Probabilistic Robust Parity Relation based Fault Detection Using Biased Minimax Probability Machine

Abstract This paper proposes a probabilistic robust parity relation based approach to fault detection of stochastic linear systems. Instead of assuming exact knowledge of disturbance distribution, the uncertainty of distribution information is taken into account by considering an ambiguity set of disturbance distributions. The biased minimax probability machine scheme is exploited to formulate an integrated design of the parity vector/matrix and the detection threshold. It maximizes the worst-case fault detection rate (FDR) with respect to selected reference faults, while ensuring a predefined worst-case false alarm rate. Firstly, a scalar residual design is derived in an analytical form. The analysis of its FDR in the presence of an arbitrary fault shows its limitation due to using a single reference fault. This issue is further addressed by proposing a vector residual design with a systematic method to select multiple reference faults. The efficacy of the proposed approach is illustrated by a simulation example.