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1
Content available remote Methods of process mining and prediction using deep learning
EN
The first part of the article presents analytical methods to understand how processes (security or business) occur and function over time. The second part presents the concept of a predictive system using deep learning methods that would enable the prediction of subsequent operations or steps that are part of the process under consideration. The article was supplemented with a review of scientific publications related to the content and theoretical foundations were provided. The research was of an applied nature, therefore the considerations are based on the example of analysis and forecasts based on historical data contained in process logs.
PL
Pierwsza część artykułu przedstawia metody analityczne pozwalające zrozumieć, w jaki sposób procesy (dotyczące bezpieczeństwa lub biznesu) zachodzą i funkcjonują w czasie. W drugiej części przedstawiono koncepcję systemu predykcyjnego wykorzystującego metody głębokiego uczenia, które umożliwiałyby przewidywanie kolejnych operacji lub kroków wchodzących w skład rozważanego procesu. Uzupełnieniem artykułu był przegląd publikacji naukowych pod kątem merytorycznym oraz podano podstawy teoretyczne. Badania miały charakter aplikacyjny, dlatego rozważania opierają się na przykładzie analiz i prognoz opartych na danych historycznych zawartych w logach procesów.
EN
We propose a new algorithmic approach for the synthesis of a Petri net from a transition system. It is first presented for a class of place/transition Petri nets we call Δ1-Petri nets. A Δ1-Petri net has an incidence matrix where entries have values 0, 1, and -1 only. The algorithm employs Tarjans union/find algorithm for managing sets of vertices. It requires just O(|V||T|) space where V is the set of vertices and T is the set of transition labels. Consequently, problem instances even beyond 1,000,000 vertices have a manageable memory footprint. Our results are experimentally validated using a prototype implementation. We further present ideas for adapting the method to various classes of Petri nets, including pure (loop-free), safe and k-bounded, ordinary nets as subclasses of Δ-1-Petri nets as well as an extension to Δk-Petri nets. This article is an extended version of [1].
EN
A representation of interval orders by sequences of antichains is discussed, and its relationship to the Fishburn’s representation by sequences of the beginnings and endings of domain elements is analysed in detail. Moreover, an operational semantics based on sequences of maximal antichains is proposed and investigated for a general class of safe Petri nets with context arcs.
EN
The boundedness problem is a well-known exponential-space complete problem for vector addition systems with states (or Petri nets); it asks if the reachability set (for a given initial configuration) is finite. Here we consider a dual problem, the co-finiteness problem that asks if the complement of the reachability set is finite; by restricting the question we get the co-emptiness (or universality) problem that asks if all configurations are reachable. We show that both the co-finiteness problem and the co-emptiness problem are exponential-space complete. While the lower bounds are obtained by a straightforward reduction from coverability, getting the upper bounds is more involved; in particular we use the bounds derived for reversible reachability by Leroux (2013). The studied problems were motivated by a result for structural liveness of Petri nets; this problem was shown decidable by Jančar (2017), without clarifying its complexity. The structural liveness problem is tightly related to a generalization of the co-emptiness problem, where the sets of initial configurations are (possibly infinite) downward closed sets instead of just singletons. We formulate the problems even more generally, for semilinear sets of initial configurations; in this case we show that the co-emptiness problem is decidable (without giving an upper complexity bound), and we formulate a conjecture under which the co-finiteness problem is also decidable.
EN
The main purpose of the paper is presentation of new opportunities for process modelling. In the literature review section, Petri nets as one of the formal modelling notation of processes is highlighted and introduction of relatively young research discipline – process mining – is presented. One of the process mining tasks is process model discovery from event logs gathered in informatics systems in enterprise. In the article practical example of process model discovery with ProM software is given with use of real event log from Volvo IT Belgium. In conclusions further opportunities of process mining techniques in process management are emphasized.
PL
W ogólności system robotyczny projektowany jest jako pojedynczy agent upostaciowiony lub ich zestaw, ale ta praca koncentruje się na działaniu pojedynczego agenta. Agent upostaciowiony dekomponowany jest na współdziałające podsystemy. W dotychczasowych pracach działanie podsystemów opisywane było za pomocą hierarchicznych automatów skończonych, z których stanami były skojarzone operacje. W tym podejściu sposób komunikacji między podsystemami traktowany był jako zagadnienie implementacyjne. W artykule przedstawiono alternatywną metodę opisu agenta upostaciowionego za pomocą hierarchicznych sieci Petriego z dozorami. Hierarchiczna sieć powstaje poprzez przekształcenie automatu skończonego opisującego działanie podsystemu w sieć Petriego wyposażoną w podsieci definiujące zachowania. Wyspecyfikowanie zachowania wymaga natomiast wyjawienia za pomocą sieci Petriego wykorzystywanych modeli komunikacyjnych określających interakcje między podsystemami. Podejście wykorzystujące sieć Petriego umożliwia całościowe określenie działania agenta upostaciowionego w fazie specyfikacji.
