Auto-regressive modeling with dynamic weighted canonical correlation analysis

Abstract

Multivariate statistical analytical methods, such as principal component analysis (PCA) and canonical correlation analysis (CCA), are widely used to extract useful information from data collected in modern industrial processes. Their dynamic extensions are also designed intensively in the literature to exploit dynamic variations in the processes. However, none of these algorithms consider the inevitably strong dependence in adjacent samples caused by high sampling frequencies or relatively slow continuous process changes, and the dependence may lead to unnecessarily large time lags and sub-optimal prediction performance. In this paper, a dynamic weighted CCA (DWCCA) algorithm is proposed to address this issue with the aid of basis functions. DWCCA constructs its latent space by maximizing the correlation between current data and a weighted representation of past data. To remove the negative effect caused by strongly collinear successive samples, it is assumed that the weights of past data rely only on a limited number of basis functions, and in this work, polynomial basis, Fourier basis, and Gaussian basis functions are considered and compared. Comprehensive modeling scheme is also designed for DWCCA with subsequent PCA decomposition to exploit static and dynamic variations concurrently. Case studies on the Tennessee Eastman process and the boiler process are presented to illustrate the effectiveness of the proposed dynamic models over other existing dynamic methods.