Shrinking Principal Component Analysis for Enhanced Process Monitoring and Fault Isolation

This article proposes a shrinking principal component analysis (ShPCA) for fault detection and isolation. Unlike traditional PCA, ShPCA employs a sparse representation of the loading vectors by incorporating the l(1) norm into the original objective function of PCA. An iterative quadratic programming (QP) algorithm is used to solve the optimization problem, and a Bayesian information criterion (BIC) is proposed to automatically determine the weight on the l(1) norm. With the sparse representation, ShPCA produces an easy-to-interpret residual space with close relation to the process mechanism. A fault detection and isolation strategy is then proposed based on ShPCA that uses the nonzero variables in the residual components to construct partial PCA models that are sensitive to specific process faults. Studies of the application of ShPCA to a simulation example and to the Tennessee Eastman (TE) process illustrate its applicability.