Statistical signal processing approaches to fault detection

Abstract

This chapter demonstrates how statistical signal processing theory can bring insights into, and contribute to fault detection and isolation problems, and vice versa how fault detection algorithms can improve statistical signal processing algorithms. An example was used to explain the intuition of the stochastic parity space and the involved model assumptions and algorithms. A mixed model with both stochastic inputs and deterministic disturbances and faults is formulated over a sliding window. Algorithms for detecting and isolating faults online and analyzing the probability for correct and incorrect decisions offline are provided. Properties of this model-based approach and generalizations to cases of incomplete model knowledge, and nonlinear non-Gaussian models are discussed as well. For this purpose, a simulation example is used throughout the chapter for numerical illustrations and real-life applications for motivations. The chapter also 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.