In-depth exploration on dynamic-controlled principal component analysis: Algorithm properties and its applications in pattern control and optimisation

Abstract

Recently, significant attention has been directed towards extracting latent pattern from measured variables to characterise the operational status of processes. Notably, dynamic-controlled principal component analysis (DCPCA) has been developed to explicitly model the dynamic causality between control inputs and the pattern. However, studies on the mathematical properties of DCPCA are still absent, which hinders understanding and limits its applications. To bridge this gap, this paper analyses the properties of the optimisation problem and solution algorithm for DCPCA, as well as showing the geometric characteristics of DCPCA models. Consequently, the method by which DCPCA is solved and its working principle are explained. Based on these theoretical explorations, a framework for DCPCA-based pattern control and optimisation is designed and discussed to highlight a standard paradigm and show the significance of DCPCA for engineering applications. Finally, a numerical example is presented to validate the effectiveness of DCPCA, which explicitly captures the dynamic-controlled relationships of the process and directly regulates the pattern for process control. Additionally, a benchmark case study using the Tennessee Eastman process shows that DCPCA has a better detection-accuracy rate than dynamic-inner PCA (DIPCA).