Analyse et conception de la fiabilité sont indispensables pour le processus de développement des systèmes mécatroniques. Toutefois, des outils puissants sont nécessaires en raison de la complexité croissante et de la cherté d'essai des systèmes mécatroniques. Cette complexité nous amène des difficultés de l'incertitude de modélisation et de la dépendance inconnus, tels que la dépendance fonctionnelle et temporelle. Pour faire face à une telle complexité, la fiabilité des outils d'analyse doivent être mathématiquement puissant, facile à utiliser et efficace de calcul.Les outils classiques ont une certaine quantité d'inconvénients lors de l'évaluation de la fiabilité au niveau du système. Par exemple, les méthodes basées sur la chaîne de Markov ont un problème infime d'explosion combinatoire et le formalisme de l'arbre de défaillance ne fonctionne que quand les composants sont indépendants les uns des autres. Bien que certaines extensions, comme les arbres de défaillance dynamiques, aient été faites pour pallier les lacunes, tous ne peuvent être traitées dans un cadre unique. Le formalisme des réseaux Bayésiens a été récemment considéré comme un outil prometteur de l'inférence statistique pour l'évaluation de fiabilité du système grâce à de nombreux avantages, tels que la capacité de modélisation de la dépendance incertaine, l'intégration de données provenant de diverses sources et les outils de raisonnement bien étudiés. D'autre part, la plus grande valeur ajoutée en mécatronique est en sous-système du contrôle et du traitement de l'information. Les ingénieurs se rendent compte que la conception de contrôleur d'un système dynamique ne peut pas négliger l'exigence de la fiabilité dynamique. Diverses incertitudes influencent non seulement les performances des contrôleurs, mais aussi la fiabilité. Cependant, peu de recherches ont examiné la fiabilité dynamique des contrôleurs.Dans cette recherche, nous avons étudié le formalisme des réseaux bayésiens et développé une méthode de l'évaluation de la fiabilité des systèmes mécatroniques complexes. Cette méthode étend l'analyse bayésienne sur les composants à celle sur les systèmes complexes et permet de considérer des incertitudes des paramètres des modèles asymétriques de temps à l'échec dans les systèmes complexes. Pour effectuer l'inférence dans notre modèle de réseau bayésien, nous avons développé un algorithme modifié de la propagation de croyances non-paramétrique qui est plus efficace dans le cas complexe par rapport à d'autres outils de raisonnement. Nous avons montré également comment effectuer l'analyse de sensibilité dans notre modèle de réseau bayésien qui a une structure non-déterministe.Un contrôleur linéaire dynamique-fiable a été conu pour le module de contrôle des systèmes mécatroniques. Nous avons établi un nouveau lien entre le probabilité de la défaillance du premier passage et les gains de rétroaction des contrôleurs, et obtenu une nouvelle contrainte dynamique de fiabilité pour les objectifs classiques. Le contrôleur linéaire dynamique-fiable est également étendu au formalisme de multiple-modèle pour que la réalisation d'un contrôleur dynamique-fiable soit applicable dans le cas nonlinéaire/non-gaussien. La performance du système peut encore être améliorée dans ce cadre en utilisant les méthodes de multiple-modèle plus avancées.Une grande quantité de résultats de simulation ont démontré que les méthodes développées ont été appliquées avec succès pour analyser et concevoir des systèmes de suspension active du véhicule et peuvent être appliquée à d'autres applications, telles que d'autres systèmes mécatroniques et systèmes de contrôle actif de construction. / Reliability analysis and design become indispensable for the development process of mechatronic systems. However, versatile tools are called for because of the increas•ing complexity and the testing expensiveness of mechatronic systems. Such complexity brings the difficulties of modeling uncertainty and unknown dependency, such as functional and temporal dependency. To deal with such complexity, reliability analysis tools need to be mathematically powerful, be easy to use and be computationally efficient.Conventional tools have a number of drawbacks when evaluating the reliability at system level. For instance, Markov chain based methods have a problem of infamous combinatorial explosion and fault trees formalism works under the assumption of component independency. Although sorne extensions, such as dynamic fault trees, have been made to make up for shortcomings, not all of them can be handled in one framework. Bayesian networks formalism is recently believed to be a promising statistical inference tool for system reliability assessment thanks to many advantages, such as the ability of modeling uncertain dependency, integrating data from diverse sources and the well-studied reasoning tools. On the other hand, the biggest value-added in mechatronics is in control/information processing subsystem. Engineers realize that the controller design of a dynamic system cannot neglect the dynamic reliability requirement. Various uncertainties influence not only the controller performance but also the reliability. However, little research has considered the dynamic reliability of controllers.In this research, we have investigated the Bayesian networks formalism and developed a new system reliability assessment method for complex mechatronic systems. This method extends Bayesian analysis on components to that on complex systems and allows to consider parameter uncertainties of various skewed time-to-failure models in complex systems. To perform the inference in our Bayesian network model, we developed a modified nonparametric beHef propagation which is more efficient in the complex case compared with other reasoning tools. We showed also how to perform the sensitivity analysis in our Bayesian network model that has a non-deterministic structure. A dynamic-reliable linear controller has been designed for the control module of mechatronic systems. We established a new link between the first-passage failure probability and controllers' feedback gains, and obtained a new dynamic-reliability constraint for classical objectives. The dynamic-reliable linear controller is also extended to the multiple model formalism for achieving a dynamic-reliable controller applicable to nonlinearjnon-Gaussian cases. The system performance can be further improved in this framework by using more advanced multiple model methods.A number of simulation results demonstrated that the developed methods have been successfully applied to analyze and design active vehicle suspension systems and can be applied to other applications, such as other mechatronic systems and active building control systems.

