Stochastic Resonance And Its Application Research Of Fractional Bistable System

Stochastic resonance was used to describe the phenomenon of the Earth's climate at the beginning,it is a nonlinear phenomenon which uses the noise to enhance signal transmission.To date,there have been a lot of research on stochastic resonance of integer order.The fractional system has some abnormalities in comparison with integer order system,which can more accurately describe some abnormal phenomena.This paper first introduces the definition and numerical solution method of fractional calculus,the character of the bistable system.The precondition of generating stochastic resonance phenomenon is to make the particles enough energy to cross the barrier,and the barrier height is closely related to the bistable system.Using fractional numerical methods and integer order Langevin equation deduces the Langevin equation whose order is fraction.There are mainly three parameters to determine stochastic resonance : dwell time distribution,power spectrum and signal-to-noise ratio.Relative to the Gaussian white noise,alpha stable distribution noise of generalized Gaussian distribution is more in line with the realities.When detecting practical failure frequency,the characteristic frequency may be more than one.So it's more practical meaningful to study stochastic resonance phenomenon of multi-frequency fractional-order bistable system in alpha stable distribution noise.Respectively,adjusting the noise intensity,the structural parameters of bistable system and fractional order show that these parameters will affect the output response.In practical production and application,weak signal input and noisy strength and the parameters of nonlinear structure is often unchanged.In order to strengthen the regulation of the system,two bistable systems can be coupled into a much bistable system by using nonlinear methods.Adjusting the coupling coefficient between two systems and structural parameters of the controlling system can make controlled system produce stochastic resonance.Finally,stochastic resonance of fractional order bistable system is studied for the practical application,using the fractional order bistable system detects the fault frequency of rolling bearings.Sampling frequency is compressed to do secondary sampling by the thought of variable scale,the fault frequency detected is restored in comparison with the theoretical value.