Graph Theoretical Methods for Finding Analytical Redundancy Relations in Overdetermined Differential Algebraic Systems
One approach for design of diagnosis systems is to use residuals based
on analytical redundancy. Overdetermined systems of equations provide
analytical redundancy and by using minimal overdetermined subsystems,
sensitivity to few faults is obtained. In this paper, overdetermined
differential algebraic systems are considered and their structure is
represented by bipartite graphs with equations and unknowns as node
sets. By differentiating equations, a new set is formed, that is an
overdetermined static algebraic system if derivatives of unknown
signals are considered as separate independent variables. The task to
derive analytical redundancy relations is thereby reduced to an
algebraic problem. It is desirable to differentiate the equations as
few times as possible and it is shown that there exists a unique
minimally differentiated overdetermined system.
Mattias Krysander and Jan Åslund
IMACS World Congress,
2005
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