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

Abstract

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.

Markovian jump system approach for the estimation and adaptive diagnosis of decreased power generation in wind farms

“…To achieve FDI, we feed the fault estimates provided by the proposed observer into decision mechanisms based on thresholds. Model‐based thresholding usually leads to too conservative results which are characterised by poor fault detectability and isolability [20], notably in the cases of Markovian jump systems [21]. Therefore, we utilise a data‐driven FDI approach based on adaptive thresholds for evaluating the FE output provided by the model‐based observer.…”

Time‐varying threshold‐based fault detection for a class of uncertain non‐linear systems in strict‐feedback form

“…Compared to a constant threshold, however, the time‐varying threshold gives a significant advantage in reducing false alarms, which is one of the most important questions in FD. In [13, 14], the time‐varying threshold is designed to detect the faults for linear systems. Since the publication of that article, FD for linear systems has a feasible and effective methodology.…”