Showing papers on "Petri net published in 2018"

Decentralized Diagnosis by Petri Nets and Integer Linear Programming

Abstract: This paper proposes a novel decentralized on-line fault diagnosis approach based on the solution of some integer linear programming problems for discrete event systems in a Petri net framework. The decentralized architecture consists of a set of local sites communicating with a coordinator that decides whether the system behavior is normal or subject to some possible faults. To this aim, some results allow defining the rules applied by the coordinator and the local sites to provide the global diagnosis results. Moreover, two protocols for the detection and diagnosis of faults are proposed: they differ for the information exchanged between local sites and coordinator and the diagnostic capability. In addition, a sufficient and necessary condition under which the second presented protocol can successfully diagnose a fault in the decentralized architecture is proved. Finally, some examples are presented to show the efficiency of the proposed approach.

Polynomial approach to optimal one-wafer cyclic scheduling of treelike hybrid multi-cluster tools via Petri nets

Abstract: A treelike hybrid multi-cluster tool is composed of both single-arm and dual-arm cluster tools with a treelike topology. Scheduling such a tool is challenging. For a hybrid treelike multi-cluster tool whose bottleneck individual tool is process-bound, this work aims at finding its optimal one-wafer cyclic schedule. It is modeled with Petri nets such that a onewafer cyclic schedule is parameterized as its robots’ waiting time. Based on the model, this work proves the existence of its onewafer cyclic schedule that features with the ease of industrial implementation. Then, computationally efficient algorithms are proposed to find the minimal cycle time and optimal onewafer cyclic schedule. Multi-cluster tool examples are given to illustrate the proposed approach. The use of the found schedules enables industrial multi-cluster tools to operate with their highest productivity.

Petri Net Modeling and Scheduling of a Close-Down Process for Time-Constrained Single-Arm Cluster Tools

Abstract: In wafer fabrication, a robotic cluster tool is required to be closed down in order for engineers to perform its on-demand and preventive maintenance and switch between different wafer lots. They often deal with a close-down process subject to wafer residency time constraints, i.e., a wafer must exit from a processing chamber before its quality degradation within a certain time limit. To obtain higher yield, it is very important to optimize a close-down process for a cluster tool. Yet the existing literature pays no or little attention to this issue. By focusing on a time-constrained single-arm cluster tool, this paper intends: 1) to build its Petri net model to analyze its schedulability and 2) to develop computationally efficient algorithms to find an optimal and feasible schedule for its closing-down process under different workloads at its steps. Industrial examples are used to illustrate the application of the proposed method.

Uncertainty-Aware Dynamic Reliability Analysis Framework for Complex Systems

Abstract: Critical technological systems exhibit complex dynamic characteristics such as time-dependent behavior, functional dependencies among events, sequencing and priority of causes that may alter the effects of failure. Dynamic fault trees (DFTs) have been used in the past to model the failure logic of such systems, but the quantitative analysis of DFTs has assumed the existence of precise failure data and statistical independence among events, which are unrealistic assumptions. In this paper, we propose an improved approach to reliability analysis of dynamic systems, allowing for uncertain failure data and statistical and stochastic dependencies among events. In the proposed framework, DFTs are used for dynamic failure modeling. Quantitative evaluation of DFTs is performed by converting them into generalized stochastic Petri nets. When failure data are unavailable, expert judgment and fuzzy set theory are used to obtain reasonable estimates. The approach is demonstrated on a simplified model of a cardiac assist system.

