The Parameter Identification Of Nonlinear System Under Gaussian White Noise

All kinds of structures in modern engineering are developing in the direction of high precision,light weight and large volume,which makes it particularly important to study the complex dynamic characteristics of structures.In the practical engineering field,the vibration source that makes the structure system vibrate is often random vibration.Therefore,it is necessary to control the random vibration of these engineering structures,especially the nonlinear random vibration.Accurately and quickly identifying the parameters of nonlinear structural system model under stochastic excitation is very important for controller design,health monitoring and damage diagnosis in engineering practice.The parameter identification of nonlinear system under Gaussian white noise is investigated.First,the general harmonic function is applied to distinguish the fast variables and the slow variables of the system,and then the average It? stochastic differential equation of the slow variables of the system is obtained by using the stochastic averaging method,and the corresponding Fokker-Plank-Kolmogorov(FPK)equation is solved to obtain the stationary probability density function of the system response.Based on dynamic behavior analysis of the equivalent averaging system,the identification equations of the physical parameters of system and the intensity of random excitation are established by using the theory of Markov stochastic diffusion process.Taking the residual of the equation as the objective function and the system parameters to be identified as the optimization variables,the method for estimating the potential energy function,the restoring force parameter,the damping force function,the damping coefficient and the excitation intensity of Gaussian white noise for the nonlinear system is investigated.Then,the parameter identification of van der Pol oscillator? Duffingvan der Pol oscillator and stochastic system with delayed feedback control are investigated by using the proposed method.The parameter identification method of nonlinear system under Gaussian white noise is verified by using the Monte Carlo simulation.The simulation results show that the proposed parameter identification method for the physical parameters of nonlinear systems and the intensity of the Gaussian white noise random excitation has higher identification accuracy.The effectiveness and reliability of the method for parameter identification of nonlinear system under Gaussian white noise excitation are proved.