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2 International Journal of Applied Mathematics and Computer Science

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

Pröll S., Lunze J., Jarmolowitz F.

International Journal of Applied Mathematics and Computer Science

2018

Vol. 28, no. 2

233--245

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 observer-based residual generator for the fault-detectable subsystem found in the first step.

Test signal generation for service diagnosis based on local structural properties

Ungermann M., Lunze J., Schwarzmann D.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 1

55-65

The paper presents a new approach to the generation of test signals used in service diagnosis. The tests make it possible to isolate faults, which are isolable only if the system is brought into specific operating points. The basis for the test signal selection is a structure graph that represents the couplings among the external and internal signals of the system and the fault signals. Graph-theoretic methods are used to identify edges that disappear under certain operating conditions and prevent a fault from changing the system behavior at this operating point. These operating conditions are identified by validuals, which are indicators obtained during the graph-theoretic analysis. The test generation method is illustrated by a process engineering example.