Integrated trade‐off design of fault detection system for linear discrete time‐varying systems

Abstract

In this study, the problem of fault detection (FD) system design for linear discrete time-varying systems is addressed. Different from most existing methods which separately handle residual generator and evaluator, this study focuses on integrated design of residual generator and evaluator. Instead of traditional trade-off design between sensitivity to faults and robustness to disturbances, this study aims at maximising FD rate given a predefined false alarm rate. The proposed approach in this study follows two steps: first, in the norm-based framework, the parity relation-based offline FD system achieves maximal FD rate by minimising the set of undetectable faults; then the optimal offline FD system is equivalently transformed into a recursive FD algorithm for online use. Relationship between the obtained solution in this study and the existing ones is analysed. The performance improvement of the proposed approach is illustrated by comparing against existing methods through Monte Carlo simulations.