Coupled Recursive Parameter Estimation For Multivariable Systems

For multivariable industrial processes with complex structures,finding an appropriate identification algorithm to establish the mathematical model is the basis of the process analysis and the control system design.Multivariable systems have high dimensions and many parameters,which results in heavy computational burdens in identification algorithms,reducing the computational complexity is an urgent problem for the multivariable system identification.In this paper,highly-efficient coupled recursive parameter estimation algorithms are proposed for the multivariable systems with colored noises by using the new identification techniques.The major results are as follows.(1)For the multivariable equation-error autoregressive moving average system which contains both the parameter matrix and the parameter vector,the decomposition technique is used to break it down into multiple single-output sub-systems which only have parameter vectors and the computationally efficient coupled recursive algorithms are presented based on the coupling identification principle.The proposed algorithms can ensure the identification accuracy and reduce the computational burdens.In addition,to reduce the effect of colored noises on the parameter estimates,the observation data are filtered,and the filtered identification model is further decomposed.The filtering based coupled recursive algorithms with higher estimation accuracy are proposed to obtain all parameters of the system by combining part of the noise model.(2)For the multivariable output-error autoregressive moving average system,the algorithms based on the Kronecker product have large computational burdens.To cut down the computational amount,the system is decomposed into multiple singleoutput sub-systems according to the number of outputs for identification.The auxiliary model is established to estimate the unmeasurable noise-free outputs inside the system,and the auxiliary model based coupled recursive algorithms are studied based on the coupling principle,which can improve the computational efficiency of parameter estimation.Moreover,the auxiliary model based filtering coupled recursive algorithms are proposed using the data filtering.By adopting the data filtering method,the algorithms can obtain more accurate estimation results.(3)Multivariate systems are the extension of multivariable linear systems and can represent some multivariable nonlinear systems.For the multivariate output-error autoregressive system,the auxiliary model based multivariate system coupled recursive algorithms are derived under the framework of the decomposition technique.By using the model transformation technique to deal with colored noises,model transformation based auxiliary model coupled recursive algorithms are studied.Different from the filtering algorithms given before,the transformed model contains all the parameters to be estimated,so it is unnecessary to combine the noise model for interactive estimation,and the model transformation based algorithms have simple steps in the implementation and can improve the parameter estimation accuracy.The computational burdens of the proposed algorithms are analyzed and compared,and the results show that the computational cost of the proposed algorithms are reduced by using the coupling principle.In addition,the main identification algorithms proposed in this paper are simulated numerically.The simulation results show that the coupled recursive algorithms can ensure the estimation accuracy,and the coupled algorithms with the data filtering and the model transformation can obtain more accurate parameter estimates,which verifies the effectiveness of the proposed algorithms.