EN
In general a robotic system is designed as a single embodied agent or a network of such agents. Nevertheless this work focuses on the activities of a single agent. An embodied agent is decomposed into interacting subsystems. Up till now the activities of subsystems have been specified by using hierarchic finite state automatons. Subsystem operations were associated with the states of those automatons. Communication between subsystems was treated as an implementation issue. This paper presents an alternative method of defining an embodied agent. A hierarchic Petri net with guards is used. A hierarchic net is the result of transformation of a finite state automaton describing the activities of a subsystem. Its subnets represent subsystem behaviours. Specification of behaviours requires the definition of inter-subsystem communication model, that also can be defined by a Petri net. Thus the resulting hierarchic Petri net specifies all of the activities of an embodied agent.
7
Content available Process Modelling Based on Event Logs
EN
Process modelling is a very important stage in a Business Process Management cycle enabling process analysis and its redesign. Many sources of information for process modelling purposes exist. It may be an analysis of documentation related directly or indirectly to the process being analysed, observations or participation in the process. Nowadays, for this purpose, it is increasingly proposed to use the event logs from organization’s IT systems. Event logs could be analysed with process mining techniques to create process models expressed by various notations (i.e. Petri Nets, BPMN, EPC). Process mining enables also conformance checking and enhancement analysis of the processes. In the paper issues related to process modelling and process mining are briefly discussed. A case study, an example of delivery process modelling with process mining technique is presented.
EN
At present, with the increase of production capacity and the promotion of production, the reserves of most mining enterprises under the original industrial indexes are rapidly consumed, and the full use of low-grade resources is getting more and more attention. If mining enterprises want to make full use of low-grade resources simultaneously and obtain good economic benefits to strengthening the analysis and management of costs is necessary. For metal underground mines, with the gradual implementation of exploration and mining projects, capital investment and labor consumption are dynamic and increase cumulatively in stages. Consequently, in the evaluation of ore value, we should proceed from a series of processes such as: exploration, mining, processing and the smelting of geological resources, and then study the resources increment in different stages of production and the processing. To achieve a phased assessment of the ore value and fine evaluation of the cost, based on the value chain theory and referring to the modeling method of computer integrated manufacturing open system architecture (CIMOSA), the analysis framework of gold mining enterprise value chain is established based on the value chain theory from the three dimensions of value-added activities, value subjects and value carriers. A value chain model using ore flow as the carrying body is built based on Petri nets. With the CPN Tools emulation tool, the cycle simulation of the model is carry out by the colored Petri nets, which contain a hierarchical structure. Taking a large-scale gold mining enterprise as an example, the value chain model is quantified to simulate the ore value formation, flow, transmission and implementation process. By analyzing the results of the simulation, the ore value at different production stages is evaluated dynamically, and the cost is similarly analyzed in stages, which can improve mining enterprise cost management, promote the application of computer modeling and simulation technology in mine engineering, more accurately evaluate the economic feasibility of ore utilization, and provide the basis for the value evaluation and effective utilization of low-grade ores.
