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. Keywords— Structural analysis, consistency based diagnosis, differential algebraic equations, bipartite graphs.