The Evolution Of Stochastic Delay System And Detection Of The Weak Signal

The world is full of changes.Since the birth of human beings,they have tried to constrain the complex objective world under a few simple laws,and mathematics and physics are even more so.Classical mechanics in Newton’s era perfectly explained the motion law of macrophysics.Under his laws,the motion trajectory of particles is definite,while the corresponding distribution is trivial.Modern quantum mechanics knows that the trajectory of a particle is uncertain based on the uncertainty principle,so it is more valuable to discuss the distribution of the corresponding wave function.Stochastic dynamics has the characteristics of the first two,with the motion trajectories of particles and the probability distribution of evolution process,which makes that there are two directions naturally for the study of stochastic dynamics:along the classic method to explore the characteristics of sample orbits and along the probabilistic method to study the transfering probability distribution governed by the Chapman-Kolmogorov equation(also known as the Fokker-Planck equation).The original intention of this paper is to detect the weak fault of the key components of the high-speed train information control system and its subsystems in the process of operation.An effective method of weak signal detection and feature extraction is proposed with stochastic delay dynamical system as the carrier.Based on the development of delay systems and stochastic dynamics related theories,a preliminary study is made for its possible engineering applications.First,the delay system with rich dynamic behavior is proposed,which is the SD oscillator with nonlinear geometric stiffness under multiplicative multiplicative Gaussian white noise excitation,harmonic external excitation and velocity feedback feedback.The chaotic threshold of the system is calculated by means of the stochastic Melnikov function and the mean-square criterion.In addition,external excitation amplitude,time delay and noise intensity are used as parameters to explore the transient vacancy in chaotic motions of the system,and the weak fault signals submerged in noise can be detected and effective feature extraction can be carried out.Secondly,the probability distribution of particle evolution process is studied.The center manifold and the normal form theory of Hopf bifurcation for the classical delay system are extended to the stochastic delay system with small perturbations.The corresponding reduction equation is given with certain accuracy,and the average It(?) equation is obtained by using the stochastic averaging method,and then stochastic bifurcation behaviors are studied.Finally,by combining the large deviation theory with deep learning,the most probable path of the transition between the steady states of the system driven by Gaussian white noise and Lévy noise is discussed,in order to conduct in-depth research on the transition of stochastic dynamic behavior,in order to provide a possible method for the stochastic control problems such as the reliability and the first crossing of the delay system.