Efficient recursive principal component analysis algorithms for process monitoring

Principal component analysis (PCA) has been successfully applied in large scale process monitoring. However, classical PCA has some drawbacks: one of these aspects is the inability to deal with parameter-varying processes, where it interprets the natural changes in the process as faults, resulting in numerous false alarms. These false alarms threaten the credibility of the monitoring system. Therefore, recursive PCA (RPCA) algorithms are recommended. The most important challenge faced by these algorithms is the high computation costs, due to repeated eigenvalue decomposition (EVD) or singular value decomposition (SVD). Motivated by this issue, we present two RPCA algorithms that will greatly reduce the computation cost. The first algorithm is based on first-order perturbation analysis (FOP), which is a rank-one update of the eigenvalues and their corresponding eigenvectors of a sample covariance matrix. The second one is based on the data projection method (DPM), which is a simple and reliable approach for adaptive subspace tracking. The effectiveness of the presented RPCA algorithms is evaluated with an application of monitoring a nonisothermal continuous stirred tank reactor (CSTR) system. The results show the efficiency of these approaches compared to the classical PCA.