Two Projection Methods for Use in the Analysis of Multivariate Process Data With an Illustration in Petrochemical Production

Principal components analysis (PCA) is often used in the analysis of multivariate process data to identify important combinations of the original variables on which to focus for more detailed study. However, PCA and other related projection techniques from the standard multivariate repertoire are not explicitly designed to address or to exploit the strong autocorrelation and temporal cross-correlation structures that are often present in multivariate process data. Here we propose two alternative projection techniques that do focus on the temporal structure in such data and that therefore produce components that may have some analytical advantages over those resulting from more conventional multivariate methods. As in PCA, both of our suggested methods linearly transform the original p-variate time series into uncorrelated components; however, unlike PCA, they concentrate on deriving components with particular temporal correlation properties, rather than those with maximal variance. The first technique finds components that exhibit distinctly different autocorrelation structures via modification of a signal-noise decomposition method used in image analysis. The second method draws on ideas from common PCA to produce components that are not only uncorrelated as in PCA, but that also have approximately zero temporally lagged cross-correlations for all time lags. We present the technical details for these two methods, assess their performance through simulation studies, and illustrate their use on multivariate output measures from a fluidized catalytic cracking unit used in petrochemical production, contrasting the results obtained with those from standard PCA.