From Structural Analysis to Observer–Based Residual Generation for Fault Detection

• Published in: International journal of applied mathematics and computer science Vol. 28; no. 2; pp. 233 - 245
• Main Authors: Pröll, Sebastian, Lunze, Jan, Jarmolowitz, Fabian
• Format: Journal Article
• Language: English
• Published: Zielona Góra Sciendo 01.06.2018; De Gruyter Poland
• Subjects: diagnosability analysis; Fault detection; fault diagnosis; Graph theory; Graphs; Linear systems; Mathematical models; Observability (systems); observer-based diagnosis; State observers; Structural analysis
• ISSN: 2083-8492; 1641-876X; 2083-8492
• DOI: 10.2478/amcs-2018-0017

This paper combines methods for the structural analysis of bipartite graphs with observer-based residual generation. The analysis of bipartite structure graphs leads to over-determined subsets of equations within a system model, which make it possible to compute residuals for fault detection. In observer-based diagnosis, by contrast, an observability analysis finds observable subsystems, for which residuals can be generated by state observers. This paper reveals a fundamental relationship between these two graph-theoretic approaches to diagnosability 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 proved which allows us to verify structural observability of a system by means of the corresponding bipartite graph. An important consequence of this result is a comprehensive approach to fault detection systems, which starts with finding the over-determined part of a given system by means of a bipartite structure graph and continues with designing an observerbased residual generator for the fault-detectable subsystem found in the first step.