On the application of interval PCA to process monitoring: A robust strategy for sensor FDI with new efficient control statistics

In principal component analysis (PCA) based fault detection and isolation (FDI), the sensor data uncertainties cause a significant difficulty in control decision making, which evokes and increases the number of false alarms and imprecise decisions. In its standard form, PCA makes no distinction between data points and the associated measurement errors which vary depending on experimental conditions. A recent and robust solution consists in capturing the variability of the multivariate observations by symbolic data analysis methods, precisely, using interval-valued variables and interval PCA methods. The key idea is to extend the methodology of conventional PCA based statistical process monitoring to handle interval-valued data. In this paper, we compare four most known interval PCA methods and investigate their use for diagnosis purpose. Based on reconstruction principle used in the classical PCA approach, an interval reconstruction is proposed and a new criterion is derived for the determination of the interval PCA model structure (number of retained principal components). The monitoring routine includes the generation of interval residuals for fault detection, and the application of the extended interval reconstruction principle for fault isolation. We also introduce a new set of Shewhart type interval statistics, based on the conventional PCA statistics, that are more suited to interval data-set case with a better overall performances. The implementation of the proposed sensor FDI methods are illustrated using a simulation example and applied to distillation column process benchmark.