Parity Space-Based Fault Detection by Minimum Error Minimax Probability Machine

Abstract

This paper deals with the problem of parity space-based fault detection (FD) for linear discrete time systems in the framework of minimum error minimax probability machine (MEMPM). Traditional parity space-based FD is usually difficult to achieve acceptable tradeoff between missed alarm rate (MAR) and false alarm rate (FAR) without the exact stochastic properties of unknown input. To solve this problem, this paper proposes a novel method of parity space-based FD by MEMPM. Firstly, the integrated design of parity space vector, threshold, MAR and FAR is formulated as a problem of binary classification, i.e., the fault-free case and faulty case. By using the method of MEMPM, a bank of parity space vectors corresponding to different faulty scenarios and a threshold are then obtained, while an optimal trade-off between MAR and FAR is achieved in the worst-case setting. To show the effectiveness of proposed method, a satellite attitude control system subject to roll momentum wheel fault and pitch gyroscope fault is considered.