Gradient Identification Methods For Systems With Irregular Missing Output Data

In the process industry,the system input is usually refreshed by the computer at a fast frequency,but the output has the phenomena of slow sampling,irregular sampling and data missing due to the limitations of sensors,channel transmission and other conditions.This type of system is called a system with missing output data.Since model parameter estimation is the basis of solving model based control problems,it is of great practical significance to study the parameter estimation method of systems with missing output data.Since the system with irregular missing output data is more general,based on the interactive estimation theory and the negative gradient search principle,this paper studies the joint identification of parameters and missing output of the system with irregular missing output data.The main contents of this study are as follows.(1)For the linear systems described by controlled autoregressive(CAR)model,in the case of irregular missing of output data,an auxiliary model based missing output estimation method is improved based on Kalman smoothing principle.A Kalman smoother based missing output estimation method is proposed,and it is proved by theoretical analysis that the estimation accuracy of the proposed method is higher than that of the traditional auxiliary model based missing output estimation method.Based on the interactive estimation theory and the negative gradient search principle,combined with the proposed missing output estimation method,the Kalman smoother based stochastic gradient algorithm and the Kalman smoother based gradient iterative algorithm are derived.In order to improve the convergence rate and track the time-varying parameters of the algorithm,based on the multi-innovation identification theory,a Kalman smoother based multi-innovation forgetting gradient algorithm is derived by extending the innovation as the innovation vector and introducing a forgetting factor.(2)For the dynamic adjustment systems described by controlled autoregressive autoregressive(CARAR)model,in the case of irregular missing of output data,based on the auxiliary model identification idea and the negative gradient search principle,two auxiliary models are designed to estimate the missing outputs and colored noise interactively,and an auxiliary model based modified stochastic gradient algorithm and an auxiliary model based gradient iterative algorithm are derived.In order to eliminate the influence of colored noise estimation term on parameter estimation accuracy and improve the estimation accuracy of missing outputs,the auxiliary model based modified stochastic gradient algorithm and the auxiliary model based gradient iteration algorithm are improved based on the model equivalence principle and the Kalman smoothing principle,and a model equivalence and Kalman smoother based modified stochastic gradient algorithm and a model equivalence and Kalman smoother based gradient iterative algorithm are derived.(3)For the nonlinear systems described by output nonlinear controlled autoregressive(ON-CAR)model,in the case of irregular missing of output data,the traditional auxiliary model based missing output estimation method is improved based on the extended Kalman smoothing principle.The nonlinear smoothing estimation problem is transformed into an approximate linear smoothing problem by locally linearizing the nonlinear basis function,and an extended Kalman smoother based missing output estimation method is proposed.Based on the interactive estimation theory and the negative gradient search principle,combined with the proposed missing output estimation method,an extended Kalman smoother based forgetting gradient algorithm and an extended Kalman smoother based gradient iterative algorithm are derived.To sum up,this paper studies the parameter estimation of the system described by CAR model,CARAR model and ON-CAR model under the condition of irregular missing of output data.The gradient identification algorithms of three systems are derived,respectively.Simulation results show the effectiveness of the proposed algorithms.