Research And Application Based On Coupled And Cascaded Linear Stochastic Resonance System

The Stochastic Resonance(SR)system is a kind of differential system based on the nonlinear potential function.Under the influence of the randomness of noise and the driving force of the external periodic signal,the noise energy is transferred to the signal to be measured,which induces the non-monotonic dependence between the noise intensity and the system,and then enhances the output of the system.Due to its noise-assisted characteristics of "seeking advantages and avoiding disadvantages",SR-based signal detection methods are different from traditional signal detection methods which are based on eliminating or suppressing noise.It stands out from a crowd of methods and has been widely used in the fields of engineering diagnostic,image detection,and biotechnology.The thesis first introduces the relevant basic theories,research methods,and performance measurement indicators.Then,the output amplitude of the system is affected by the mass and frequency fluctuations in the system,and the related research literature of coupled and cascaded fluctuation system is less.Therefore,under the under-damped condition,the different SR characteristics produced by the fluctuations of all aspects of the system caused by the Brownian particle movement and the randomness of noise are studied.The main contents and innovations points of the thesis are shown as follows:(1)The SR output characteristics of a fractional-order coupled linear oscillator with nonlinear frequency fluctuation are studied.Based on the Shapiro-Loginov formula and the mathematical characteristics of dichotomous noise,the average motion behavior of the coupled Brownian particles is completely synchronized by using Laplace transform and its inverse transform;On this basis,the specific mathematical expression of output amplitude gain(hereinafter referred to as G)of a single subsystem is derived,and the formula simulation is conducted;Finally,the validity of the formula is verified by the simulation based on Simulink.(2)The SR output characteristics of coupled time-delay linear harmonic oscillators with fluctuations in mass and frequency are studied.Using the small delay approximation theory to transform a non-Markov process with a delay term into a Markov process without a delay term,an approximate system model is obtained;On this basis,the thesis explores the influence of the system parameters on the stochastic resonance characteristics of the system and performs numerical simulation to verify the correctness of the theoretical analysis;Finally,it diagnoses the bearing fault of the system and explores its signal extraction performance in engineering.(3)In order to further improve the signal enhancement performance of the system,two single-stage nonlinear mass fluctuation linear systems are cascaded to construct a cascaded nonlinear mass fluctuation stochastic resonance system.The output response of the system under the influence of asymmetric dichotomous noise under the under-damped condition is studied.Firstly,the output characteristics of a single-stage nonlinear mass fluctuation system are explored;Then,it conducts specific research on the two-stage output signal of the cascaded system to explore the superiority of the cascaded system in signal enhancement performance;Finally,the bearing fault diagnosis of the cascaded system proves that it has good signal enhancement performance and the superiority of fault signal frequency extraction.