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Towards optimal maintenance planning of existing structures based on time-dependent reliability analysis

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Civil engineering structures play an important role in any country for improving the economy together with the social and environmental welfare. An unwanted failure might cause significant impacts at different levels for the structure owner and for users. Fatigue is one of the main degradation processes on steel structures that causes structural failure before the end of the designed service life. To avoid unexpected failures due to fatigue, a comprehensive structural Life Cycle Management (LCM) is required to minimize the life-cycle cost and maximize the structural service life. One of the main objectives within the LCM can be related to optimizing the structural maintenance planning. Achieving this goal is a challenging task which requires to address some challenges such as predicting the structural performance under uncertainty, employing Structural Health Monitoring (SHM) data to reduce uncertainties, taking into account crack propagation behavior for given components, reliability and cost-informed decision making, and effect of maintenance actions among others. Accordingly, following contributions are considered in this research to improve the capabilities of structural LCM which are explained shortly in the sequel.Developing a new time-dependent reliability method for fatigue reliability analysis.Investigating the effectiveness of advanced crack propagation tools to study unwanted fatigue cracking problems and characterizing some possible repair actions on a real case study.Introducing the assumptions and simplification steps required to integrate the proposed time-dependent reliability method with crack propagation models to approximate the time-dependent fatigue reliability.As the first contribution of this thesis, a new time-dependent reliability method called AK-SYS-t is proposed. This method provides an efficient and accurate tool to evaluate time-dependent reliability of a component compared to other available methods. AK-SYS-t relates the time-dependent reliability to system reliability problems and tries to exploit the efficient system reliability methods such as AK-SYS towards time-dependent reliability analysis. It is worth mentioning that time-dependent reliability analysis is necessary in this context since the performance deterioration (such as fatigue) is a time-dependent process associated with time-dependent parameters such as fatigue loading.Another related topic is the study of crack propagation phenomenon with advanced modeling tools such as Finite Element Method (FEM) and eXtended Finite Element Method (XFEM). For illustration purposes, the crack in the root of a fillet weld is considered (common fatigue detail in bridges with orthotropic deck plates). One important issue investigated herein is the influence of the transversal tension in the deck plate on the direction of the crack propagation. It is shown how increasing the transversal tension in the deck plate may change the crack propagation towards the deck plate. Such cracks are considered dangerous since they are hard to inspect and detect. In the end, XFEM is used to investigate the effectiveness of two possible repair solutions.A supplementary contribution is related to introducing the required steps in order to integrate the newly developed time-depend reliability method with crack propagation problems through some applicational examples. This is a challenging task since performing the time-dependent reliability analysis for such problems requires a cycle-by-cycle calculation of stress intensity factors which requires huge computational resources. Therefore, the aim here is to introduce the assumptions and simplification steps in order to adopt the AK-SYS-t for fatigue reliability analysis. Accordingly, two examples are considered. (...)
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Thesis
Cette thèse porte sur le développement des méthodes de l'analyse de fiabilité dans le contexte des modèles numériques coûteux en temps de calcul. L'analyse de fiabilité consiste à calculer et à prédire la probabilité de défaillance d'une structure. Ceci est généralement assuré par les méthodes de simulation qui sont à ce jour un moyen incontournable vue leur capacité à traiter des problèmes complexes. Toutefois, ces méthodes souffrent des temps de calcul considérables engendrés par les multiples appels à des fonctions de performance coûteuses en temps de calcul et qui impliquent des modèles numériques onéreux. L'utilisation des méthodes d'apprentissage actif du méta-modèle de type krigeage, notamment les méthodes AK, est une des alternatives proposées pour diminuer les temps de calcul. Elle consiste à substituer la fonction de performance coûteuse à évaluer par un modèle mathématique simplifié dont les temps d'évaluation sont largement inférieurs par rapport au premier. Le méta-modèle est calibré à partir d'un nombre limité d'évaluations de la fonction de performance, appelé plan d'expériences. Ce dernier est constitué d'une façon adaptative dans le contexte de l'apprentissage actif. Cette thèse a pour objectif d'étendre l'utilisation des méthodes AK afin d'apporter des éléments de réponse au choix du type et de la configuration du méta-modèle en premier lieu et de proposer ensuite une nouvelle méthode pour le traitement des problèmes soumis à l'aléa spatial. La première contribution de la thèse propose donc de substituer la fonction de performance par un ensemble de méta-modèles afin de de s'affranchir du choix ad hoc du type et/ou de la configuration du méta-modèle. Une méthode dénommée AKE-MCS est proposée pour l'estimation de la probabilité de défaillance, où la mise en place d'un ensemble de méta-modèles est effectuée par l'agrégation pondérée des prédictions de trois krigeages ordinaires ayant différents noyaux. Cet ensemble est calibré itérativement en utilisant une nouvelle fonction d'apprentissage basée sur la probabilité de mauvais classement du point de prédiction par l'ensemble de méta-modèles. La seconde contribution porte sur l'analyse de fiabilité des structures sujettes à une variabilité spatiale aléatoire. Cette dernière peut générer de multiples lieux de défaillance qui sont généralement non pris en compte lors de l'estimation de la probabilité de défaillance à cause de l'hypothèse d'unicité du lieu de la défaillance. Ceci entraine généralement une mauvaise estimation de la probabilité de défaillance. La considération des multiples lieux de défaillance potentiels est ici effectuée par des méthodes de fiabilité système, par analogie entre la formulation mathématique des systèmes série et celle du problème abordé. Une extension de la méthode AK-SYS est proposée, dénommée AK-SYSs. Les lieux de défaillance potentiels ne sont pas sélectionnés à l'avance puisqu'ils sont méconnus, ils sont identifiés itérativement. La méthode proposée combine donc le processus d'enrichissement de la méthode AK-SYS avec une stratégie de recherche active des lieux de défaillance potentiels.
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Chapter
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