Principal Predictor Analysis with Application to Dynamic Process Monitoring

Modern engineering and scientific systems are usually equipped with abundant sensors to collect large-dimensional time series for monitoring and operations. In this article, we develop a novel principal predictor analysis (PPA) framework with reduced-dimensional dynamics to obtain parsimonious predictor models of large-dimensional time series data. Principal predictors are obtained by maximizing the variance of predictions from their past values. Unlike classical principal component analysis (PCA), which reduces the dimensionality without emphasizing the prediction, PPA focuses on extracting latent variables with the maximum predictive capability. The PPA application to dynamic process monitoring is performed with predictive monitoring indices to account for variations in the predictors and the unpredicted residuals, which can be subsequently modeled with PCA. PPA-based monitoring and diagnosis are demonstrated in an illustrative closed-loop system and the industrial Dow Challenge Problem and an extension to include known first-principles relations to show their effectiveness.