Process fault detection, isolation, and reconstruction by principal component pursuit

A common approach to process monitoring based on principal component analysis (PCA) assumes that fault-free, noise-free data is sampled from a low-dimensional subspace. Although widely described and applied, process fault detection and isolation using PCA is not robust to outliers in the training data, is hard to properly tune, and is not capable of isolating multiple faults. A newly introduced method called principal component pursuit (PCP) optimally decomposes a data matrix as the sum of a low-rank matrix and a sparse matrix. When applied to the process monitoring problem, PCP simultaneously accomplishes the objectives of model building, fault detection, fault isolation, and process reconstruction with a single convex optimization problem, thereby overcoming the key shortcomings of PCA-based approaches for process monitoring. The use of PCP for process monitoring is described and illustrated using data from a manufacturing process.