Research And Application Of Piecewise Nonlinear Bistable And Exponential Power Function Combination Type Stochastic Resonance System

Weak signal detection technology is a method to extract weak signals from strong background noise in the fields of biomedical,image processing,mechanical fault detection,radar system,geology and so on.The traditional noise processing method is to use different noise reduction technology to deal with the impact of noise,but it also weakens the energy of the signal.This thesis first introduces the rise of chaotic oscillator and Stochastic Resonance(SR)detection with the development of nonlinear science.This thesis focuses on Stochastic resonance detection technology,which uses the synergistic effect among signals,nonlinear system and noise to enhance detection,which changes the viewpoint that noise is harmful in weak signal detection in the past.Firstly,this thesis briefly introduces the development status of stochastic resonance.Based on the classical bistable stochastic resonance(CBSR)system,the applications of the piecewise nonlinear bistable type system,the delay feedback exponential monostable system and exponential power function combination type system in weak signal detection are mainly studied.The main works and innovation points of the thesis are summarized as following:(1)Based on the output saturation of traditional bistable random resonance,a new type of piecewise nonlinear bistable(PNB)potential function is constructed.The mean signal-to-noise ratio gain is regarded as an index to measure the stochastic resonance phenomenon.The laws for the resonant output of piecewise nonlinear bistable system are explored under the Levy noise.Then the quantum particle swarm optimization algorithm is used to find the optimal range of system parameters,so that weak signals,noises and nonlinear system can produce the best stochastic resonance effect.At the same time,the influence of the characteristic index,the symmetry parameter and the system coefficient of Levy noise on the output of PNBSR system is analyzed.Finally,the ouput influence of system parameters on PNBSR phenomenon under different distribution environments of Levy noise is explored,and the application of PNBSR in bearing fault signal diagnosis.The practical value of piecewise nonlinear bistable stochastic resonance system is demonstrated.(2)Based on the exponential monostable potential,an exponential monostable system with time-delayed feedback driven by weak periodic signals and additive Gaussian white noises is studied.The small delay approximation is used to deduce the steady-state probability distribution and the effective potential function is derived.The mean first-passage time(MFPT)is calculated,which plays an extremely important role in the research of particles escape.And the signal-to-noise ratio(SNR)of the system can be obtained by using the adiabatic approximation theory.Finally,the phenomenon of stochastic resonance is investigated under different system parameters and time-delayed feedback parameters.(3)The exponential function and the power function are organically combined together.An exponential power combination bistable(EPCB)system model power functions is proposed.Firstly,the stochastic resonance phenomenon of EPCB system with output SNR varying with noise intensity D under different system parameters is analyzed theoretically.This is the setup for the actual detection.Then the proposed EPCB system is used to detect low-frequency and high-frequency weak periodic signals,as well as simulated attenuated impulse signals.The effectiveness of EPCB system in practical application is verified.Finally,the EPCB system is used to detect bearing fault.The fault detection of the outer ring and inner ring of the bearing is realized and compared with the fault detection of CBSR system.