Modeling of dynamic systems using latent variable and subspace methods

Abstract

Dynamic models that capture the transient behavior of a process are often needed in a variety of industrial problems. In system identification, causal dynamic models between a small to medium number of manipulated variables and controlled variables are obtained from designed experiments for use in control system design. In multivariate statistical process control, using autocorrelated data, non-causal dynamic models on large numbers of measured variables are obtained from routine process operating data for use in fault detection and diagnosis. The basis for all these empirical dynamic models is relationships among the past, present and future values of the measured variables. The number of lagged variables can be very large and the effective rank of the data matrices is usually much smaller than the number of lagged variables. Therefore latent variable and subspace methods have become popular in building dynamic models. In these approaches a low-dimensional subspace or latent variable space is identified which contains most of the information relevant to the problem at hand. Latent variable methods include partial least squares (PLS), principal component regression (PCR) and canonical correlation analysis (CCA) and lead to models based on a small number of latent variables that are linear combinations of the lagged measured variables. Subspace methods involve the use of singular value decomposition (N4SID) and canonical variates (CVA) on the lagged data followed by fitting the resulting subspace variables in a more parsimonious state space model form. This paper reviews these methods, discusses their essential differences and gives a critical discussion of them in the context of their intended end use (system identification and multivariate SPC). Copyright © 2000 John Wiley & Sons, Ltd.