Yes / System safety, reliability and risk analysis are important tasks that are performed throughout the system lifecycle to ensure the dependability of safety-critical systems. Probabilistic risk assessment (PRA) approaches are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to, Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). Growing complexity of modern systems and their capability of behaving dynamically make it challenging for classical PRA techniques to analyse such systems accurately. For a comprehensive and accurate analysis of complex systems, different characteristics such as functional dependencies among components, temporal behaviour of systems, multiple failure modes/states for components/systems, and uncertainty in system behaviour and failure data are needed to be considered. Unfortunately, classical approaches are not capable of accounting for these aspects. Bayesian networks (BNs) have gained popularity in risk assessment applications due to their flexible structure and capability of incorporating most of the above mentioned aspects during analysis. Furthermore, BNs have the ability to perform diagnostic analysis. Petri Nets are another formal graphical and mathematical tool capable of modelling and analysing dynamic behaviour of systems. They are also increasingly used for system safety, reliability and risk evaluation. This paper presents a review of the applications of Bayesian networks and Petri nets in system safety, reliability and risk assessments. The review highlights the potential usefulness of the BN and PN based approaches over other classical approaches, and relative strengths and weaknesses in different practical application scenarios. / This work was funded by the DEIS H2020 project (Grant Agreement 732242).

A fairly general model of the elevator system is presented. Coloured Petri Nets (CPN) and CPN tools are adopted as modeling tools. The model, which is independent of the number of floors and elevators, covers different stages of the elevator system in substantial detail. The model assists simulation-based analysis of different algorithms and rules which govern real elevator systems. The results prove the compatibility and applicability of this model in various situations and demonstrate the expressive power and convenience of CPN. / Thesis / Master of Applied Science (MASc)

This thesis is focused on distributed systems modeling using Petri nets. Distributed systems are increasingly being implemented in applications and computing systems, where their task is to ensure sufficient performance and stability for a large number of its users. When modeling a distributed systems, stochastic behavior of Petri nets is important, which will provide more realistic simulations. Therefore, this thesis focuses mainly on timed Petri nets. The theoretical part of this thesis summarizes distributed systems, their properties, types and available architectures, as well as Petri nets, their representation, types and the principle of an operation. In the practical part, two models were implemented, namely a horizontally scaled web application divided into several services with a distributed database and a large grid computing system, more precisely the BOINC platform with the Folding@home project. Both models were implemented using the PetNetSim library of Python. The goal of this thesis is to perform simulations on the created models for different scenarios of their behavior.

This diploma thesis formally defines the Object Oriented Petri Nets and presents term a virtual machine. Then it introduces the concept of Object Oriented Petri Nets Virtual Machine. Finally, project describes a procedure for implementation of the OOPN Virtual Machine.

[pt] Lógica Proposicional Dinâmica (PDL) é um sistema lógico multi-modal utilizada para especificar e verificar propriedades em programas sequenciais. Redes de Petri são um formalismo largamente utilizado na especificação de sistemas concorrentes e possuem uma interpretação gráfica bastante intuitiva. Neste trabalho apresentam-se extensões da Lógica Proposicional Dinâmica onde os programas são substituídos por Redes de Petri. Define-se uma codificação composicional para as Redes de Petri através de redes básicas, apresentando uma semântica composicional. Uma axiomatização é definida para a qual o sistema é provado ser correto, e completo em relação à semântica proposta. Três Lógicas Dinâmicas são apresentadas: uma para efetuar inferências sobre Redes de Petri Marcadas ordinárias e duas para inferências sobre Redes de Petri Estocásticas marcadas, possibilitando a modelagem de cenários mais complexos. Alguns sistemas dedutivos para essas lógicas são apresentados. A principal vantagem desta abordagem concerne em possibilitar efetuar inferências sobre Redes de Petri [Estocásticas] marcadas sem a necessidade de traduzí-las a outros formalismos. / [en] Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyze concurrent programs with a very intuitive graphical representation. In this work, we propose some extensions of Propositional Dynamic Logic for reasoning about Petri Nets. We define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Then we present an axiomatization and prove completeness regarding our semantics. Three versions of Dynamic Logics to reasoning with Petri Nets are presented: one of them for ordinary Marked Petri Nets and two for Marked Stochastic Petri Nets yielding to the possibility of model more complex scenarios. Some deductive systems are presented. The main advantage of our approach is that we can reason about [Stochastic] Petri Nets using our Dynamic Logic and we do not need to translate it into other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.

