Structural Analysis for FDI: a modified, invertibility-based canonical decomposition

International audienceStructural analysis is a simple but efficient method in the field of Fault Detection and Isolation (FDI), to determine system properties such as observability, fault detectability or diagnosability. Our method is based on the study of a bipartite graph derived from the behavioral model of the system, which represents the links between the variables of the system. A graph-decomposition tool, known as the Dulmage-Mendelsohn decomposition (also named canonical decomposition) is used in order to determine the monitorable and observable subsystems. Additionally, a structural analysis can be performed with the objective of designing fault indicators, i.e. residuals, which are used for FDI. Invertibility constraints of the relations of the behavioral model, are used to determine the calculability of the residuals. These invertibility constraints are not considered to derive the canonical decomposition. Consequently, some structurally monitorable subsystems may correspond to non-realizable (non-computable) residuals. In this paper, we propose a new canonical decomposition algorithm which takes into account the invertibility constraints: our modified decomposition redefines the monitorable and observable part of the system, so that each of these parts do not contain elements which would turn out to be unusable, from a calculability standpoint