Statistical fault detection using PCA-based GLR hypothesis testing

Safe process operation requires effective fault detection (FD) methods that can identify faults in various process parameters. In the absence of a process model, principal component analysis (PCA) has been successfully used as a data-based FD technique for highly correlated process variables. Some of the PCA detection indices include the T² or Q statistics, which have their advantages and disadvantages. When a process model is available, however, the generalized likelihood ratio (GLR) test, which is a statistical hypothesis testing method, has shown good fault detection abilities. In this work, a PCA-based GLR fault detection algorithm is developed to exploit the advantages of the GLR test in the absence of a process model. In fact, PCA is used to provide a modeling framework for the develop fault detection algorithm. The PCA-based GLR fault detection algorithm provides optimal properties by maximizing the detection probability of faults for a given false alarm rate. The performance of the PCA-based GLR fault detection algorithm is illustrated and compared to conventional fault detection methods through two simulated examples, one using synthetic data and the other using simulated continuously stirred tank reactor (CSTR) data. The results of these examples clearly show the effectiveness of the developed algorithm over conventional methods.