Selection of the number of principal components based on fault signal-to-noise ratio

The number of principal components (PCs) is critical parameter of principal component analysis (PCA) and its selection determines the performance of fault detection. In this paper, we pay attention to the relationship between selection of the number of PCs and sensitivity of fault detection. The fault signal-to-noise ratio (fault SNR) that depends on the number of PCs for a certain fault is presented. It indicates the sensitivity of fault detection. Accordingly, the number of PCs that gives the maximum fault SNR is considered as the optimum principal component. The presented method was applied to detection of the sensor fault and process fault with a prior information. Furthermore, in the process fault simulation, Fisher discriminant analysis (FDA) is applied to obtain the fault direction, showing its superior capability for isolating fault data.