Identification Of Linear Parameter Varying Systems Based On Variational Bayesian Algorithm

Technological progress in the industrial field mainly depends on the development of control and optimization strategies,and the implementation of control and optimization strategies are based on the system model.However,the increasing scale and complexity of industrial processes make it extremely difficult or even impossible to build corresponding mechanism models.Since process data contains the main dynamic characteristics of system operation,the data-driven modeling method provides a new solution for complex industrial process modeling.Linear parameter varying(LPV)models can accurately describe complex nonlinear systems through simple linear model structure and time-varying parameters,which have attracted wide attention.Various disturbance factors in industrial processes result in stochasticity of system modeling,while regular identification methods for the LPV model can only derive point estimates of unknown parameters without considering the system uncertainty.In order to further improve the identification accuracy of LPV systems,this paper mainly discusses the identification of LPV systems under the framework of variational Bayesian(VB)algorithm.The main contents are as follows:(1)The problem of LPV system identification under the framework of VB algorithm is studied.In order to solve the identification problem of uncertain industrial processes,VB algorithm is introduced into LPV system identification.In this method,the uncertainties of the system are characterized by the uncertainties of the parameters.After prior probaility distributions are assigned to variables and parameters,posterior distributions of these variables and parameters are estimated by maximizing lower limits of objective functions.Not only the point estimations of the parameters are obtained,but also the uncertainty of the estimated values can be quantified.The superiority of the proposed identification method is proved by simulations.(2)Furthermore,the identification of LPV systems with unknown delay is studied.For nonlinear systems with constant delay and piecewise time-varying delay,this paper proposes system identification methods based on VB algorithm respectively.In order to deal with the time-delay characteristics of the system,the unknown delays are treated as hidden variables,and the uncertainty of model parameters is described in the form of probability distribution.The posterior distributions of delays and parameters can be estimated by analytic approximation reasoning method,and the point estimations of delay can be obtained based on the maximum posterior probability criterion.The simulation results show the effectiveness of the method.(3)The identification of LPV models with missing outputs is investigated.Considering the uncertainties of the system and the random missing of the output data,a recursiveidentification algorithm for LPV system is derived based on VB algorithm.In each iteration,the posterior distributions over hidden variables and parameters are updated by maximizing the lower bound of the marginal likelihood function.In this way,the Bayesian estimates of missing outputs and unknown parameters can be realized until the algorithm converges.The simulation results illustrate that the VB method can provide reliable parameter estimates.