Research On The Principle,Control And Application Of Fractional Stochastic Resonance

Fractional calculus has features such as time memory and extensive spatial correlation,so that it is more accurate than the integer order to describe the memory and genetic,path-dependent nature of the physical process and the actual project.It has been widely studied in recent years,but the mathematical theory of fractional calculus differential equation is still in the initial research stage.On the other hand,due to the complexity of the fractional dynamical system structure and the fact that the signal and noise are often unknown and cannot be adjusted in real engineering,how to realize the control of fractional stochastic resonance is the key to solve the practical engineering application.In this paper,the theoretical basis of fractional order is analyzed,an improved Oustaloup numerical simulation algorithm is proposed and a modular encapsulation is carried out in Matlab Simulink.A fractional stochastic dynamical system based on Langevin equation and Gaussian white noise is constructed.The stochastic resonance behavior of the system is analyzed,the stochastic resonance phenomena are found with different parameters and the influence of the parameters on the stochastic resonance is analyzed.Due to the complexity of the system structure,the fractional stochastic resonance generation mode still stays in the simulation stage of "attempting".This cumbersome and time-consuming determination method is very detrimental to the control of fractional stochastic resonance.Therefore,the concept of coupled system is introduced,and the control of fractional stochastic dynamical system is realized by adjusting the parameters of resonance controller.Alpha stable noise is a more widely distributed random distribution than Gaussian white noise.Based on the fractional stochastic dynamical system with alpha stable noise,the power spectrum of the output signal under different system parameters are observed.In the background of stable noise,the feasibility of stochastic resonance is achieved by adjusting the parameters of the system.When the potential function is bistable function and Gaussian white noise as the excitation and the applied signal is cosine function and the logical square wave,the paper analyzes the logical stochastic resonance phenomenon of the system described by the fractional Langevin equation.The results show that when the fractional order is less than the critical value,even if no additional Gaussian white noise or weak periodic signal the logical stochastic resonance phenomenon can be observed;when the fractional order is greater than the critical value,the additional Gaussian white noise or weak periodic signal is necessary,the success rate of logical output can be increased by appropriate noise intensity,amplitude and frequency of weak periodic signal.In the last,the paper discusses the application of fractional stochastic resonance in two aspects.First,aiming at the problem that failure detection of the rolling bearing,the experimental results show that the characteristic frequency of the fault can be extracted from the weak noise background and the strong noise background.Second,aiming the binary baseband signal is affected by the noise during the transmission process,taking the error rate of logical output as performance,the simulation results show that the binary baseband signal under strong noise background can be recovered by this method.