Research On Weak Signal Detection And Application Based On Two-dimensional Duffing Stochastic Resonance

The detection of weak signal is widely used in many fields such as military,biomedical,and deep-sea detection,especially in early fault diagnosis.This thesis adopts a two-dimensional Duffing system with stochastic resonance and chaos characteristics to realize the detection of weak signal characteristic parameters,which not only solves the problem that the stochastic resonance method cannot detect the amplitude of weak signals,but also avoids the chaotic theory in detecting weak signals disadvantages in frequency.Firstly,the two-dimensional Duffing system is theoretically studied.The stochastic resonance characteristics are explained from the perspective of the potential well function and stable solution of the system,and the chaotic characteristics are explained from the way of suppressing the occurrence of chaos.And the influence of system parameters on the system output is studied.The results show that small parameter changes affect both characteristics.Then,the output signal-to-noise ratio and the Kramers rate are used as the measurement criteria of the system to analyze the influence of the parameters on the stochastic resonance effect of the system.The results show that the existence of optimal parameter interval makes stochastic resonance effect of the system more and the damping ratio has a certain hindrance to the system.Then the two-dimensional Duffing adaptive stochastic resonance system based on the brainstorm optimization algorithm realizes the adaptive synchronization optimization of the system parameters and the use of parameter compensation to detect high-frequency signals.Aiming at the problem of misjudgment of the weak signal amplitude in the detection,the maximum Lyapunov exponent criterion is used to determine the amplitude range first,and then find the threshold corresponding to the chaotic critical state in the amplitude interval.Several specific implementation steps of high-frequency weak signal frequency and amplitude detection are given.For the shock signal in the non-periodic signal,the weighted kurtosis is used as the target function to realize the detection of the shock signal by the system.To detect the composite signal,different objective functions are used to detect the two components in the composite signal.According to this detection method,the detection idea of using stochastic resonance to detect early composite fault is proposed.Finally,the researched theory and method were used to detect the boundary voltage,the frequency and amplitude of multiple high-frequency periodic signals submerged in noise during electrical impedance imaging,and the actual mechanical fault signals of the inner and outer ring of the bearing are detected by using the open bearing fault data.