Abstract
This paper presents a method for the identification of stochastic timed discrete event systems, based on the analysis of the behavior of the input and output signals, arranged in a timeline. To achieve this goal stochastic timed interpreted Petri nets are defined. These nets link timed discrete event systems modelling with stochastic time modelling. The procedure starts with the observation of the input/output signals; these signals are converted into events, so that the sequence of events is the observed language. This language arrives to an identifier that builds a stochastic timed interpreted Petri net which generates the same language. The identified model is a deterministic generator of the observed language. The identification method also includes an algorithm that determines when the identification process is over.
Highlights
Industrial systems usually have a sequential evolution, so they behave as discrete event systems (DES)
The external signals not related with control commands define the operating modes, which affects the controller and allows modelling the system under different strategies; in [2] the authors use a similar concept to differentiate production patterns in batch processes, called multimode; they propose to separate the original space of a mode into two different parts and a monitoring process is carried out in each block; the multiblock monitoring method proposed is used for fault diagnosis purposes in multimode multivariate continuous processes; some of its proposals could be applied in stochastic DES regarding times identification, so it will probably reduce the sizes of time matrices and the complexity of the identification method
A Petri net structure N is a bipartite digraph represented by the five-tuple N = (P, TR, Pre, Post, M0), where P is a set of places with cardinality n and TR is a set of transitions with cardinality m, and Pre : P × TR → N, Post : TR × P → N are the pre- and postincidence matrices, respectively, which specify the arcs connecting places and transitions
Summary
Industrial systems usually have a sequential evolution, so they behave as discrete event systems (DES). The other contribution in this area is given in [28], presenting a method that uses ILP with IPN, to prevent exhaustive generation of reachable states; it is considered nondeterminism in the model, since different observable transitions share the same label; it has a timing structure of events leading to the imposition of new restrictions and provides the most accurate diagnosis. It is a very efficient method in small models but to find an optimal solution in complex models has very high computational requirements.
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