As online casino and betting increases in popularity across the globe, the importance of green gambling has become an important subject of discussion. The Swedish betting company, ATG, realises the benefits of this and would like to prevent their gamblers from falling into problem gambling. To predict problem gambling, Bayesian networks were trained on previously identified problem gamblers, separated into seven risk groups. The network was then able to predict the risk group of previously unseen gamblers with an ac- curacy of 94%. It also achieved an average precision of 89%, an average recall of 96% and an average f1-score of 93%. The features in the data set were also ranked, to find which were most important in predicting problem gambling. It was found that municipality, which day of the week the transaction was made and during which hour of the day were the most important features. Also, the Bayesian network was also made as simple as possible, by removing irrelevant features and features which carry very low importance.

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This thesis explores the application of Graph Neural Networks (GNNs), a subset of Geometric Deep Learning methods, for medical image analysis and causal structure learning. Tracking the progression of pathologies in chest radiography poses several challenges in anatomical motion estimation and image registration as this task requires spatially aligning the sequential X-rays and modelling temporal dynamics in change detection. The first part of this thesis proposes a novel approach for change detection in sequential Chest X-ray (CXR) scans using GNNs. The proposed model CheXRelNet utilizes local and global information in CXRs by incorporating intra-image and inter-image anatomical information and showcases an increased downstream performance for predicting the change direction for a pair of CXRs. The second part of the thesis focuses on using GNNs for causal structure learning. The proposed method introduces the concept of intervention on graphs and attempts to relate belief propagation in Bayesian Networks (BN) to message passing in GNNs. Specifically, the proposed method leverages the downstream prediction accuracy of a GNN-based model to infer the correctness of Directed Acyclic Graph (DAG) structures given observational data. Our experimental results do not reveal any correlation between the downstream prediction accuracy of GNNs and structural correctness and hence indicate the harms of directly relating message passing in GNNs to belief propagation in BNs. Overall, this thesis demonstrates the potential of GNNs in medical image analysis and highlights the challenges and limitations of applying GNNs to causal structure learning. / Master of Science / Graphs are a powerful way to represent different real-world data such as interactions between patient observations, co-morbidities, treatments, and relationships between different parts of the human anatomy. They are also a simple and intuitive way of representing causeand- effect relationships between related entities. Graph Neural Networks (GNNs) are neural networks that model such graph-structured data. In this thesis, we explore the applicability of GNNs in analyzing chest radiography and in learning causal relationships. In the first part of this thesis, we propose a method for monitoring disease progression over time in sequential chest X-rays (CXRs). This proposed model CheXRelNet focuses on the interactions within different regions of a CXR and temporal interactions between the same region compared in two CXRs taken at different times for a given patient and accurately predicts the disease progression trend. In the second part of the thesis, we explore if GNNs can be used for identifying causal relationships between covariates. We design a method that uses GNNs for ranking different graph structures based on how well the structures explain the observed data.

