On-Line Monitoring of Large Petri Net Models Under Partial Observation

This paper deals with the on-line monitoring of large systems modeled as Petri Nets under partial observation. The plant observation is given by a subset of transitions whose occurrence is (always) acknowledged by emitting a label received by the monitoring agent at the time of the occurrence. Other transitions not in this subset are silent (unobservable). Usually on-line applications require the computation of how the system has evolved from the last known (or estimated) marking(s) by enumerating the set of all the explanations of the observation received by the monitoring agent, i.e. the set of all allowable traces, such that the execution of these traces from the initial marking would generate the sequence of observed labels in the correct order. This can be accomplished by a forward search algorithm starting from the initial marking. However, the application of forward search techniques to large systems has several disadvantages. Firstly, the set of current allowable markings of the system can be large. Hence, its enumeration can be computationally demanding. Secondly, forward search techniques require knowing the exact initial marking, which can be a problem in case of systems with uncertain initial marking e.g. when only a lower bound on the initial marking is known. To alleviate these drawbacks, we propose a backward search method, which, starting from observation(s), enumerates a subset of explanations called the set of minimal explanations. The set of markings that are reached from the initial marking firing minimal explanations has the property that its unobservable reach (the markings obtained by firing legal, unobservable strings from any of its marking) is equal to the entire set of current estimated markings. Moreover, the faults are typically not predictable i.e. at every reachable marking there is at least one non-fault transition that is enabled. Making this assumption that the faults are not predictable allows us to conclude that the set of minimal explanations obtained via a reduced observer analysis detects the occurrence of all faults that must have happened for sure according to the complete set of explanations. Furthermore, the presented approach can deal with Petri Nets with an uncertain initial marking, which is a common situation in a distributed setting. In this case, local components modeled by Petri Nets and supervised by local agents interact unobservably by exchanging tokens via common places. G. Jiroveanu is with Romanian Power Grid Company Transelectrica SA, Brestei 5, Craiova 200581, DJ, Romania e-mail: [email protected]. R.K. Boel is with EESA SYSTeMS Research Group, University of Ghent, Tehnologiepark 914, Zwijnaarde 9052, Belgium e-mail: [email protected]. B. Bordbar is with The School of Computer Science, University of Birmingham, Edgbaston, Birmingham B152TT, United Kingdom e-mail: [email protected].