Joint diagnosis of process and sensor faults using principal component analysis

Abstract

This paper presents a unified approach to process and sensor fault detection, identification, and reconstruction via principal component analysis. The principal component analysis model partitions the measurement space into a principal component subspace where normal variation occurs, and a residual subspace that faults may occupy. Both process faults and sensor faults are characterized by a direction vector, which describes the behavior of the fault. Fault reconstruction is accomplished by sliding the sample vector as close as possible to the principal component subspace. When the actual fault is assumed, the maximum reduction in the squared prediction error is achieved. A fault-identification index is defined in terms of the reconstructed squared prediction error. Fault detectability, reconstructability, and identifiability conditions are derived and demonstrated with a geometric interpretation. Numerous examples are provided to verify the method and conditions derived in the paper. An unreconstructed variance is defined and used to determine the number of principal components for best reconstruction. The proposed approach is applied to a data set from an industrial boiler process.