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A Bayesian network is graphical representation of the probabilistic relationships among set of variables and can be used to encode expert knowledge about uncertain domains. The structure of this model represents the set of conditional independencies among the variables in the data. Bayesian networks are widely applicable, having been used to model domains ranging from monitoring patients in an emergency room to predicting the severity of hailstorms. In this thesis, I focus on the problem of learning the structure of Bayesian networks from data. Under certain assumptions, the learned structure of a Bayesian network can represent causal relationships in the data. Constraint-based algorithms for structure learning are designed to accurately identify the structure of the distribution underlying the data and, therefore, the causal relationships. These algorithms use a series of conditional hypothesis tests to learn independence constraints on the structure of the model. When sample size is limited, these hypothesis tests are prone to errors. I present a comprehensive empirical evaluation of constraint-based algorithms and show that existing constraint-based algorithms are prone to many false negative errors in the constraints due to run- ning hypothesis tests with low statistical power. Furthermore, this analysis shows that many statistical solutions fail to reduce the overall errors of constraint-based algorithms. I show that new algorithms inspired by constraint satisfaction are able to produce significant improvements in structural accuracy. These constraint satisfaction algo- rithms exploit the interaction among the constraints to reduce error. First, I introduce an algorithm based on constraint optimization that is sound in the sample limit, like existing algorithms, but is guaranteed to produce a DAG. This new algorithm learns models with structural accuracy equivalent or better to existing algorithms. Second, I introduce an algorithm based constraint relaxation. Constraint relaxation combines different statistical techniques to identify constraints that are likely to be incorrect, and remove those constraints from consideration. I show that an algorithm combining constraint relaxation with constraint optimization produces Bayesian networks with significantly better structural accuracy when compared to existing structure learning algorithms, demonstrating the effectiveness of constraint satisfaction approaches for learning accurate structure of Bayesian networks.

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).

Yes / Bayesian Network (BN)-based methods are increasingly used in system reliability analysis. While BNs enable to perform multiple analyses based on a single model, the construction of robust BN models relies either on the conversion from other intermediate system model structures or direct analyst-led development based on experts input, both requiring significant human effort. This article proposes an architecture model-based approach for the direct generation of a BN model. Given the architectural model of a system, a systematic bottom-up approach is suggested, underpinned by failure behaviour models of components composed based on interaction models to create a system-level failure behaviour model. Interoperability and reusability of models are supported by a library of component failure models. The approach was illustrated with application to a case study of a steam boiler system. / The full text will be available at the end of the publisher's embargo: 18th Nov 2023

We develop the necessary theory in algebraic geometry to place Bayesian networks into the realm of algebraic statistics. This allows us to create an algebraic geometry--statistics dictionary. In particular, we study the algebraic varieties defined by the conditional independence statements of Bayesian networks. A complete algebraic classification, in terms of primary decomposition of polynomial ideals, is given for Bayesian networks on at most five random variables. Hidden variables are related to the geometry of higher secant varieties. Moreover, a complete algebraic classification, in terms of generating sets of polynomial ideals, is given for Bayesian networks on at most three random variables and one hidden variable. The relevance of these results for model selection is discussed. / Ph. D.