Petri Net Diagnosability Analyzer

Identification of labeled Petri nets from finite automata

Given a labeled Petri net with silent (unobservable) transitions, we are interested in performing initial marking estimation in a probabilistic setting. We assume a known finite set of initial markings, each with some a priori probability, and our goal is to obtain the conditional probabilities of initial markings of the Petri net, conditioned on an observed sequence of labels. Under a Markovian assumption on the probabilistic model, we develop a recursive algorithm that allows us to efficiently determine the conditional probabilities for each possible initial marking (conditioned on the sequence of observations seen so far). We illustrate the proposed methodology via an example and discuss potential applications in the context of initial state opacity for security applications.

This paper addresses the problem of online fault detection and diagnosis in discrete event systems modeled by labeled Petri nets and using Integer Linear Programming Problem (ILPP) solutions. In particular, unobservable (silent) transitions model faults and both observable and unobservable transitions model the nominal system behavior. Furthermore, observable transitions exhibit a kind of non determinism since several different transitions may share the same event label. This paper proposes two diagnosers that work in two different system settings. The first one is a centralized fault detection strategy: the diagnoser waits for an observable event and an algorithm defines and solves some ILPPs to decide whether the system behavior is normal or may exhibit some faults. In the second setting, the system consists of a set of interacting PN modules and each module is monitored by a diagnoser that has local information on the module structure. Moreover, each diagnoser observes and detects the faults of the module it is attached to and shares information in some of its places that are shared with other modules of the system. Some case studies show the two different approaches and point out the peculiarities of the proposed strategies.

Secret inference and attacktability analysis of discrete event systems

The interleaved expansion presented in [QLP93] is a method to compute and represent the global events of a system preserving parallelism. As a side effect, this method provides important advantages in the technology of translation from LOTOS to Petri nets over static (direct) transformations and opens a simple process algebra form of representation for an important class of Petri nets. This work presents an algorithm that maps ITcalulus elements into labeled Petri nets and gives a comprehensive overview of different aspects of the translation from LOTOS to Petri nets using this intermediate form of representation.

Extended labeled Petri nets (ELPNs), i.e., labeled Petri nets with inhibitor arcs, are usually used to model the desired closed-loop behavior of a controlled discrete-event system, and, as such, their states are formed with both the controller and the plant states. However, the control logic is based on the controller states only and the interaction between controller and plant is carried out through sensor readings from the plant and control actions (forced events) from the controller. This makes ELPN not suitable for modeling the controller. Control interpreted Petri nets (CIPNs), on the other hand, include control actions in the places and sensor readings in the transitions as part of their formal structure, and so provide a better formalism for controller modeling. In this paper, we propose a two-step approach to discrete-event controller implementation, as follows: (i) we first propose a set of transformation rules to convert the initial ELPN to an equivalent CIPN, therefore extracting the control logic from the desired closed-loop behavior and (ii) we present a straightforward systematic way to translate the CIPN into a ladder diagram. We apply the results presented here to the implementation of the automation system of a plastic molding machine.

Individuals, populations and fluid approximations: A Petri net based perspective

This article addresses the problem of optimal sensor selection for diagnosability enforcement of discrete event systems modeled with Petri nets. Given a nondiagnosable labeled Petri netlabeled Petri net (LPN) that may reach deadlocks, it can be enforced to be diagnosable by a novel systematic strategy through a mask labeling function. The proposed strategy employs a special nondeterministic finite automaton, namely, a simplified verifierSV, obtained from the original labeled Petri netLPN and a particular set of labels. Since we only need to silence sensors of some particular transitions rather than add or replace new sensors to transitions, it is more computationally efficient compared with other documented methods in the literature. In addition, we formulate and solve an integer linear programming problemILPP to optimize a set of given mask labeling functions. Finally, an algorithm is constructed to calculate the minimum value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> -diagnosable system with multiple faults under the mask labeling function. Examples are presented to demonstrate the proposed method.

A petri-net-based synthesis methodology for use-case-driven system design

PurposeAs widely used by the design and decision-making of resource allocation and communications in manufacturing, monitoring of mobile robot network and other engineering fields, minimum initial marking (MIM) estimation is to determine the initial marking(s) with a minimum total number of tokens in labeled Petri net models of real-world application systems in engineering. This paper addresses the MIM estimation under the observation of a label sequence. We aim to find all possible solutions while reducing the computational cost in solving this NP-hard problem by a hybrid evolutionary heuristic.Design/methodology/approachFirst, a set of transition firing sequences (TFSs) consistent with the observed label sequences is found to generate the initial population of the genetic algorithm (GA). Second, we calculate the initial markings that correspond to each TFS and are minimal, and the quality of individuals is assessed. Third, simulated annealing (SA) is used to improve the individuals in the population, and then GA is used for a global search. Finally, the above operations are repeated until the termination condition is satisfied.FindingsIn comparison with the existing methods for finding MIMs with heuristic algorithms, our algorithm improves 51.5–316.7% in the number of obtained MIMs. Moreover, the computation time is reduced by 90.1% compared with a classical algorithm.Originality/valueIn this paper, an effective evolutionary algorithm by hybridizing GA and SA is developed to estimate MIMs. The proposed approach can obtain the complete MIM set at a lower computational cost.

This paper studies the marking diagnosis problem in labeled Petri nets, i.e., to determine whether a plant has reached a given set of faulty markings or not in the past, from the observation history. We observe that the conventional basis reachability graphs cannot be used for marking diagnosis due to the existence of partially faulty basis markings. To overcome such a problem, we propose a notion called the diagnostic basis partition such that the corresponding basis reachability graphs does not contain any partially-faulty basis markings. By properly selecting a set of explicit transitions, a diagnostic agent is synthesized to perform the online diagnosis.

This article addresses the problem of verifying co-detectability for a labeled Petri net (LPN) that is observed at multiple observation sites, each with its own observation map. A system is strongly co-detectable if at least one site is able to determine the state of the system uniquely following any long enough sequence of observations. We check strong co-detectability for an LPN using an approach that exploits the notion of basis markings, which avoids an exhaustive enumeration of all reachable markings of the net. Specifically, a structure based on the basis reachability graph (BRG) of the system, called a BRG-based co-verifier, is obtained for the verification of strong co-detectability. In addition, using the proposed BRG-based co-verifier, some rules and relabeling options are provided to identify a new relabeling function such that a system that is not strongly co-detectable becomes strongly co-detectable. An integer programming problem is formulated to find an optimal relabeling function when considering different relabeling costs on transitions. Finally, two application examples are presented to illustrate the proposed approach.

On fluidification of Petri Nets: from discrete to hybrid and continuous models

Perfomrance analysis is a critical component of workflow system management. Workflow models represented in Petri net have advantages of abundant analysis techniques available. Reachability analysis is useful to detect errorneous states of the business logic, however, it has the problem of state explosion. In this paper, we propose the method of hierarchical reachability analysis for workflow models represented in classical Petri net, even for the cases with cycles. Our method allows analyzing with smaller decomposed reachability graphs, each composed of less places, without losing relevant information. In this way, the proposed method conducts reachability analysis efficiently within each smaller block and with simplified upper layer models after abstraction rather than tracing the large one of the whole model.

Control theories for discrete event systems modeled as finite state machines have been well developed over the years in addressing various fundamental control issues. However, modeling in finite state machines has long suffered the potential problem of state explosion that renders it unsuitable for many practical applications. In this paper, we propose an approach that appends finite sets of parameters to finite state machines in modeling discrete event systems. We show with an example that many discrete event applications can then be represented efficiently in this approach and the state explosion problem can then been mitigated.