Dynamic Process Monitoring

Abstract

Unlike steady-state process variables that do not change meaningfully over time, continuous dynamic systems exhibit stable dynamic behaviour or (quasi)periodic behaviour within a bounded region in the variable space. As a consequence, steady-state process monitoring methods may not be able to account for such behaviour and may therefore be unsuitable for monitoring such systems. In this chapter, a methodology for monitoring dynamic process systems is outlined, based on embedding of the variables in a phase space prior to the extraction of diagnostic features from the data. Three different techniques are considered, namely, singular spectrum analysis, feature extraction with random forests and feature extraction from the data with inverse nonlinear principal component analysis by the use of an autoassociative neural network. In addition, the application of recurrence quantification analysis is also investigated. Recurrence quantification analysis characterizes an attractor in the phase space by identifying and quantifying the repeated occurrences (recurrences) of points in the same neighbourhood. This can then be used as a sensitive diagnostic of changes in the underlying dynamics of the process system. The use of these methods is illustrated by the use of three nonlinear systems, that is, a Lotka–Volterra predator–prey model, the Belousov–Zhabotinsky reaction as well as a simulated autocatalytic process. Although the different strategies considered are all in principle capable of detecting changes in complex data structures, in the case studies associated with the autocatalytic process, detection of change was difficult, since the change in the geometry of the attractor was very subtle. The trajectory of the new data remained mostly within the decision envelopes of the monitoring schemes, although the density distribution of the new data within this envelope changed. However, in this instance, diagnostic variables derived from the recurrence plots of the data were able to detect these changes, and the use of such methods to complement machine learning methods could lead to more capable diagnostic approaches to deal with complex data.