Gap metric techniques and their application to fault detection performance analysis and fault isolation schemes

Abstract

The main objective of this paper is to initiate a systematic application of gap metric techniques to the performance analysis and design issues of detecting and isolating multiplicative faults in uncertain systems. To be specific, in the first part of this paper, the K-gap and L2-gap metrics are introduced, which measure the distance between two kernel subspaces and serve as an efficient tool to deal with fault detection and isolation issues. Based on it, the K-gap and L2-gap aided analysis of residual dynamics with respect to model uncertainties is presented for the open-loop and feedback control systems, respectively. Furthermore, they are applied to deal with the performance analysis of fault detection systems. For this purpose, the concepts of fault detectability indicators and fault-to-uncertainty ratio are introduced. The second part of this paper is dedicated to the isolation of multiplicative faults. To this end, the definition for fault isolability is studied first with the aid of K-gap metric. The further efforts are devoted to the application of K-gap metric to two online fault isolation algorithms. The first one is an observer-based scheme, which adopts a bank of residual generators and an observer-based decision unit. The second scheme is based on the data-driven identification of the kernel representation of the faulty plant and the data-driven computation of the K-gap metric. Case and example studies are finally given to illustrate the proposed approaches.