Consistent dynamic PCA based on errors-in-variables subspace identification

In this paper, we make a comparison between dynamic principal component analysis (PCA) and errors-in-variables (EIV) subspace model identification (SMI) and establish consistency conditions for the two approaches. We first demonstrate the relationship between dynamic PCA and SMI. Then we show that when process variables are corrupted by measurement noise dynamic PCA fails to give a consistent estimate of the process model in general whether or not process noise is present. We then propose an indirect dynamic PCA approach for the consistent estimate of the process model resorting to EIV SMI algorithms. Consistent dynamic PCA models are obtained with and without process disturbances. Additional features of the indirect approach include (i) easy determination of the number of lagged variables in the model; (ii) determination of the number of significant process disturbances; and (iii) consistent estimate of the dynamic PCA models with and without process disturbances. We conduct two simulation examples and an industrial case study to support our theoretical results, where the relationship between dynamic PCA and EIV SMI is numerically verified.