Stochastic Resonance Of Nonlinear Fractional Systems And Its Application

Stochastic resonance(SR)is a nonlinear phenomenon that is based on the input weak periodic signal and noise signal.In recent years,a large number of scholars have done a lot of researches on the integer resonance,but the study of fractional stochastic resonance is little.This paper is mainly talked about the stochastic resonance in bistable system.First,the article will introduce the theoretical knowledge of fractional order,the numerical solution of fractional order,and the fractional order Langevin equation.The Langevin equation is the foundation of the study of complexity bistable system,and it is an important theoretical basis for this paper.Second,the article will also introduce the numerical measurement method of stochastic resonance,and its main parameters are included dwell time distribution,power spectrum and signal to noise ratio.What's more,the article will introduce the advantages of the compound bistable system,and the deficiencies of the bistable system of traditional quadratic polynomial.Due to the single structure of the traditional bistable system,the structure of the bistable system becomes simple.And when the parameters of the traditional bistable system are changed,the change of the system is larger,it can't change the single system variably,that is to say,when the parameters are changed,the system potential barrier and the potential well location will be changed a lot,and it is the limitation of the traditional bistable system.The compound bistable system can control the single variable well,so it has a great advantage.Secondly,this paper is mainly studied the advantages of compound bistable system relative to the traditional binomial bistable system.The stochastic resonance induced the test of compound bistable system that is conducted to verify whether the compound bistable system can produce stochastic resonance and its stochastic resonance characteristics.The experimental results show that the stochastic resonance can occur under certain parameters of compound bistable system.Each parameter has some promotion and suppression effect on the stochastic resonance.Then,with the actual situation,the weak periodic signal will be affected by the noise pollution during the actual transmission procedure.The weak signal in the simulation experiment is replaced by the weak periodic signal,and it also conducted the stochastic resonance experiment.The results show that the weak periodic signal of the pollution can also occur stochastic resonance under certain conditions,but the stochastic resonance is affected by the parameters of pollution.Finally,the stochastic resonance phenomenon of fractional order bistable system is introduced and applied to practical rolling bearing fault detection.The fault frequency of the inner ring of rolling bearing is measured by means of experimental signals,and the value of the composite stochastic resonance system in practical application is demonstrated.