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Diagnosis-time assessment in discrete event systems using timed Petri nets

Tabakow I.

Systems Science

2008

Vol. 34, no 3

17-23

This paper describes a method of diagnosis-time assessment in discrete event systems. Any such system is modelled by a live, bounded, and reversible place-transition Petri net N. There are assumed some deterministically given delays associated with the transitions of N, and hence, N is assumed to be deterministic timed. Without loss of generality, the single place fault model is considered below and the corresponding diagnosis process is assumed to be sequential. 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. 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 additional places called test points and at the same time preserving the original net properties. In accordance with the above assumption of sequential fault diagnosis, the process of fault isolation is carried out step by step, where each step depends on the result of the diagnostic experiment at the previous step. Hence, the diagnosis-time assessment is realised by computing the absolute value of the time difference between the minimum cycle time of N and the worst-case fault-isolation time according to the diagnostic tree obtained. The complexity of the method proposed depends on the effectivity of the existing algorithms for computation of the P-cover, i.e., the set of P-invariants covering N. The approach proposed can be extended to higher level Petri nets, e.g., such as coloured ones. Several examples are given.

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).