<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

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

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This paper combines methods for the structural analysis of bipartite graphs with observer-based residual generation. The analysis of bipartite structure graphs...

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

Published Online: Jun 29, 2018

Page range: 233 - 245

Received: Mar 29, 2017

Accepted: Jan 29, 2018

DOI: https://doi.org/10.2478/amcs-2018-0017

Keywords
fault diagnosis, structural analysis, observer-based diagnosis, diagnosability analysis

© 2018 Sebastian Pröll, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jun 29, 2018

Page range: 233 - 245

Received: Mar 29, 2017

Accepted: Jan 29, 2018

DOI: https://doi.org/10.2478/amcs-2018-0017

Keywordsfault diagnosis, structural analysis, observer-based diagnosis, diagnosability analysis

© 2018 Sebastian Pröll, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
fault diagnosis, structural analysis, observer-based diagnosis, diagnosability analysis