Abstract
In process industries, data-based statistical methods have become important techniques for ensuring product quality and operation safety, where principal component analysis (PCA) may be the most commonly used method among them. However, PCA assumes that the training data matrix only contains an underlying low-rank structure with some dense noise. When gross sparse errors, i.e. outliers, exist, the results of PCA are seriously affected. In this thesis, a robust matrix recovery method called stable principal component pursuit (SPCP) is utilized to solve this problem. By replacing PCA by SPCP in process modeling and monitoring, robust process monitoring is achieved. In addition, SPCP is also applied to non-destructive testing (NDT) of carbon fiber reinforced polymer (CFRP) for eliminating noise and non-uniform backgrounds contained in thermographic images. In doing so, the performance of NDT is enhanced and the defects can be better detected.