We study the problem of fault isolation in linear systems with actuator and sensor faults within a data-driven framework. We propose a nullspace-based filter that uses solely fault-free input-output data collected under process and measurement noises. By reparameterizing the problem within a behavioral framework, we achieve a direct fault isolation filter design that is independent of any explicit system model. The underlying classification problem is approached from a geometric perspective, enabling a characterization of mutual fault discernibility in terms of fundamental system properties given a noise-free setting. In addition, the provided conditions can be evaluated using only the available data. Finally, a simulation study is conducted to demonstrate the effectiveness of the proposed method.

This paper considers the problem of fault estimation in linear time-invariant systems when actuators are subject to unknown additive faults. A data-driven approach is proposed to design an inverse-system-based filter for reconstructing fault signals when the underlying fault subsystem can be either a minimum phase or non-minimum phase system. Unlike traditional two-step data-driven methods in the literature, the proposed method directly computes the filter parameters from input-output data to avoid the propagation of identification errors through an inverse operation into the fault estimates, which is the case in state-of-the-art filter designs. Furthermore, regarding out-of-sample performance of the filter, a kernel-based regularization is exploited to not only reduce the model complexity but also enable the design scheme to take advantage of available prior knowledge on the underlying system behavior. This knowledge can be incorporated into basis functions, promoting the desired solution to the optimization problem. To validate the effectiveness of the proposed method, a simulation study is conducted, demonstrating a notable reduction in estimation error compared to state-of-the-art methods.