Presently information systems are increasingly penetrating to our daily life. Recently it is relevant to integrate the newest technologies. In that way traditional system becomes “smart” who are more economical, optimal, and self-sufficient. The biggest problem is to make a model of “smart” system. There were analyzed modeling methods, heating and cooling control systems in this job. Mathematical model for heating and cooling controller using timed Petri nets was presented. According to analyzed problems it was made verification with Matlab during experimental phase. There was made comparison evaluation of mathematical model made with timed Petri nets and fuzzy logic.

Maintenance models are critical for evaluation of the alternative maintenance policies for modern engineering systems. A poorly selected policy can result in excessive life-cycle costs as well as unnecessary risks for catastrophic failures of the system. Economic dependence refers to the difference between the cost of combining the maintenance of a number of components and the cost of performing the same maintenance actions individually. Maintenance that takes advantage of this difference is often called opportunistic. Large number of components and economic inter-dependence are two pervasive characteristics of modern engineering systems that make the modeling of their maintenance processes particularly challenging. Simulation is able to handle both of these characteristics computationally, but the complexity, especially from the model verification perspective, becomes overwhelming as the number of components increases. This research introduces a new procedure for maintenance models of multi-unit repairable systems with economic dependence among its components and under opportunistic maintenance policies. The procedure is based on the stochastic Petri net with aging tokens modeling framework and it makes use of a component-level model approach to overcome the state explosion of the model combined with a novel order-reduction scheme that effectively combines the impact of other components into a single distribution. The justification for the used scheme is provided, the accuracy is assessed, and applications for the systems of realistic complexity are considered.

In 1996, a concept was proposed by the UK Ministry of Defence with the intention of making the field of reliability more useful to the end user, particularly within the field of military aerospace. This idea was the Maintenance Free Operating Period (MFOP), a duration of time in which the overall system can complete all of its required missions without the need to undergo emergency repairs or maintenance, with a defined probability of success. The system can encounter component or subsystem failures, but these must be carried with no effect to the overall mission, until such time as repair takes place. It is thought that advanced technologies such as redundant systems, prognostics and diagnostics will play a major role in the successful use of MFOP in practical applications. Many types of system operate missions that are made up of several sequential phases. For a mission to be successful, the system must satisfactorily complete each of the objectives in each of the phases. If the system fails or cannot complete its goals in any one phase, the mission has failed. Each phase will require the system to use different items, and so the failure logic changes from phase to phase. Mission unreliability is defined as the probability that the system fails to function successfully during at least one phase of the mission. An important problem is the efficient calculation of the value of mission unreliability. This thesis investigates the creation of a modelling method to consider as many features of systems undergoing both MFOPs and phased missions as possible. This uses Petri nets, a type of digraph allowing storage and transit of tokens which represent system states. A simple model is presented, following which, a more complex model is developed and explained, encompassing those ideas which are believed to be important in delivering a long MFOP with a high degree of confidence. A demonstration of the process by which the modelling method could be used to improve the reliability performance of a large system is then shown. The complex model is employed in the form of a Monte-Carlo simulation program, which is applied to a life-size system such as may be encountered in the real world. Improvements are suggested and results from their implementation analysed.

Nous proposons dans cette thèse plusieurs contributions relatives à la vérification quantitative des systèmes. Cette discipline vise à évaluer les propriétés fonctionnelles et les performances d'un système. Une telle vérification requiert deux ingrédients : un modèle formel de représentation d'un système et une logique temporelle pour exprimer la propriété considérée. L'évaluation est alors faite par une méthode statistique ou numérique. La complexité spatiale des méthodes numériques, proportionnelle à la taille de l'espace d'états, les rend impraticables si les systèmes présentent une combinatoire importante. La méthode de comparaison stochastique basée sur les chaînes de Markov censurées réduit la mémoire occupée en restreignant l'analyse à un sous-ensemble des états de la chaîne originale. Dans cette thèse nous fournissons de nouvelles bornes dépendant de l'information disponible relative à la chaîne. Nous introduisons une nouvelle logique temporelle quantitative appelée Hybrid Automata Stochastic Logic (HASL), pour la vérification des processus stochastiques à événements discrets (DESP).HASL emploie les automates linéaires hybrides (LHA) pour sélectionner des préfixes de chemins d'exécution d'un DESP. LHA permet de collecter des informations élaborées durant la génération des chemins, fournissant ainsi à l'utilisateur un moyen d'exprimer des mesures sophistiquées. HASL supporte donc des raisonnements temporels mixés avec une analyse à base de récompenses. Nous avons aussi développé COSMOS, un outil qui implémente la vérification statistique de formules HASL pour des réseaux de Petri stochastiques. Les ateliers flexibles (FMS) ont souvent été modélisés par des réseaux de Petri. Cependant le modélisateur doit avoir une bonne connaissance de ce formalisme. Afin de faciliter cette modélisation nous proposons une méthodologie de modélisation compositionnelle orientée vers les applications qui ne requiert aucune connaissance des réseaux de Petri. / We propose in this thesis several contributions related to the quantitative verification of systems. This discipline aims to evaluate functional and performance properties of a system. Such a verification requires two ingredients: a formal model to represent the system and a temporal logic to express the desired property. Then the evaluation is done with a statistical or numerical method. The spatial complexity of numerical methods which is proportional to the size of the state space of the model makes them impractical when the state space is very large. The method of stochastic comparison with censored Markov chains is one of the methods that reduces memory requirements by restricting the analysis to a subset of the states of the original Markov chain. In this thesis we provide new bounds that depend on the available information about the chain. We introduce a new quantitative temporal logic named Hybrid Automata Stochastic Logic (HASL), for the verification of discrete event stochastic processes (DESP). HASL employs Linear Hybrid Automata (LHA) to select prefixes of relevant execution paths of a DESP. LHA allows rather elaborate information to be collected on-the-fly during path selection, providing the user with a powerful mean to express sophisticated measures. In essence HASL provides a unifying verification framework where temporal reasoning is naturally blended with elaborate reward-based analysis. We have also developed COSMOS, a tool that implements statistical verification of HASL formulas over stochastic Petri nets. Flexible manufacturing systems (FMS) have often been modelized by Petri nets. However the modeler should have a good knowledge of this formalism. In order to facilitate such a modeling we propose a methodology of compositional modeling that is application oriented and does not require any knowledge of Petri nets by the modeler.