PL
Obecnie wraz ze wzrostem zapotrzebowania na surowce mineralne, zasoby większości tych surowców podlegają bardzo szybkiemu sczerpaniu, a wykorzystanie zasobów o niskiej jakości jest brane pod uwagę coraz powszechniej. Jeśli przedsiębiorstwa wydobywcze chcą w pełni wykorzystać zasoby surowców mineralnych niskiej jakości i jednocześnie uzyskać dobre wyniki ekonomiczne, niezbędna jest szeroka analiza i zarządzanie kosztami. W przypadku podziemnych kopalń rud metali, przy stopniowej realizacji projektów poszukiwawczo-wydobywczych, nakłady inwestycyjne i nakłady pracy są dynamiczne i wzrastają stopniowo w realizowanych procesach. W związku z tym, w ocenie wartości rudy powinno się uwzględniać szereg procesów, takich jak: poszukiwanie, wydobycie, przeróbkę i hutnictwo, a następnie rozpatrywać przyrosty wartości i kosztów na poszczególnych etapach produkcji i przetwarzania. Aby osiągnąć etapową ocenę wartości rudy i dokładną ocenę kosztów, w oparciu o teorię łańcucha wartości, należy zastosować metodę komputerowego modelowania zintegrowanej produkcji otwartej architektury systemu (CIMOSA). Ramy analizy łańcucha wartości przedsiębiorstwa wydobywczego złota są ustalane z trzech ocen: wartości dodanej, wartości podmiotów i wartości nośników. Model łańcucha wartości wykorzystujący przepływ rudy zbudowany jest w oparciu o sieci Petriego. Symulacja cyklu modelu jest realizowana przez kolorowe sieci Petriego, które zawierają hierarchiczną strukturę. Przykładem jest wielkoskalowe przedsiębiorstwo wydobywcze złota, w którym model łańcucha wartości jest określany ilościowo w celu symulacji procesów tworzenia, przepływu, przeniesienia i realizacji. Analizując wyniki symulacji, wartość rudy na poszczególnych etapach produkcji jest oceniana dynamicznie, a koszty są również analizowane etapami, co może: poprawić zarządzanie kosztami przedsiębiorstw górniczych, promować zastosowanie modelowania komputerowego i technologii symulacji w inżynierii górniczej, bardziej dokładnie ocenić ekonomiczną wykonalność wykorzystania rudy i zapewnić podstawę do oceny wartości i efektywnego wykorzystania rud niskiej jakości.
EN
Reversible computation deals with mechanisms for undoing the effects of actions executed by a dynamic system. This paper is concerned with reversibility in the context of Petri nets which are a general formal model of concurrent systems. A key construction we investigate amounts to adding ‘reverse’ versions of selected net transitions. Such a static modification can severely impact on the behaviour of the system, e.g., the problem of establishing whether the modified net has the same states as the original one is undecidable. We therefore concentrate on nets with finite state spaces and show, in particular, that every transition in such nets can be reversed using a suitable set of new transitions.
10
PL
Barwne sieci Petriego zastosowano do zilustrowania warunków przebiegu procesu, w którym wytwarzano puszki i nakrywki polipropylenowe z powierzchniowymi nadrukami. Sieci te umożliwiły stworzenie szczegółowych modeli tego dość złożonego procesu przemysłowego. Analiza modeli pozwoliła na zrozumienie roli poszczególnych operacji i procesów jednostkowych oraz na określenie krytycznych węzłów na schemacie technologicznym, które normalnie pozostałyby niezauważone. W efekcie wykryto rezerwy produkcyjne i osiągnięto pewne oszczędności, poprawiając tym samym konkurencyjność przedsiębiorstwa.
EN
Colored Petri nets were used for modeling a process for com. prodn. of polypropylene cups and lids and colorprinting their surface. Use of the nets resulted in a better understanding of the individual operations and in an identification of weak points of the technol. process.
PL
W artykule przedstawiona została analiza wskaźników niezawodnościowych stacji elektroenergetycznych 110kV/SN oraz rozdzielni sieciowych RS w oparciu o cząstkowe wskaźniki niezawodnościowe poszczególnych urządzeń oraz elementów tych stacji. Obliczenia zostały przeprowadzone w oparciu o metody analityczne oraz symulacyjne. Jako metodę analityczną zastosowano metodę minimalnych ścieżek niesprawności, natomiast metoda symulacyjna bazowała na teorii rozszerzonych sieci Petriego.
EN
The article presents an analysis of reliability indicators of 110kV / MV substations and switchgear station based on reliability partial indicators of the devices and elements of these stations. The calculations were carried out based on analytical and simulation methods. As an analytical method used method of minimal pathways malfunction, while the simulation method was based on the theory of extended Petri nets.
EN
This work presents a modelling approach for nonlinear process plan (NLPP) implementation in discrete event manufacturing system (DEMS). NLPP is used for the building of the modular structure of an Object Observable Petri Net model of DEMS. The general capabilities of DEMS are defined by resources’ operation templates and the transition incidence relation. Based on system specification and NLPP executed in the system, the modular model of DEMS is defined. The required steps for constructing a modular model through the integration of resource models are presented. The proposed approach to modular modelling is illustrated by means of a sample DEMS and an example of NLPP.
