Subspace identification for two-dimensional dynamic batch process statistical monitoring

Abstract Dynamics are inherent characteristics of batch processes, which may be not only within a batch, but also from batch to batch. Two-dimensional dynamic principal component analysis (2-D-DPCA) method [Lu, N., Yao, Y., Gao, F., 2005. Two-dimensional dynamic PCA for batch process monitoring. A.I.Ch.E. Journal 51, 3300–3304] can model both kinds of batch dynamics, but may lead to the inclusion of large number of lagged variables and make the contribution plot difficult to read. To solve this problem, subspace identification technique is combined with 2-D-DPCA in this paper. The state space model of a 2-D batch process can be identified with canonical variate analysis (CVA) method based on the auto-determined support region (ROS). In 2-D-DPCA modeling, the utilization of state variables instead of lagged process variables reduces the number of variables and provides a clearer contribution plot for fault diagnosis.

[1]  H. Hotelling.  Relations Between Two Sets of Variates , 1936 .

[2]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[3]  John F. MacGregor,et al.  Modeling of dynamic systems using latent variable and subspace methods , 2000 .

[4]  U. Kruger,et al.  Dynamic Principal Component Analysis Using Subspace Model Identification , 2005, ICIC.

[5]  Jonathan E. Cooper,et al.  Dynamic Multivariate Statistical Process Control using Subspace Identification , 2004 .

[6]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[7]  J. Edward Jackson,et al.  A User's Guide to Principal Components. , 1991 .

[8]  Svante Wold,et al.  Hierarchical multiblock PLS and PC models for easier model interpretation and as an alternative to variable selection , 1996 .

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

[10]  P. Miller,et al.  Contribution plots: a missing link in multivariate quality control , 1998 .

[11]  A. J. Morris,et al.  Confidence limits for contribution plots , 2000 .

[12]  Ningyun Lu,et al.  TWO-DIMENSIONAL DYNAMIC PCA WITH AUTO-SELECTED SUPPORT REGION , 2007 .

[13]  D. Lainiotis,et al.  System identification : advances and case studies , 1976 .

[14]  Dale E. Seborg,et al.  Identification of Multivariable, Linear, Dynamic Models: Comparing Regression and Subspace Techniques , 2002 .

[15]  John F. MacGregor,et al.  Adaptive batch monitoring using hierarchical PCA , 1998 .

[16]  Fuli Wang,et al.  Sub-PCA Modeling and On-line Monitoring Strategy for Batch Processes (R&D Note) , 2004 .

[17]  H. Akaike.  A new look at the statistical model identification , 1974 .

[18]  Dale E. Seborg,et al.  Reduced-Rank ARX and Subspace System Identification for Process Control , 1998 .

[19]  George W. Irwin,et al.  Improved reliability in diagnosing faults using multivariate statistics , 2006, Comput. Chem. Eng..

[20]  J. Macgregor,et al.  Monitoring batch processes using multiway principal component analysis , 1994 .

[21]  Furong Gao,et al.  Batch Process Monitoring in Score Space of Two-Dimensional Dynamic Principal Component Analysis (PCA) , 2007 .

[22]  Wallace E. Larimore,et al.  Optimal Reduced Rank Modeling, Prediction, Monitoring and Control using Canonical Variate Analysis , 1997 .

[23]  S. Joe Qin,et al.  Subspace approach to multidimensional fault identification and reconstruction , 1998 .

[24]  Fuli Wang,et al.  Two‐dimensional dynamic PCA for batch process monitoring , 2005 .