Statistical performance monitoring of dynamic multivariate processes using state space modelling

Abstract

There is increasing interest in extending the concept of multivariate statistical process control to incorporate system dynamics into the process performance monitoring representation. A methodology has previously been proposed where the system dynamics and the correlation structure of the process data are captured within a state space representation. The system states and the state space model parameters are identified using the multivariate statistical projection techniques of canonical variate analysis (CVA) and partial least squares (PLS). A number of metrics based on Hotelling's T 2 statistic are proposed for the monitoring of the state of the system. Control limits for these metrics are calculated using the empirical reference distribution and assuming the metrics follow the known, theoretically derived, probability distributions. Two model forms are proposed. In the first the number of inputs and outputs in the model are constant for all variables, whilst the second approach assumes that number of inputs and outputs can vary. The modelling and process performance monitoring ability of the CVA and PLS state space representations, and the sensitivity of the various metrics in identifying faults, is investigated using a comprehensive simulation of a continuous stirred tank co-polymerisation reactor.