# Structural Methodologies for Distributed Fault Detection and Isolation
## 1 Introduction  
As the complexity of industrial systems grows, system monitoring and fault diagnosis systems are becoming essential to assure system reliability and functional safety; see for example [1, 2] and the references therein. Safety-critical systems must detect and isolate faults quickly and reliably to enable effective safety maneuvers and fault-tolerant control so as not to endanger operations and human lives [3]. Traditional approaches have focused on designing centralized diagnosers for complex systems, e.g., the Aircraft Diagnostic and Maintenance Systems (ADMS) used on modern aircraft systems [4, 5]. However, since many industrial applications involve large dynamic systems with many subsystems, distributed approaches to fault detection and isolation are becoming necessary for a number of reasons [6]. Centralized diagnosers are less reliable because they create a single point of failure, and designing centralized diagnosers for large, complex systems may become computationally intractable. Transferring sensor data from the distributed subsystems to a central fault diagnosis unit can become error prone, for example because of packet losses and networking delays, which can then affect the accuracy and timeliness of diagnosis decisions [7]. Furthermore, from a practical point of view, different subsystems are designed by different manufacturers, who may not be willing to pass along all of their knowledge of the subsystems to the system integrator to protect their intellectual property. This makes it difficult for the system integrator to design centralized diagnosers since they to do not have access to subsystem models. A number of approaches have been developed for distributed fault detection and isolation in discrete event systems. In the simplest case, a group of distributed fault detection and isolationapproaches considers each subsystem as a node that reports its state as \"OK\" or \"faulty\" without providing any details of the nature of the fault and how it was inferred. This approach is prevalent for wireless sensor networks [8] and computer network [9] diagnosis. For most systems that exhibit hybrid and continuous behaviors, distributed fault detection and isolation is more complicated. In these systems, a subsystem has several components, and a fault could occur in a sensor, actuator, or other components in the subsystem. Therefore, it is not enough to simply declare a subsystem as \"OK\" or \"faulty,\" since the isolation of component faults requires deeper reasoning processes. [PERSON] et al. [10] used a bank of unknown input observers for distributed Fault Detection and Isolation (FDI) in time-invariant linear systems. A three-layer distributed diagnosis architecture design was proposed by [11]. [PERSON] et al. [12] proposed a distributed residual generation and computation approach for distributed diagnosis. To achieve accurate fault detection and isolation of a known set of potential faults in a distributed framework, subsystems may have to share data so that the necessary residuals may be derived for fault isolation. [PERSON] et al. [13] developed an algorithm that searches for the minimal number of additional external measurements to add to each local diagnoser in order to make all faults detectable and isolable in that subsystem. [PERSON] et al. [14] used a similar approach for distributed fault detection and isolation in mobile robots. [PERSON] et al. [15] used breadth-first search to find the minimum number of measurements to add to each subsystem to make all the faults detectable and isolable by using information from all local diagnosers. The algorithm guarantees minimum communication among subsystems; however, it is exponential in the number of system measurements. To address this problem, we have proposed a greedy search algorithm that is computationally efficient, but suboptimal. [PERSON] et al.