EN
Weighted Petri nets provide convenient models of many man-made systems. Real applications are often required to possess the fundamental Petri net properties of liveness and reversibility, as liveness preserves all the functionalities (fireability of all transitions) of the system and reversibility lets the system return to its initial state (marking) using only internal operations. Characterizations of both behavioral properties, liveness and reversibility, are known for wellformed weighted Choice-Free and ordinary Free-Choice Petri nets, which are special cases of Equal-Conflict Petri nets. However, reversibility is not well understood for this larger class, where choices must share equivalent preconditions, although characterizations of liveness are known. In this paper, we provide the first characterization of reversibility for all live Equal-Conflict Petri nets by extending, in a weaker form, a known condition that applies to the Choice-Free and Free-Choice subclasses. We deduce the monotonicity of reversibility in the live Equal-Conflict class. We also give counter-examples for other classes where the characterization does not hold. Finally, we focus on well-formed Equal-Conflict Petri nets, for which we offer the first polynomial sufficient conditions for liveness and reversibility, contrasting with the previous exponential time conditions.
PL
Przemysłowa produkcja polipropylenowych puszek i przykrywek przez wtryskiwanie została sformalizowana w postaci sieci Petriego i skutecznie wykorzystana do poprawy ekonomiki i konkurencyjności przedsiębiorstwa.
EN
Com. prodn. of polypropylene cans and lids by injection moulding was formalized as a Petri net and successfully evaluated to improve the economy and competitiveness of the company.
EN
A concurrent system is persistent if throughout its operation no activity which became enabled can subsequently be prevented from being executed by any other activity. This is often a highly desirable (or even necessary) property; in particular, if the system is to be implemented in hardware. Over the past 40 years, persistence has been investigated and applied in practical implementations assuming that each activity is a single atomic action which can be represented, for example, by a single transition of a Petri net. In this paper we investigate the behaviour of GALS (Globally Asynchronous Locally Synchronous) systems in the context of VLSI circuits. The specification of a system is given in the form of a Petri net. Our aim is to re-design the system to optimise signal management, by grouping together concurrent events. Looking at the concurrent reachability graph of the given Petri net, we are interested in discovering events that appear in ‘bundles’, so that they all can be executed in a single clock tick. The best candidates for bundles are sets of events that appear and re-appear over and over again in the same configurations, forming ‘persistent’ sets of events. Persistence was considered so far only in the context of sequential semantics. In this paper, we move to the realm of step based execution and consider not only steps which are persistent and cannot be disabled by other steps, but also steps which are nonviolent and cannot disable other steps. We then introduce a formal definition of a bundle and propose an algorithm to prune the behaviour of a system, so that only bundled steps remain. The pruned reachability graph represents the behaviour of a re-engineered system, which in turn can be implemented in a new Petri net using the standard techniques of net synthesis. The proposed algorithm prunes reachability graphs of persistent and safe nets leaving bundles that represent maximally concurrent steps.
EN
For designing and analyzing complex workflow nets the notion of hierarchical decomposition can be essential for keeping the structure of the workflow comprehensible. In this paper we study two classes of nets: hierarchical nets and extended hierarchical nets. The first have a simple hierarchical structure and can be defined in terms of five simple refinement rules. We show that for arbitrary nets it can be easily verified if they can be constructed this way, thus confirming their good design and the properties following from it. As we prove, this can be done by performing the refinements in reverse, i.e., by contracting subnets into single nodes. It is shown that the choice of the contracted subnet does not change the final result of the process, and therefore this procedure for checking the hierarchical structure requires no back-tracking. The second class, extended hierarchical nets, is an extension of the first class where two types of extra refinements are introduced that allow to indicate (1) the synchronization between two parallel running subworkflows or (2) the transfer of a thread from one subworkflow to another one. These refinements come with natural and necessary preconditions that ensure that result is still a sound workflow net. In case (1) where we want to synchronize two actions in two subworkflows, we should convince ourselves that the subworkflows represent parallel threads which always execute together, otherwise a deadlock could easily arise. Dually, in case (2), if after the moment that a choice was made between two subworkflows we at a later point in the workflow want to allow a transfer between them, this can be done safely provided that we did not enter any thread fork in the meantime. We show that the class of extended hierarchical nets, which is defined by adding these two additional types of refinement, is a proper superset of the hierarchical nets, but still all such nets exhibit the correctness property of *-soundness. We do this by showing that the class is a proper subset of the AND-OR nets which were in earlier work shown to have this property.
