From structural analysis to observer-based residual generation for fault detection

Structural analysis methods use bipartite graphs to find over-determined subsets of equations within a system model which allow to compute residuals. In observer-based diagnosis by contrast, observable subsystems are used to build residuals by state estimation. The observability of a system can be verified by structural techniques using directed graphs. This paper reveals a fundamental relationship between the two graph-theoretic approaches to system analysis and shows that for linear systems the structurally over-determined set of model equations equals the output connected part of the system. Moreover, a condition is provided which allows to verify structural observability of a system by means of the corresponding bipartite graph. The important consequence of this result is a comprehensive way to fault detection systems. It starts with finding the over-determined part of a given system by means of a bipartite structure graph and continues with designing an observer-based residual generator for the fault-detectable subsystem found in the first step.