A data-driven approach to UIO-based fault diagnosis
Giulio Fattore, Maria Elena Valcher
TL;DR
This work addresses data-driven fault detection and isolation for discrete-time LTI systems with disturbances and actuator faults by designing a residual generator based on a dead-beat unknown-input observer (UIO). It derives necessary and sufficient solvability conditions from both the system model and offline data, and provides a constructive algorithm to obtain the residual-generator matrices from history data alone, avoiding system identification. A key contribution is showing that data-based solvability conditions are equivalent to model-based rank conditions (e.g., $ ext{rank}([CBCE])=m+r$) under a persistence-of-excitation assumption, and providing an explicit procedure to compute $A_{UIO}$, $B_{UIO}^u$, $B_{UIO}^y$, $D_{UIO}$, and $C$ using data. The paper demonstrates the method with a numerical example and discusses limitations and extensions, such as moving to asymptotic UIOs or using multiple residual generators, highlighting the practical impact of data-driven FDI without requiring full system identification.
Abstract
In this paper we propose a data-driven approach to the design of a residual generator, based on a dead-beat unknown-input observer, for linear time-invariant discrete-time state-space models, whose state equation is affected both by disturbances and by actuator faults. We first review the modelbased conditions for the existence of such a residual generator, and then prove that under suitable assumptions on the collected historical data, we are both able to determine if the problem is solvable and to identify the matrices of a possible residual generator. We propose an algorithm that, based only on the collected data (and not on the system description), is able to perform both tasks. An illustrating example and some remarks on limitations and possible extensions of the current results conclude the paper.