Statistical monitoring of multivariable dynamic processes with state‐space models

TLDR

Industrial continuous processes involve many variables, operate long periods at fixed points under closed‑loop control, and produce autocorrelated, cross‑correlated, and collinear measurements. The authors introduce a statistical process monitoring method that combines multivariate statistics with system theory to track process variability. They model in‑control variability with a canonical‑variate state‑space representation equivalent to a VARMA model, derive CV state variables as principal dynamic directions, and employ an A T² statistic on these states for monitoring. Simulations and a high‑temperature milk pasteurization experiment demonstrate the method’s advantages over conventional approaches.

Abstract

Abstract Industrial continuous processes may have a large number of process variables and are usually operated for extended periods at fixed operating points under closed‐loop control, yielding process measurements that are autocorrelated, cross‐correlated, and collinear. A statistical process monitoring (SPM) method based on multivariate statistics and system theory is introduced to monitor the variability of such processes. The statistical model that describes the in‐control variability is based on a canonical‐variate (CV) state‐space model that is an equivalent representation of a vector autoregressive moving‐average time‐series model. The CV state variables obtained from the state‐space model are linear combinations of the past process measurements that explain the variability of the future measurements the most. Because of this distinctive feature, the CV state variables are regarded as the principal dynamic directions A T 2 statistic based on the CV state variables is used for developing an SPM procedure. Simple examples based on simulated data and an experimental application based on a high‐temperature short‐time milk pasteurization process illustrate advantages of the proposed SPM method.