The Reachability Problem for Petri Nets is Not Elementary

Abstract: Petri nets, also known as vector addition systems, are a long established model of concurrency with extensive applications in modelling and analysis of hardware, software and database systems, as well as chemical, biological and business processes. The central algorithmic problem for Petri nets is reachability: whether from the given initial configuration there exists a sequence of valid execution steps that reaches the given final configuration. The complexity of the problem has remained unsettled since the 1960s, and it is one of the most prominent open questions in the theory of verification. Decidability was proved by Mayr in his seminal STOC 1981 work, and the currently best published upper bound is non-primitive recursive Ackermannian of Leroux and Schmitz from LICS 2019. We establish a non-elementary lower bound, i.e. that the reachability problem needs a tower of exponentials of time and space. Until this work, the best lower bound has been exponential space, due to Lipton in 1976. The new lower bound is a major breakthrough for several reasons. Firstly, it shows that the reachability problem is much harder than the coverability (i.e., state reachability) problem, which is also ubiquitous but has been known to be complete for exponential space since the late 1970s. Secondly, it implies that a plethora of problems from formal languages, logic, concurrent systems, process calculi and other areas, that are known to admit reductions from the Petri nets reachability problem, are also not elementary. Thirdly, it makes obsolete the currently best lower bounds for the reachability problems for two key extensions of Petri nets: with branching and with a pushdown stack.

A Novel Approach for Constraint Transformation in Petri Nets With Uncontrollable Transitions

Abstract: The main contribution of this correspondence paper consists in a linear algebraic characterization of the admissible marking set relative to a Petri net with uncontrollable transitions, subject to a linear constraint. In more detail, given a linear constraint that limits the number of tokens in one place, an algorithm is proposed to compute an approximation of the admissible marking set in terms of a disjunction of transformed linear constraints. The optimality of the solution is guaranteed provided that certain conditions are satisfied during the intermediate steps of the iterative approach. In all the other cases, the set of markings described by the transformed constraints could be surely contained in the admissible marking set.

Online conformance checking using behavioural patterns

Abstract: New and compelling regulations (e.g., the GDPR in Europe) impose tremendous pressure on organizations, in order to adhere to standard procedures, processes, and practices. The field of conformance checking aims to quantify the extent to which the execution of a process, captured within recorded corresponding event data, conforms to a given reference process model. Existing techniques assume a post-mortem scenario, i.e. they detect deviations based on complete executions of the process. This limits their applicability in an online setting. In such context, we aim to detect deviations online (i.e., in-vivo), in order to provide recovery possibilities before the execution of a process instance is completed. Also, current techniques assume cases to start from the initial stage of the process, whereas this assumption is not feasible in online settings. In this paper, we present a generic framework for online conformance checking, in which the underlying process is represented in terms of behavioural patterns and no assumption on the starting point of cases is needed. We instantiate the framework on the basis of Petri nets, with an accompanying new unfolding technique. The approach is implemented in the process mining tool ProM, and evaluated by means of several experiments including a stress-test and a comparison with a similar technique.

Linguistic Petri Nets Based on Cloud Model Theory for Knowledge Representation and Reasoning

Abstract: Fuzzy Petri nets (FPNs) are a vital modeling technique for the construction of knowledge-based systems, which have been commonly used in many fields, such as fault diagnosis, risk assessment, workflow management, and disassembly process planning. However, the conventional FPNs have been blamed for the following reasons: 1) the representation parameters in FPNs cannot precisely model experts' experience since it is difficult to manage the fuzziness and randomness of knowledge assessments simultaneously, and 2) the weight coefficients in the existing approximate reasoning algorithms are hardly enough to reflect the associated weights of reordered places. In response, we propose a new type of FPNs, called cloud reasoning Petri nets (CRPNs) based on the concept of interval clouds and the hybrid averaging operator. The cloud production rules in a knowledge-based system are modeled by CRPNs, where the truth degrees of places, the certainty factors of rules, and the thresholds of transitions are represented by interval clouds. Moreover, a matrix operation-based reasoning algorithm is proposed to improve the efficiency of calculating final truth degrees, in which both local and ordered weight coefficients are taken into consideration. Finally, a practical example concerning a power system is provided to demonstrate the usefulness and advantages of the proposed CRPN model.

