Statistical signal processing approaches to fault detection

The parity space approach to fault detection and isolation (FDI) has been developed during the last 20 years, and the focus here is to describe its application to stochastic systems. A mixed model with both stochastic inputs and deterministic disturbances and faults is formulated over a sliding window. Algorithms for detecting and isolating faults on-line and analyzing the probability for correct and incorrect decisions off-line are provided. A major part of the paper is devoted to discussing properties of this model-based approach and generalizations to cases of incomplete model knowledge, and non-linear non-Gaussian models. For this purpose, a simulation example is used throughout the paper for numerical illustrations, and real-life applications for motivations. The final section discusses the reverse problem: fault detection approaches to statistical signal processing. It is motivated by three applications that a simple CUSUM detector in feedback loop with an adaptive filter can mitigate the inherent trade-off between estimation accuracy and tracking speed in linear filters.