Threshold computation for fault detection in linear discrete-time Markov jump systems

This paper proposes a threshold computation scheme for an observer-based fault detection (FD) in linear discrete-time Markovian jump systems. An observer-based FD scheme typically consists of two stages known as residual generation and residual evaluation. Even information of faults is contained inside a residual signal, a decision of faults occurrence is consequently made by a residual evaluation stage, which consists of residual evaluation function and threshold setting. For this reason, a successful FD strongly depends on a threshold setting for a given residual evaluation function. In this paper, Kalman filter (KF) is used as a residual generator. Based on an accessibility of Markov chain to KF, two types of residual generations are considered, namely mode-dependent and mode-independent residual generation. After that threshold is computed in a residual evaluation stage such that a maximum fault detection rate is achieved, for a given false alarm rate. Without any knowledge of a probability density function of residual signal before and after fault occurrence, a threshold is computed by using an estimation of residual evaluation function variance in a fault-free case. Finally, a detection performance is demonstrated by a numerical example. Copyright (c) 2013 John Wiley & Sons, Ltd.