Just-in-Time Selection of Principal Components for Fault Detection: The Criteria Based on Principal Component Contributions to the Sample Mahalanobis Distance

Principal component analysis (PCA) has been widely used in the field of fault detection. A main difficulty in using PCA is the selection of principal components (PCs). Different PC selection criteria have been developed in the past, but most of them do not connect the selection of PCs with the fault detection. The selected PCs may be optimal for data modeling but not for fault detection. In this paper, the just-in-time cumulative percent contribution (JITCPC) criterion and the just-in-time contribution quantile (JITCQ) criterion are proposed to select PCs from the viewpoint of fault detection. In the JITCPC and JITCQ criteria, the contributions of PCs to the sample Mahalanobis distance are used to evaluate the importance of PCs to fault detection. The larger contribution the PC makes, the more important it is to detect a fault. The JITCPC criterion selects the leading PCs with the cumulative percent contribution (CPC) larger than a predefined threshold (e.g., 90%). The JITCQ criterion selects the PCs with contributions larger than a quantile (e.g., median) of contributions of all PCs. The PCs selected by the JITCPC or JITCQ criterion vary with samples to guarantee that the key features of each sample are captured. The selected and nonselected PCs are used to define the primary and secondary T-2 statistics, respectively. A fault detection method is then proposed. The effectiveness and advantages of the proposed PC selection criteria and the fault detection method are illustrated by case studies in a simulation example and in an industrial process.