Generalized expectation–maximization approach to LPV process identification with randomly missing output data

Abstract This paper considers parameter estimation for linear parameter varying (LPV) systems with randomly missing output data. The multi-model LPV model is adopted and the identification problem is formulated under the scheme of the generalized expectation–maximization (GEM) algorithm. In order to deal with the missing output data, the local models are firstly taken to have the finite impulse response (FIR) model structure. To alleviate potential overparameterization problem, a prior on FIR model coefficients is imposed and the GEM algorithm is modified to derive the maximum a posterior (MAP) estimates of the multi-mode LPV FIR model parameters. Since the FIR model is not suitable for general control applications, a multi-mode LPV output error (OE) model is then identified by applying the GEM algorithm to the same identification data set with parameters initialized based on the estimated FIR models. One simulation example and two experiments are presented to demonstrate the efficiency of the proposed method.

[1]  Xavier Bombois,et al.  Optimal experimental design for LPV identification using a local approach , 2009 .

[2]  Zuhua Xu,et al.  A method of LPV model identification for control , 2008 .

[3]  Zhongyang Fei,et al.  Applications and data of generalised dynamic wake theory of the flow in a rotor wake , 2015 .

[4]  Biao Huang,et al.  Multiple model approach to nonlinear system identification with an uncertain scheduling variable using EM algorithm , 2013 .

[5]  Yucai Zhu,et al.  System identification using slow and irregular output samples , 2009 .

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

[7]  P.M.J. Van den Hof,et al.  Modeling and Identification of Linear Parameter-Varying Systems, an Orthonormal Basis Function Approach , 2004 .

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

[9]  P. Heuberger,et al.  Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation , 2007, 2007 European Control Conference (ECC).

[10]  F. Ding,et al.  Least‐squares parameter estimation for systems with irregularly missing data , 2009 .

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

[12]  Biao Huang,et al.  FIR model identification of multirate processes with random delays using EM algorithm , 2013 .

[13]  Huijun Gao,et al.  Saturated Adaptive Robust Control for Active Suspension Systems , 2013, IEEE Transactions on Industrial Electronics.

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

[15]  Thierry Poinot,et al.  Continuous-Time Linear Parameter-Varying Identification of a Cross Flow Heat Exchanger: A Local Approach , 2011, IEEE Transactions on Control Systems Technology.

[16]  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).

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

[18]  Biao Huang,et al.  Multiple-Model Based Linear Parameter Varying Time-Delay System Identification with Missing Output Data Using an Expectation-Maximization Algorithm , 2014 .

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

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

[21]  Huijun Gao,et al.  Identification of Linear Parameter Varying Systems with Missing Output Data Using Generalized Expectation-Maximization Algorithm , 2014 .

[22]  Junghui Chen,et al.  Correntropy Kernel Learning for Nonlinear System Identification with Outliers , 2014 .