A Parallel Workflow Pattern Modeling Using Spiking Neural P Systems With Colored Spikes

Abstract: Spiking neural P systems, otherwise known as named SN P systems, are bio-inspired parallel and distributed neural-like computing models. Due to the spiking behavior, SN P systems fall into the category of spiking neural networks, and are considered to be an auspicious candidate of the 3G of neural networks. It has been reported that SN P systems with colored spikes are computationally capable, and perform well in describing behaviors of complex systems. Nonetheless, some practical issue is open to be investigate, such as workflow and traffic flow modeling. In this paper, a parallel workflow pattern modeling using SN P systems with colored spikes is proposed. As results, 20 designs are constructed using SN P systems for 20 classical workflow patterns. The functioning processes that operate both sequentially and simultaneously in the workflow pattern are able to be modeled and simulated. SN P systems with colored spikes have some similarity with Petri nets, hence can be used to model workflow patterns. This will provide a novel neural-like modeling method for modeling traffic flow.

Detecting data-flow errors based on Petri nets with data operations

Abstract: In order to guarantee the correctness of business processes, not only control-flow errors but also data-flow errors should be considered. The control-flow errors mainly focus on deadlock, livelock, soundness, and so on. However, there are not too many methods for detecting data-flow errors. This paper defines Petri nets with data operations U+0028 PN-DO U+0029 that can model the operations on data such as read, write and delete. Based on PN-DO, we define some data-flow errors in this paper. We construct a reachability graph with data operations for each PN-DO, and then propose a method to reduce the reachability graph. Based on the reduced reachability graph, data-flow errors can be detected rapidly. A case study is given to illustrate the effectiveness of our methods.

A Survey on Petri Net Models for Freight Logistics and Transportation Systems

Abstract: The benefits of logistics and transportation systems to citizens, economy, and society can strongly increase when considering a smart, safe, and environmentally friendly management. This results in the implementation of intelligent transportation systems that combine innovative technologies and transportation frameworks at the aim of finding proper solutions to the related decision problems. To achieve such a goal, the intrinsic discrete event dynamics of these systems should be considered when deriving a model to be used for simulation, analysis, optimization, and control. Among the different discrete event models, Petri Nets (PNs) are particularly effective due to a series of relevant features. In addition, several high-level PN models (e.g., colored, continuous, or hybrid) allow the solution of complex and large-dimension problems that typically arise from real-life applications in the area of freight logistics and transportation systems. This paper presents a survey on contributions in this area. Papers are classified according to the addressed problem, namely, strategic/tactical or operational decision-making-level problem, and the adopted PN formalism. We also debate the approaches’ viability, discussing contributions and limitations, and identify future research directions to enhance the successful application of PNs in freight logistics and transportation systems.

Dependability Analysis of Safety Critical Real-Time Systems by Using Petri Nets

Abstract: The failure of such systems leads to the catastrophic effects, including injury or death to humans, and harm to the environment. Petri nets (PNs) have been widely used for verification and validation of real-time systems. However, the existing approaches do not consider the critical aspects of reliability and safety that include nonliveness, deadlock, stability, and throughput. In this paper, we introduce these as metrics of reliability and safety for safety critical real-time systems. This paper also proposes an innovative methodology for analysis of nonliveness, deadlock, stability, and throughput metrics by linear programming using PN modeling. The application of the proposed techniques has been validated by applying it on four different safety critical systems, running in six nuclear power plants and shown for reactor protection system.

Method of power grid fault diagnosis using intuitionistic fuzzy Petri nets

Abstract: The uncertainty of alarm information in power grids can lead to incorrect diagnosis of faults. The authors propose a method for diagnosing power grid faults that considers the uncertainty of alarm information using intuitionistic fuzzy logic. To consider the influence of the uncertainty of alarm information in fault diagnosis, an intuitionistic fuzzy set is used to represent the certainty and the uncertainty of alarm information. Using topological analysis and the logical relationships among electrical devices, protective actions, and circuit breaker trips, the authors establish a diagnostic model for power systems based on intuitionistic fuzzy Petri nets. The certainty and the uncertainty of electrical device fault events are calculated using the reasoning method for intuitionistic fuzzy Petri nets. The results for some test cases show that this method can effectively diagnose complex faults in power systems when multiple components operate incorrectly in the complicated data environment and the information is not trusted.

