Performance Evaluation and Order Selection for Pattern Modeling Methods Through Granger Causality Analysis

In the realm of processes modeling and control, the monitoring of processes is crucial for ensuring safety, and a key task in multivariate statistical process monitoring is to extract the operating patterns of the process. Dynamic strategies, exemplified by dynamic-inner principal components analysis (DIPCA), dynamic-inner partial least squares (DIPLS), and dynamic-inner canonical correlation analysis (DICCA), are employed to tackle temporal correlation and the ever-changing nature of processes using AR structures. Dynamic controlled principal components analysis (DCPCA) additionally considers dynamic controlled characteristics, showcasing remarkable accuracy in both the monitoring of processes and dynamic prediction. Notwithstanding the precision demonstrated by DCPCA, the task of ascertaining optimal control input orders remains intricate, often necessitating reliance on empirical methodologies or trial-and-error approaches. This research introduces an innovative methodology, drawing inspiration from Granger causality analysis, to establish causal relationships between control inputs and patterns. Causal influence (CI) was employed to assess the impact of introducing control inputs and the effects of control inputs at different orders, aiding the model in selecting the optimal control input order. Theoretically supported performance evaluation and order selection, providing assurance for practical applications.