Validation and verification of continuous plants operating modes using multivariate statistical methods

Abstract

A method to identify and monitor the operating modes of continuos plants, is presented and discussed. The criterion uses principal component analysis (PCA) to remove the collinearity and to reduce the dimensionality of the original data set. Typical data sets consist of several variables measured on-line at a constant sampling rate. The reduction in dimension is obtained by the projection of the data set onto a smaller subspace defined by the principal components (PC). In the PC subspace, clusters are identified, and each cluster represents a particular steady-state. Later measurements, if taken while the plant operates at any of these steady-states, lie on the relevant cluster. Such clusters provide the basis for a process validation method. While using the cluster directly would be cumbersome and not intuitive, we propose the use of statistical process control (SPC) charts. An example is given using CUSUM plots. SPC charts are applied to a derived measure. This is the Euclidean distance of the sample from the center of the cluster on the principal component subspace. The definition of the derived measure and its usage are discussed using a multicomponent distillation unit. The method allows the engineer to identify whether the plant operates at the steady state and, possibly at which steady-state among the known ones. Deviations from steady state are easily detected as well as dynamic transients between different steady-states. This approach is particularly suitable for monitoring applications as it allows faster and easier detection than by monitoring individual physical variables. Typical applications of the method are discussed along with future extensions and refinements.