Research And Application Of Stochastic Resonance System Based On Cascaded Tristable And Improved Potential Function

Weak signal detection technology is an emerging technology discipline in modern times.It is a signal processing method that extracts weak signals from noise.This technology has a wide range of applications,involving aerospace technology,biomedicine,image processing,electronic science,industrial inspection and so on.Most of the traditional signal detection methods improve the system's output signal-to-noise ratio(SNR)by eliminating or suppressing noise,but these methods may also eliminate the signals which are measured.The new method of stochastic resonance(SR)detection utilizes noise,and transfer part of the energy of the noise to the signal through the synergy of the non-linear system,signal and noise,so as to achieve the purpose of detecting the signal.SR detection method makes up for the shortcomings of traditional signal detection method.This unique signal processing method makes it develop rapidly in the field of signal detection.The thesis introduces the background of weak signal detection and the development history and current situation of SR in detail.Based on the existed theory,it focuses on the research of the cascaded tristable systems and two improved potential functions.The main work and innovations of the thesis are as follows:1.This thesis studies the SR characteristics of cascaded tristable systems driven by Levy noise,discusses the relationship between the characteristic index of Levy noise,symmetry parameters,noise intensity and the output of cascaded tristable SR systems.and studies the influence of system parameters on the phenomenon of cascaded tristable SR under adaptive optimization.The cascaded tristable system is used to detect the high-frequency and low-frequency signals.Comparing the detection results of the two-stage system,it is found that the performance of the SR system can be enhanced by cascading.2.The New Woods-Saxon model and the Gaussian model are efficiently and organically combined to form a new potential function model—the NWSG system model.Firstly,the SR phenomenon of NWSG system driven by ternary noise is studied,and it is found that NWSG system can transform among three kinds of steady-state under different parameter conditions;Then,the system is applied to signal detection and compared with the traditional three kinds of steady-state SR system;Finally,the NWSG system is used to diagnose the bearing fault signal and compared with the classical bistable system.Thesimulation results show that the NWSG system has better detection effect than the traditional SR system.3.The time-delayed feedback ecological vegetation growth(EVG)system is used as a model to analyze the SR phenomenon in detail.The equivalent potential function of the system is calculated by Fokker Planck equation,the curves of the equivalent potential function under different parameters are observed,and the relationship between the parameters and the potential function is analyzed;Then the Cardano formula is used to calculate the stable and unstable points of the potential function,and the expression of the system steady-state probability density(SPD)and SNR is further deduced.The influence of noise intensity and system parameters on the potential function,SPD and SNR is analyzed in detail theoretically.Finally,the SR method of time-delayed EVG system is successfully applied to weak signal detection and bearing fault diagnosis by choosing appropriate parameters.