Stable recursive canonical variate state space modeling for time-varying processes

Abstract An adaptive recursive process modeling approach is developed to improve the accuracy of modeling time-varying processes. We adopt the exponential weighted moving average approach to update the covariance and cross-covariance of past and future observation vectors. Forgetting factors are adjusted in the recursive modeling process based on the residual of model outputs. To ensure the stability of the identified model, we introduce a constrained nonlinear optimization approach and propose a stable recursive canonical variate state space modeling (SRCVSS) method. The performance of the proposed method is illustrated with an open-loop numerical example and simulation with the closed-loop data from a continuous stirred tank heater (CSTH) system. The results indicate that the accuracy of proposed SRCVSS modeling method is higher than that of state space modeling with traditional canonical variate analysis.

[1]  Dale E. Seborg,et al.  Fault Detection Using Canonical Variate Analysis , 2004 .

[2]  Yi Cao,et al.  Nonlinear Dynamic Process Monitoring Using Canonical Variate Analysis and Kernel Density Estimations , 2010, IEEE Transactions on Industrial Informatics.

[3]  A. Negiz,et al.  Statistical monitoring of multivariable dynamic processes with state-space models , 1997 .

[4]  A. Çinar,et al.  PLS, balanced, and canonical variate realization techniques for identifying VARMA models in state space , 1997 .

[5]  J. Baillieul,et al.  Identification and filtering of nonlinear systems using canonical variate analysis , 1990, 29th IEEE Conference on Decision and Control.

[6]  In-Beum Lee,et al.  Adaptive multivariate statistical process control for monitoring time-varying processes , 2006 .

[7]  Akira Ohsumi,et al.  RECURSIVE SUBSPACE PREDICTION OF LINEAR TIME-VARYING STOCHASTIC SYSTEMS , 2005 .

[8]  Ali Cinar,et al.  Multivariable Adaptive Identification and Control for Artificial Pancreas Systems , 2014, IEEE Transactions on Biomedical Engineering.

[9]  Stéphane Lecoeuche,et al.  Propagator-based methods for recursive subspace model identification , 2008, Signal Process..

[10]  Zhihuan Song,et al.  Recursive Subspace Model Identification Based on Vector Autoregressive Modelling , 2008 .

[11]  Wallace E. Larimore,et al.  Canonical variate analysis in identification, filtering, and adaptive control , 1990, 29th IEEE Conference on Decision and Control.

[12]  Nina F. Thornhill,et al.  A continuous stirred tank heater simulation model with applications , 2008 .

[13]  A. J. Morris,et al.  Application of exponentially weighted principal component analysis for the monitoring of a polymer film manufacturing process , 2003 .

[14]  Orest Iftime,et al.  Proceedings of the 16th IFAC World congress , 2006 .

[15]  Si-Zhao Joe Qin,et al.  An overview of subspace identification , 2006, Comput. Chem. Eng..

[16]  Michel Verhaegen,et al.  Recursive subspace identification of linear and non-linear Wiener state-space models , 2000, Autom..

[17]  In-Beum Lee,et al.  Adaptive monitoring statistics with state space model updating based on canonical variate analysis , 2008 .

[18]  Ali Cinar,et al.  Hypoglycemia Early Alarm Systems Based On Multivariable Models. , 2013, Industrial & engineering chemistry research.

[19]  Ali Cinar,et al.  Adaptive multivariable closed-loop control of blood glucose concentration in patients with Type 1 Diabetes , 2013, 2013 American Control Conference.

[20]  Michel Verhaegen,et al.  Recursive Predictor-Based Subspace Identification With Application to the Real-Time Closed-Loop Tracking of Flutter , 2012, IEEE Transactions on Control Systems Technology.

[21]  Marco Lovera,et al.  Convergence analysis of instrumental variable recursive subspace identification algorithms , 2007, Autom..

[22]  Ben C. Juricek,et al.  Process control applications of subspace and regression-based identification and monitoring methods , 2005, Proceedings of the 2005, American Control Conference, 2005..

[23]  Michel Verhaegen,et al.  Fast-array Recursive Closed-loop Subspace Model Identification , 2009 .

[24]  Ivo Houtzager,et al.  VARMAX-based closed-loop subspace model identification , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[25]  T. R. Fortescue,et al.  Implementation of self-tuning regulators with variable forgetting factors , 1981, Autom..

[26]  Bart De Moor,et al.  Subspace Identification for Linear Systems: Theory ― Implementation ― Applications , 2011 .

[27]  Jie Zhang,et al.  Fault detection in dynamic processes using a simplified monitoring-specific CVA state space modelling approach , 2012, Comput. Chem. Eng..

[28]  Kevin Judd,et al.  Modelling the dynamics of nonlinear time series using canonical variate analysis , 2002 .

[29]  H. Akaike,et al.  Information Theory and an Extension of the Maximum Likelihood Principle , 1973 .