Structured Principal Component Analysis Model With Variable Correlation Constraint

Principal Component Analysis (PCA) is a widely used technique in process monitoring, fault diagnosis, and soft sensing of industrial systems. Despite its popularity, PCA suffers from the limitations of poor interpretability and robustness. In order to improve the PCA model, this article considers a structured sparse method--Laplace sparse principal component analysis (LSPCA), by integrating domain knowledge and sparsity constraint in the form of Laplace matrix and elastic net regularization constraint. Different from previous work, this article focuses on the advantages brought by the Laplace matrix and sparsity constraint on revealing the true latent process structure. When variable correlations are known in advance, the Laplace matrix can help extract sparse principal components that are consistent with the variable correlations. The increased accuracy of extracted latent process structure enhances the capability of PCA in soft sensing. The performance of the proposed method is verified by a simulation example and an application study to a distillation process.