Nonlinear Stochastic System Based On UKF-MCMC Parameter Identification

In this paper,Unscented Kalman Filter(UKF)and Markov Chain Monte Carlo(MCMC)methods are used to study the parameter identification of nonlinear stochastic dynamic systems.With the development of science and technology,more and more systems with high integration and complex structure are designed and applied in engineering practice.Therefore,it is of great significance to study the dynamic properties of these complex systems for their wide application.However,for practical problems,there are inevitably system parameter errors through the traditional abstract modeling method,which will seriously affect the understanding of its dynamic behavior.Therefore,it is necessary to use the output data of the system to accurately identify its system parameters which is very important to fully understand the dynamic characteristics of nonlinear systems,especially nonlinear stochastic systems.The existing parameter recognition methods mainly include: state observation method,neural network method,Bayesian inference method and Kalman Filter method.When these methods are used to identify the parameters of nonlinear stochastic systems,the recognition accuracy is reduced due to the multi-field coupling effect of nonlinear and stochastic excitation.In this paper,we will use the UKF-MCMC algorithm,which combines UKF and MCMC,and use the MCMC method to sample the posterior distribution and estimate the expected value,so as to obtain a higher precision estimate.To solve the above problems,the following researches are carried out:1.Parameter identification of nonlinear stochastic system based on UKFBased on the output data of nonlinear stochastic system,this part analyzes the time-varying characteristics and statistical characteristics of the data in detail,and then establishes the approximate posterior distribution that fully reflects the statistical characteristics of nonlinear stochastic system.Compared with the existing methods,the proposed method can not only make full use of the statistical information of the output data under the condition of random disturbance,but also improve the speed of parameter identification on the premise of ensuring the accuracy.Simulation results verify the effectiveness of the proposed method.2.Parameter identification of nonlinear stochastic system based on UKF-MCMCIn this part,by means of the repeated sampling characteristics of MCMC method,UKF method is combined with MCMC method.The MCMC method is used to repeatedly sample the posterior distribution and estimate the statistical characteristics of the output samples of the system.This strategy greatly improves the anti-interference ability of the method and the estimation ability of the posterior distribution required by UKF.Therefore,it has obvious effect on improving the identification accuracy and robustness of unknown parameters of nonlinear stochastic system.Finally,the effectiveness of the proposed method is verified by simulation results.