A Bayesian Approach for LPV Model Identification and Its Application to Complex Processes

Obtaining mathematical models that can accurately describe nonlinear dynamics of complex processes and be further used for model-based control design is a challenging task. In this brief, a Bayesian approach is introduced for data-driven identification of linear parameter-varying regression models in an input–output dynamic representation form with an autoregressive with exogenous variable (ARX) noise structure. The applicability of the proposed approach is then investigated for the modeling of complex nonlinear process systems. In this approach, the dependence structure of the model on the scheduling variables is identified based on a Gaussian process (GP) formulation. The GP is used as a prior distribution to describe the possible realization of the scheduling-dependent coefficient functions of the estimated model. Then, a posterior distribution of these functions is obtained given the measured data and the mean value of this distribution is used to determine the estimated model. The properties and performance of the proposed method are evaluated using an illustrative example of a chemical process, namely, a distillation column, as well as an experimental case study with a three tank system.

[1]  Javad Mohammadpour,et al.  A Robust MPC for Input-Output LPV Models , 2016, IEEE Transactions on Automatic Control.

[2]  Bassam Bamieh,et al.  Identification of linear parameter varying models , 2002 .

[3]  R. Pearson.  Nonlinear Input/Output Modeling , 1994 .

[4]  Henrik Ohlsson,et al.  On the estimation of transfer functions, regularizations and Gaussian processes - Revisited , 2012, Autom..

[5]  Alessandro Chiuso,et al.  Bayesian and nonparametric methods for system identification and model selection , 2014, 2014 European Control Conference (ECC).

[6]  Roland Tóth,et al.  Asymptotically optimal orthonormal basis functions for LPV system identification , 2009, Autom..

[7]  V. Peterka.  BAYESIAN APPROACH TO SYSTEM IDENTIFICATION , 1981 .

[8]  Wallace E. Larimore,et al.  Identification of linear parameter-varying engine models , 2013, 2013 American Control Conference.

[9]  Wen Yu.  A Novel Fuzzy-Neural-Network Modeling Approach to Crude-Oil Blending , 2009, IEEE Transactions on Control Systems Technology.

[10]  Roland Tóth,et al.  Order and structural dependence selection of LPV-ARX models using a nonnegative garrote approach , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[11]  Kevin P. Murphy,et al.  Machine learning - a probabilistic perspective , 2012, Adaptive computation and machine learning series.

[12]  Alessandro Chiuso,et al.  Tuning complexity in kernel-based linear system identification: The robustness of the marginal likelihood estimator , 2014, 2014 European Control Conference (ECC).

[13]  Michel Verhaegen,et al.  Subspace identification of Bilinear and LPV systems for open- and closed-loop data , 2009, Autom..

[14]  Lennart Ljung,et al.  Kernel methods in system identification, machine learning and function estimation: A survey , 2014, Autom..

[15]  Giuseppe De Nicolao,et al.  A new kernel-based approach for system identification , 2008, 2008 American Control Conference.

[16]  R. Tóth,et al.  Nonparametric identification of LPV models under general noise conditions : an LS-SVM based approach , 2012 .

[17]  Jan-Willem van Wingerden,et al.  LPV Identification of Wind Turbine Rotor Vibrational Dynamics Using Periodic Disturbance Basis Functions , 2013, IEEE Transactions on Control Systems Technology.

[18]  Wei Xing Zheng,et al.  Model structure learning: A support vector machine approach for LPV linear-regression models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[19]  Giuseppe De Nicolao,et al.  A new kernel-based approach for linear system identification , 2010, Autom..

[20]  A. A. Bachnas,et al.  A review on data-driven linear parameter-varying modeling approaches: A high-purity distillation column case study , 2014 .

[21]  Wei Xing Zheng,et al.  An instrumental least squares support vector machine for nonlinear system identification , 2013, Autom..

[22]  R. Pearson.  Nonlinear Input/Output Modeling , 1994 .

[23]  Jan-Willem van Wingerden,et al.  Global Identification of Wind Turbines Using a Hammerstein Identification Method , 2013, IEEE Transactions on Control Systems Technology.

[24]  Ali Keyhani,et al.  Nonlinear neural-network modeling of an induction machine , 1999, IEEE Trans. Control. Syst. Technol..

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

[26]  Herbert Werner,et al.  Closed-loop system identification of LPV input-output models - application to an arm-driven inverted pendulum , 2008, 2008 47th IEEE Conference on Decision and Control.

[27]  Carl E. Rasmussen,et al.  Gaussian processes for machine learning , 2005, Adaptive computation and machine learning.

[28]  Alessandro Chiuso,et al.  A Bayesian approach to sparse dynamic network identification , 2012, Autom..

[29]  Alessandro Chiuso,et al.  Subspace identification using predictor estimation via Gaussian regression , 2008, 2008 47th IEEE Conference on Decision and Control.

[30]  Siep Weiland,et al.  Identification of low order parameter varying models for large scale systems , 2009 .

[31]  Roland Tóth,et al.  LPV model order selection in an LS-SVM setting , 2013, 52nd IEEE Conference on Decision and Control.

[32]  Ali Mesbah,et al.  Perspectives of data-driven LPV modeling of high-purity distillation columns , 2013, 2013 European Control Conference (ECC).

[33]  Yaojie Lu,et al.  Robust multiple-model LPV approach to nonlinear process identification using mixture t distributions , 2014 .

[34]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .

[35]  Tyrone L. Vincent,et al.  Nonparametric methods for the identification of linear parameter varying systems , 2008, 2008 IEEE International Conference on Computer-Aided Control Systems.

[36]  Sheng Chen,et al.  NARX-Based Nonlinear System Identification Using Orthogonal Least Squares Basis Hunting , 2008, IEEE Transactions on Control Systems Technology.

[37]  Javad Mohammadpour,et al.  A Bayesian approach for estimation of linear-regression LPV models , 2014, 53rd IEEE Conference on Decision and Control.

[38]  Luigi del Re,et al.  ON PERSISTENT EXCITATION FOR PARAMETER ESTIMATION OF QUASI-LPV SYSTEMS AND ITS APPLICATION IN MODELING OF DIESEL ENGINE TORQUE , 2006 .

[39]  David T. Westwick,et al.  Identification of Auto-Regressive Exogenous Hammerstein Models Based on Support Vector Machine Regression , 2013, IEEE Transactions on Control Systems Technology.