Petri Net Model Checking with LoLA 2

Abstract: LoLA 2 offers a suite of algorithms for verifying place/transition Petri nets. It combines structural with state space methods and general purpose with Petri net-specific techniques. The methods are easily accessible to people with little knowledge of Petri nets since there is a uniform query language based on temporal logic, and the tool takes care of sound application of its methods. Unlike its predecessor LoLA 1, LoLA 2 is based on a strict modularisation and integration of various standard tools. A careful software engineering approach has been used for coding. Through its code quality and its frequent comparison to other tools in the yearly model checking contests, LoLA 2 has become one of the most reliable verification tools for distributed systems.

Localization and Navigation for Autonomous Mobile Robots Using Petri Nets in Indoor Environments

Abstract: In this paper, mobile robotics and present tools used in localization, mapping, and navigation of a mobile robot are discussed. The main purpose of this paper is, given a map represented by the incidence matrix of a petri net (PN), to evaluate the use of radio-frequency identification (RFID) technology to recognize the position of a robot in this map as well as the use of the PN dynamics as the cognition system of this robot. Thus, cards with RFID technology were placed at each intersection of structured environment (labyrinth) ways. A robot equipped with an RFID reader at its bottom moves until it passes over these cards. When this happens, the vehicle performs actions, such as turning right or left according to the map defined in its algorithm. Once the above-mentioned actions are performed, it goes straight to the next card. To ensure that this happens, there is a black line connecting each card to its neighbor cards. The robot is equipped with three infrared sensors, so it can detect and follow these lines. The results show that the robot can get out of one RFID card and reach the next one since they are connected by a black line. Without these lines, due to the limitations in the structure of the robot, it loses its way and cannot return. Still, the robot is able to execute the necessary navigation movements, in the case of stopping, moving forward, and turning right and left. These movements are correctly coordinated by the PN dynamics. The robot knows which card it is on and goes to the next card according to the previously established map. Each path of the robot is mathematically modeled by the incidence matrix of a petri net. Therefore, it managed to reach the destination in each of the four proposed paths. The PN that represents path 1 has the same number of places and transitions and has curves only to the left. On path 2, a right turn was added. In path 3, besides the two-way curves, RP has more places than transitions. Lastly, in path 4, there is a crossing in the path, that is, the robot goes through the same card twice, making the right and different decisions in each case according to the respective maps. Experimental results show that this approach has feasibility and effectiveness.

Improved Multi-Step Look-Ahead Control Policies for Automated Manufacturing Systems

Abstract: The deadlock control problem in automated manufacturing systems (AMSs) has received much attention in recent years due to the flexibility of an AMS. In the framework of Petri nets, resource-transition circuits and siphons are often used to characterize and derive a deadlock control policy for an AMS. This paper mainly focuses on a class of Petri nets, namely, the system of simple sequential processes with resources, which contains some special resource places. For such a class of Petri nets, the relationship between a multi-step look-ahead deadlock avoidance control method and the structure of the model is established and expanded in a mathematical way. Unlike the one-step look-ahead deadlock avoidance policy (DAP) proposed in the literature, the DAPs reported in this research are applicable to more complex situations, including a model with one-unit resource shared by two or more perfect resource-transition circuits that do not contain each other. Compared with the existing work, some results are archived for expanded models. Finally, for the model with two shared one-unit resources, specific solutions are also presented. Meanwhile, examples are used to demonstrate the proposed results.

Modeling Self-Adaptive Software Systems by Fuzzy Rules and Petri Nets

Abstract: A self-adaptive software system is one that can autonomously modify its behavior at runtime in response to changes in the system and its environment. It is a challenge to model such a kind of systems since it is hard to predict runtime environmental changes at the design phase. In this paper, a formal model called intelligent Petri net (I-PN) is proposed to model a self-adaptive software system. I-PN is formed by incorporating fuzzy rules to a regular Petri net. The proposed net has the following advantages. 1) Since fuzzy rules can express the behavior of a system in an interpretable way and their variables can be reconfigured by the runtime data, the proposed model can model runtime environment and system behavior. 2) Since a fuzzy inference system with well-defined semantics can be used in a complementary way with other model languages for the analysis, thus the proposed model can be analyzed, even though it is described in two different languages: component behaviors in Petri nets while logic control in fuzzy rules. 3) The proposed model has self-adaption ability and can make adaptive decisions at runtime with the help of fuzzy inference reasoning. We adopt a manufacturing system to show the feasibility of the proposed model.