Cette thèse traite de l'identification des systèmes à événements discrets (SED) automatisés dans un contexte industriel. En particulier, le travail aborde les systèmes formés par un processus et un automate programmable (AP) fonctionnant en boucle fermée - l'identification a pour but d’obtenir un modèle approximatif exprimé en réseaux de Petri interprétés (RPI) à partir du comportement externe observé sous la forme d'une seule séquence de vecteurs d’entrée-sortie de l’AP. Tout d'abord, une analyse des méthodes d'identification est présentée, ainsi qu’une étude comparative des méthodes récentes pour l'identification des SED. Puis le problème abordé est décrit - des importantes caractéristiques technologiques dans les systèmes automatisés par l’AP sont détaillées. Ces caractéristiques doivent être prises en compte dans la résolution du problème, mais elles ne peuvent pas être traitées par les méthodes existantes d’identification. La contribution principale de cette thèse est la création de deux méthodes d’identification complémentaires. La première méthode permet de construire systématiquement un modèle RPI à partir d'une seule séquence entrée-sortie représentant le comportement observable du SED. Les modèles RPI décrivent en détail l’évolution des entrées et sorties pendant le fonctionnement du système. La seconde méthode considère des SED grands et complexes - elle est basée sur une approche statistique qui permettre la construction des modèles en RPI compactes et expressives. Elle est composée de deux étapes - la première calcule à partir de la séquence entrée-sortie, la partie réactive du modèle, constituée de places observables et de transitions. La deuxième étape fait la construction de la partie non-observable, en rajoutant des places pour permettre la reproduction de la séquence entrée-sortie. Les méthodes proposées, basées sur des algorithmes de complexité polynomiale, ont été implémentées en outils logiciels, lesquels ont été testés avec des séquences d’entrée-sortie obtenues à partir des systèmes réels en fonctionnement. Les outils sont décrits et leur application est illustrée à travers deux cas d’étude. / This thesis deals with the identification of automated discrete event systems (DES) operating in an industrial context. In particular the work focuses on the systems composed by a plant and a programmable logic controller (PLC) operating in a closed loop- the identification consists in obtaining an approximate model expressed in interpreted Petri nets (IPN) from the observed behaviour given under the form of a single sequence of input-output vectors of the PLC. First, an overview of previous works on identification of DES is presented as well as a comparative study of the main recent approaches on the matter. Then the addressed problem is stated- important technological characteristics of automated systems and PLC are detailed. Such characteristics must be considered in solving the identification problem, but they cannot be handled by previous identification techniques. The main contribution in this thesis is the creation of two complementary identification methods. The first method allows constructing systematically an IPN model from a single input-output sequence representing the observable behaviour of the DES. The obtained IPN models describe in detail the evolution of inputs and outputs during the system operation. The second method has been conceived for addressing large and complex industrial DES- it is based on a statistical approach yielding compact and expressive IPN models. It consists of two stages- the first one obtains, from the input-output sequence, the reactive part of the model composed by observable places and transitions. The second stage builds the non observable part of the model including places that ensure the reproduction of the observed input-output sequence. The proposed methods, based on polynomial-time algorithms, have been implemented in software tools, which have been tested with input-output sequences obtained from real systems in operation. The tools are described and their application is illustrated through two case studies.