Number selection of principal components with optimized process monitoring performance

Principal component analysis (PCA) is a powerful tool in chemical process monitoring and product quality control. The number of principal components (PCs) is the essential parameter of PCA and ultimately determines the performance of this useful statistical method. However, few methods in the literature considered the issue of the selection of PCs with the PCA fault diagnosis performance. Furthermore, traditional selection methods are very subjective due to the monotonically increasing or decreasing indices they adopted. By exploring the minimum detectable fault magnitudes in the PCs space and residual space simultaneously, a new index of optimal critical fault magnitude (OCFM) is introduced and the number of PCs is selected by optimizing a function of the OCFM. The proposed method can incorporate the PCA fault diagnosing performance with the PCs selection procedure effectively, and has the advantages of forecasting PCA detection behavior of a specific fault and estimating the real detectable fault magnitude (RDFM). The acquired results are then illustrated and verified by monitoring a simulated double-effective evaporator.