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## Using Place Invariants and Test Point Placement to Isolate Faults in Discrete Event Systems.

Tabakow, Iwan
In:
*Journal of Universal Computer Science, vol.13, no.2, Springer*, pages 224-243.
2007.
In English.

Abstract:
This paper describes a method of using Petri net P-invariants in system
diagnosis. To model this process a net oriented fault classification is
presented. Hence, the considered discrete event system is modelled by a
live, bounded, and reversible place-transition Petri net. 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. Then
the corresponding net place invariants are computed. The system
k-distinguishability measure is obtained in a unique way from the
place-invariant matrix. For a large value of k , the system model is
extended by using some set of addi tional places called test points and at
the same time preserving the original net properties. To obtain a
1-distinguishable net the notion of a marked graph component is used. It
is shown a sufficient condition for 1-distinguishability of an arbitrary
place-transition net and a corresponding algorithm is presented. Next two
different diagnosis test strategies are discussed, i.e. combinational and
sequential fault diagnosis. Corresponding (single) place and transition
fault models are introduced. The complexity of the proposed method depends
on the effectivity of the existing algorithms for computation of the
P-cover, i.e. the set of P-invariants covering N. The proposed approach
can be extended for higher level Petri nets, e.g such as coloured nets or
also to design self-diagnosable circuit realisations of Boolean
interpreted Petri nets. Several examples are given

Keywords:
fault diagnosis; discrete event system; place-transition net; P-invariant;
D-partition; k-distinguishability; test point.

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