the adaptive SR of the optimal IMF of each sub-segment signal and reconstruct the enhanced NLFM signal. Finally, the effectiveness of the proposed method is highlighted with the analysis of the short-time Fourier transform spectrum of the simulation results. As an application example, the proposed method is verified adaptability in bearing fault diagnosis under the speed-varying condition that represents a typical and complicated NLFM signal in mechanical engineering. The research provides a new way for the enhancement of weak non-stationary signals. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

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.

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