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System diagnosis using Petri nets

Tabakow I.

Systems Science

2002

Vol. 28, nr 2

95-106

This paper describes a possibility of using Petri net P-invariants in system diagnosis. To model this process a net oriented fault classification is presented. The notions of D-partition of the set of places P of a given place-transition net N and net k-distinguishability are first introduced. Next these two notions are extended to the set of all vertices, i.e., places and transitions of N. So the problem of fault identification of the vertices of N is transformed as a problem of fault identification of the places of a new net N' called a net simulator of N. Any transition in N' is assumed to be fault-free. To improve the inherent net fault distinguishability first some additional places called test points are introduced. Then, some structural properties concerning the net fault distinguishability measure are shown. The above mentioned possibility of using P-invariants in system diagnosis is dependent on the cardinality r of the corresponding P-cover of N. Hence the test point set reduction seems to be an important problem with respect to the required net fault distinguishability. In particular, it is shown that instead of (2/sup r/ - 1) r-variable intersection operations, for determination of the net k-distinguishability only 4r set operations can be used (3r 2-variable intersection operations, beginning with the computation of r sums of (r - 1) arguments, where r [right angle bracket]or= 3).