Identification of Linear Parameter Varying Systems with Missing Output Data Using Generalized Expectation-Maximization Algorithm

Abstract This paper is concerned with the identification problems of linear parameter varying (LPV) systems with randomly missing output data. Since one local linearized model cannot capture the global dynamics of the nonlinear industrial process, the multiple-model LPV model in which the global model is constructed by smoothly weighted combination of multiple local models is considered here. The problem of missing output variables data is commonly encountered in practice. In order to handle the multiple-model identification problems of LPV systems with incomplete data, the local model is taken to have a finite impulse response (FIR) model structure and the generalized expectation-maximization (EM) algorithm is adopted to estimate the unknown parameters of the global LPV model. To avoid the problems of ill-conditioned matrices and high sensitivity of parameters to noise, the prior information on the coefficients of each local FIR model is employed to construct the prior probability of unknown parameters. Then the maximum a posteriori (MAP) estimates of the global model parameters are derived via the generalized EM algorithm. The numerical example is presented to demonstrate the effectiveness of the proposed method.

[1]  Biao Huang,et al.  Multiple model based soft sensor development with irregular/missing process output measurement , 2011, 2011 International Symposium on Advanced Control of Industrial Processes (ADCONIP).

[2]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[3]  Ping Zhang,et al.  A comparison study of basic data-driven fault diagnosis and process monitoring methods on the benchmark Tennessee Eastman process , 2012 .

[4]  Biao Huang,et al.  Identification of nonlinear parameter varying systems with missing output data , 2012 .

[5]  Yucai Zhu,et al.  Nonlinear MPC using an identified LPV model , 2009 .

[6]  R. B. Gopaluni.  A particle filter approach to identification of nonlinear processes under missing observations , 2008 .

[7]  Thierry Bastogne,et al.  Identification of a Managed River Reach by a Bayesian Approach , 2009, IEEE Transactions on Control Systems Technology.

[8]  Hugues Garnier,et al.  Refined instrumental variable methods for identification of LPV Box-Jenkins models , 2010, Autom..

[9]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[10]  Biao Huang,et al.  Multiple model LPV approach to nonlinear process identification with EM algorithm , 2011 .

[11]  Hongye Su,et al.  Prediction error method for identification of LPV models , 2012 .

[12]  Biao Huang,et al.  Dealing with Irregular Data in Soft Sensors: Bayesian Method and Comparative Study , 2008 .

[13]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[14]  Hugues Garnier,et al.  Instrumental variable scheme for closed-loop LPV model identification , 2012, Autom..

[15]  Steven X. Ding,et al.  Real-Time Implementation of Fault-Tolerant Control Systems With Performance Optimization , 2014, IEEE Transactions on Industrial Electronics.

[16]  Okko H. Bosgra,et al.  LPV control for a wafer stage: beyond the theoretical solution , 2005 .