Fault isolation in industrial processes using Fisher's discriminant analysis

The limited availability of quality data can pose problems for any process monitoring scheme. The problem is especially difficult when the dimensionality of the data is very high, such as the data collected from a paper machine or an entire chemical plant. By projecting the data into a lower dimensional space that more accurately characterizes the state of the process, dimensionality reduction techniques can greatly improve and simplify the process monitoring procedures, fault detection, and isolation. The application of principal component analysis (PCA) as a dimensionality reduction tool for monitoring chemical processes has been studied by several academic and industrial engineers. Although PCA contains certain optimality properties in terms of fault detection, it is not well-suited for fault isolation. Fisher's discriminant analysis (FDA), a dimensionality reduction technique heavily studied in the pattern classification literature, has advantages from a theoretical point of view. In this paper, we develop an information criterion that automatically determines the order of the dimensionality reduction for FDA, and show that FDA is more proficient than PCA for isolating faults, both theoretically and by applying these techniques to paper machine data provided by International Paper and simulated data collected from the Tennessee Eastman problem.