Characteristics And Application Research Of Multi-stable Stochastic Resonance With Damping

Enhancing the resonance effect and exploring new resonance phenomena are the keys for the application of stochastic resonance in the actual weak signal detection.The nonlinearity of the system plays a decisive role in the stochastic resonance effect.A multi-stable system has rich nonlinear characteristics and diverse dynamic characteristics.Firstly,in this paper,a multi-stable system with large-scale and small-scale bistable structures is constructed,and the characteristics of multistable stochastic resonance with damping are studied.Then,a two-scale bistable stochastic resonance circuit with variable damping is designed and the experimental analysis is carried out.Finally,the detection method of damping double peaks is proposed.This method has good application effect in the detection of bearing early fault signals and small flow vortex signals.The main research contents of this paper are as follows:(1)According to the complete Langevin equation with the inertial term and the variable damping term,the relationship between Kramers escape rate and damping coefficient is modified.The approximate analytical expression of this system output response is established.Furthermore,the work which is a physical quantity is introduced to measure the strength of the resonance effect from the viewpoint of the energy.Theoretical analysis combined with numerical simulation,the mechanism of double resonance and resonance effect enhancement induced by damping and strong resonance excited by small damping is further revealed.(2)A analog circuit of two-scale bistable stochastic resonance with damping is designed and nonlinear dynamics experiments were carried out.The results show that the best damping makes the resonance effect strongest,and there is also the phenomenon of double stochastic energy resonance induced by damping.The effect of the first resonance caused by small damping is stronger than the second resonance caused by large damping.(3)The weak signal detection method based on damping bimodality is proposed.The early fault signals of bearing inner ring and outer ring and small flow vortex signals are selected for detection.The detection results show that by adjusting the damping coefficient,the system generates resonances of different scales and the double resonances accurately detect the characteristic frequency of the signals to be measured,which confirms each other,and improves the reliability and accuracy of weak signal detection.So the proposed method has a good application prospect.