EN
This paper presents a practical application of Petri nets to model a control algorithm for concurrent and sequential processes in a warehouse. To implement the model of the algorithm in the PLC environment, the properties of the CASE OF statement of the structured language ST are used.
PL
W artykule przedstawiono możliwości wykorzystania metody opartej na teorii sieci Petriego do analizy niezawodnościowej układów elektroenergetycznych. Metoda pozwala na wyznaczanie wypadkowych wartości wielkości niezawodnościowych złożonych układów elektroenergetycznych, a także poszczególnych elementów układu. Pozwala uwzględnić wpływ awaryjności poszczególnych urządzeń na kolejne. Uzyskane informacje, w postaci rozkładów podstawowych wielkości określających niezawodność analizowanych struktur układów elektroenergetycznych, mogą być wykorzystane do dalszych analiz niezawodnościowych.
EN
The paper presents the possibilities of using the method based on the theory of Petri nets to analyze the reliability of power systems. The method allows the determination of the size of the resultant reliability of complex electrical power systems, as well as the individual components of the system. This method take into account the impact of failure of individual devices for next. The information obtained in the form of distributions of basic determining the reliability of the structures of power systems can be used for further reliability analysis.
PL
W niniejszym artykule przedstawiono propozycję uzupełnienia dotychczas spotykanej w literaturze metody oceny niezawodności, opartej o teorię sieci Petriego, o możliwość uwzględniania w badaniach niezawodności układów elektroenergetycznych niezawodności urządzeń sterowniczych oraz zabezpieczających. Analizie poddano przykładowy układ zasilający składający się z czterech urządzeń. Używając programu symulacyjnego stworzono schemat w terminach sieci Petriego oraz zamodelowano pracę tego układu, z uwzględnieniem niezawodności poszczególnych elementów oraz układów automatyki zabezpieczeniowej. Wyznaczono rozkłady czasów poprawnej pracy całego układu zasilającego, z uwzględnieniem awaryjności urządzeń automatyki zabezpieczeniowej oraz pomijając ten aspekt. Wyznaczając wartość oczekiwaną czasu 2625 poprawnej pracy dla otrzymanych rozkładów udowodniono, iż ważnym lecz często pomijanym problemem jest awaryjność tych właśnie urządzeń. Metoda oparta o teorię sieci Petriego oraz opracowany w celu analizy niezawodnościowej program daje możliwość uwzględnienia dodatkowych czynników wpływających na pracę poszczególnych elementów oraz całego układu.
XX
This article presents a proposal to expend previously encountered in the literature of reliability evaluation method based on the theory of Petri nets, about the possibility of taking into account the reliability of the analyzed power systems reliability and safety control devices. An example of the arrangement supply cosisting of four units were analysed. Using the simulation program developed scheme in terms of Petri nets and modeled the work of the system, taking into account the reliability of individual components and systems protection automation. Distributions of lifetimes of the whole supply system were designated, including equipment failure protection automation and ignoring this aspect. Setting the expected value of the lifetime for the obtained distributions proven that an important but often overlooked problem is the failure of these devices. The method is based on the theory of Petri nets and developed in order to analyze the reliability program gives the opportunity to include additional factors affecting the operation of individual components and the entire system.
EN
In this paper we consider workflow nets as dynamical systems governed by ordinary difference equations described by a particular class of Petri nets. Workflow nets are a formal model of business processes. Well-formed business processes correspond to sound workflow nets. Even if it seems necessary to require the soundness of workflow nets, there exist business processes with conditional behavior that will not necessarily satisfy the soundness property. In this sense, we propose an analytical method for showing that a workflow net satisfies the classical soundness property using a Petri net. To present our statement, we use Lyapunov stability theory to tackle the classical soundness verification problem for a class of dynamical systems described by Petri nets. This class of Petri nets allows a dynamical model representation that can be expressed in terms of difference equations. As a result, by applying Lyapunov theory, the classical soundness property for workflow nets is solved proving that the Petri net representation is stable. We show that a finite and non-blocking workflow net satisfies the sound property if and only if its corresponding PN is stable, i.e., given the incidence matrix A of the corresponding PN, there exists a Φ strictly positive m vector such that AΦ ≤ 0. The key contribution of the paper is the analytical method itself that satisfies part of the definition of the classical soundness requirements. The method is designed for practical applications, guarantees that anomalies can be detected without domain knowledge, and can be easily implemented into existing commercial systems that do not support the verification of workflows. The validity of the proposed method is successfully demonstrated by application examples.
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