Sparse Robust Principal Component Analysis with Applications to Fault Detection and Diagnosis

Principal component analysis (PCA) is a popular method for modeling and analysis of high-dimensional data. In spite of its advantages, classical PCA also has two drawbacks. First, it is very sensitive to outliers in the data. Second, it cannot yield interpretable PCs because most of the loadings are nonzero. To overcome these drawbacks, we propose a new PCA method that has the properties of robustness and sparsity at the same time, called sparse robust PCA (SRPCA). The robustness is achieved by taking a robust covariance matrix instead of the classical covariance matrix used in PCA. Meanwhile, an additional penalty is imposed on the number of nonzero loadings to achieve the sparsity. SRPCA is not only robust against outliers, but also can yield interpretable PCs. A robust process monitoring method is developed using SRPCA. A cumulative percent contribution criterion is proposed for selecting the optimal PCs for process monitoring. The selected PCs are used to define two fault detection indices. Based on the sparsity of PCs, two-level contribution plots are developed for fault diagnosis. This fault diagnosis method narrows down the faulty variables to active variables (with nonzero loadings) in a dominant PC contributing the most to a fault. The effectiveness and advantages of the proposed method are illustrated with a case study.