An Approach for Enumerating Minimal Siphons in a Subclass of Petri Nets

Abstract: Siphons, as a structural object of Petri nets (PNs), are closely related to deadlock-freedom in PNs. Efficient siphon computation is of great importance in developing siphon-based deadlock control strategies with good performance. This paper is concerned with the enumeration of minimal siphons in a subclass of PNs called systems of sequential systems with shared resources (S4PR). First, a method with polynomial complexity is proposed to decide whether a subset of resource places can generate a minimal siphon. Next, by utilizing the technique of problem partitioning, we develop an approach to compute all minimal siphons in S4PR. The proposed approach is illustrated by an example and its advantage is finally demonstrated via a comparison with other approaches.

Verification of Prognosability for Labeled Petri Nets

Abstract: This technical note is concerned with the fault prognosis problem for partially observed discrete-event systems modeled by unbounded labeled Petri nets. The goal of this problem is to predict the occurrence of each fault before its occurrence. The condition of prognosability provides the necessary and sufficient condition under which any fault can be predicted with no missed detection and no false alarm. In this technical note, we investigate the verification of prognosability for unbounded labeled Petri nets. First, we show that checking prognosability is decidable for Petri net languages. Our approach is based on a reduction from this verification problem to an existing Petri nets model checking problem. Then, we show that the complexity of this problem is EXPSPACE-complete. Our results extend previous works on the verification of language-based prognosability from regular languages to Petri net languages.

Robot Planning Based on Boolean Specifications Using Petri Net Models

Abstract: In this paper, we propose an automated method for planning a team of mobile robots such that a Boolean-based mission is accomplished. The task consists of logical requirements over some regions of interest for the agents’ trajectories and for their final states. In other words, we allow combinatorial specifications defining desired final states whose attainment includes visits to, avoidance of, and ending in certain regions. The path planning approach should select such final states that optimize a certain global cost function. In particular, we consider minimum expected traveling distance of the team and reduce congestions. A Petri net (PN) with outputs models the movement capabilities of the team and the regions of interest. The imposed specification is translated to a set of linear restrictions for some binary variables, the robot movement capabilities are formulated as linear constraints on PN markings, and the evaluations of the binary variables are linked with PN markings via linear inequalities. This allows us to solve an integer linear programming problem whose solution yields robotic trajectories satisfying the task.

A holistic approach for soundness verification of decision-aware process models

Abstract: The last decade has witnessed an increasing transformation in the design, engineering, and mining of processes, moving from a pure control-flow perspective to more integrated models where also data and decisions are explicitly considered. This calls for methods and techniques able to ascertain the correctness of such integrated models. Differently from previous approaches, which mainly focused on the local interplay between decisions and their corresponding outgoing branches, we introduce a holistic approach to verify the end-to-end soundness of a Petri net-based process model, enriched with case data and decisions. In addition, we present an effective, implemented technique that verifies soundness by translating the input net into a colored Petri net with bounded color sets, on which standard state space analysis techniques are subsequently applied. Experiments on real life illustrate the relevance and applicability in real settings.

Prototyping of Concurrent Control Systems With Application of Petri Nets and Comparability Graphs

Abstract: This paper shows a novel prototyping technique for concurrent control systems described by interpreted Petri nets. The technique is based on the decomposition of an interpreted Petri net into concurrent sequential automata. In general, minimum decomposition requires runtime that is exponential in the number of Petri net places. We show that in many cases, including the real-life ones, the minimum decomposition problem can be solved in polynomial time. The proposed method allows implementing a concurrent control system using minimal number of sequential components, which requires polynomial time and can be applied to most of the considered cases. The presented concept is illustrated by a real-life industrial example of a beverage production and distribution machine implemented in a field programmable gate array.