The Evolution Of Stochastic Delay Differential System And Detection Of Weak Signals

The detection of weak fault effective signal has become a research hotspot nowadays.The main research methods include nonlinear parameter identification method,chaotic theory method,stochastic resonance method and artificial intelligence method.This paper mainly conducts signal detection research based on chaotic theory and stochastic resonance theory.In this paper,the evolution process and nonlinear dynamic behavior of the stochastic delay Mathieu-Duffing system were studied,and the weak periodic signal was detected by using its abundant nonlinear dynamic behavior.Firstly,the evolution process and dynamic behavior of the stochastic delay Mathieu-Duffing oscillator are studied,including the Mathieu-Duffing oscillator driven by additive noise and controlled by speed delay feedback,the Mathieu-Duffing oscillator driven by multiplicity noise and controlled by speed delay feedback,and the Mathieu-Duffing oscillator driven by multiplicity noise and controlled by speed and displacement feedback.The ?Ito differential equation and FPK equation of the Mathieu-Duffing system which is driven by additive or multiplier noise and controlled by speed feedback are obtained by using the center manifold method and the stochastic average method,and the stationary probability density function is obtained.Based on the singular boundary classification of one-dimensional diffusion process,the stochastic stability behavior and stochastic bifurcation phenomenon of the system are obtained.The one-dimensional average equation of Mathieu-Duffing system with displacement velocity feedback controlled driven by multiplicity noise is obtained by perturbation method.Based on the change of bifurcation parameter and stationary probability density function,the stochastic stability and bifurcation of the system are obtained,and we can obtain that the feedback of displacement delay will make the P bifurcation of the system disappear.Secondly,the stochastic Melnikov function is used to predict the chaos of the Mathieu-Duffing oscillator which is controlled by feedback of multiplicative noise-driven velocity delay.By analyzing the control of noise intensity and time delay on the theoretical chaotic threshold,it is concluded that delay can improve the system's ability to detect weak periodic signals.In the context of practical engineering,the sequence of weak periodic signal detection is proposed as follows: frequency ? phase ? amplitude,the corresponding detection methods are given respectively.The bifurcation sequence diagram is used to detect the chaotic transient phenomena,and then the frequency of weak periodic signals is detected by the chaotic transient phenomena,and the phase and amplitude of weak periodic signals are detected by the chaotic transition under the premise of the known frequency.Finally,the stochastic resonance method is discussed to detect weak periodic signals.The three main conditions of stochastic resonance are nonlinear system,periodic signal and noise.Through the analysis of the signal to noise ratio of output power,it can be obtained that adjusting system parameters will make the output signal to noise ratio reach the peak.And the fault signal can be simulated,through filtering by the filter constructed based on the Mathieu-Duffing oscillator,the frequency characteristics of the weak periodic signal to be detected under the noise can be obtained.