This thesis presents a reliability analysis of a technical system. It is divided into three main sections. The first section introduces some of the most significant problems of reliability. It deals with a definition and an expresion of reliability, a reliability diagram selection and a detailed description of the reliability analysis. This part also includes an overview of reliability analysis types. Some of the most widely used reliability analyses are briefly described; further advantages and disadvantages of using each method are listed. Failure Modes and Effects Analysis - FMEA is then described in a greater detail. The second section contains an analysis of aviation conditions as well as a design of a reliability analysis that concerns a selected digital system; the system under analysis is a pitch trim indicator. The main design issue lies in a choice of a most suitable method. This choice stems from the overview of reliability analyses presented in the first section of the thesis. In the last section, a FMEA reliability analysis of the pitch trim indicator is conducted. This part includes a discussion of the results as well as a design action that is to lead to an increase in reliability of the analyzed system.

This diploma thesis deals with probability of fracture ceramic head of total hip endoprosthesis during tests by the standard ISO 7206-5. In the first part is made stress analysis with method of finite elements in program ANSYS. Six types of ceramic head with different geometry was analysed for ideal geometry of head and shaft, and also for shape imperfections from nominal conical shaft and head. The final values of principal stress from stress analysis were entry values for the second part – probability of fracture analysis. Weibull weakest-link theory was applied, namely 3-Parameter and 2-Parameter Weibull distribution.

In order to have safe and economy construction, different sources of uncertainty should be properly characterized and considered in structural design and verification. Commonly, reliability analysis is being used to evaluate the consistency of design process, including the uncertainty. A full probabilistic approach is an appropriate tool to consider the aleatory portion of uncertainty. However, in dealing with epistemic uncertainty in reliability analysis, modern mathematical tools such as fuzzy logic is required. Unreinforced masonry (URM) is known as sustainable building material and is on the top of worldwide building materials consumed in residential buildings. In this thesis, based on the available information on material, probabilistic models including the involved uncertainty for masonry properties has been provided for reliability study. Furthermore, a new experimental procedure for initial shear and friction coefficient, which theoretically reduces epistemic uncertainty, has been introduced. The unreinforced masonry walls that are important structural members in typical masonry buildings have been chosen as the cases of reliability study. Different verification methods for combination of in-plane shear and compression according to various codes has been collected and direct deterministic equations to predict the capacity has been extracted. In order to identify uncertainty (inaccuracy in design models), the observed (experimental results) load-carrying capacity are compared with predicted values and then the relevant uncertainty in models has been derived. Several reliability analysis using only stochastic method and using fuzzy-randomness technique has been conducted. The effect of uncertainty on assessed reliability has been highlighted. Additionally, the distinction between linear and non-linear application of partial safety factors has been investigated. Finally, by means of 3D graphs the actual reliability level of various masonry walls designed according to the latest German National Annex code DIN EN 1996-1-1 /NA :2012-05 on different load situation has been illustrated. / Analyse von unbewehrten Mauerwerkskonstruktionen mit unscharfen Daten Ingenieurmethoden zur Überprüfung von unbewehrten Mauerwerkswänden unter Scheibenschub (Probabilistische und Fuzzy-Methoden) Um sichere und ökonomische Konstruktionen zu planen, sollten die Datenunschärfe mit ihren verschiedenen Quellen bzw. Ursachen richtig charakterisiert und bei der Tragwerksplanung bzw. dem Nachweis berücksichtigt werden. Üblicherweise wird eine Zuverlässigkeitsanalyse angewendet, um einen konsistenten Tragwerksentwurf einschließlich der Unschärfe zu beurteilen. Eine vollständige probabilistische Näherungslösung ist ein brauchbares Werkzeug, um aleatorische Unschärfe zu berücksichtigen. Für die Erfassung der epistemischen Unschärfe bei der Zuverlässigkeitsanalyse sind moderne mathematische Werkzeuge wie z.B. die Fuzzy-Set-Theorie erforderlich. Unbewehrtes Mauerwerk (URM) ist als nachhaltiges Baumaterial bekannt und weltweit an der Spitze der verbauten Baumaterialien in Wohngebäuden. In dieser wissenschaftlichen Arbeit, die sich auf die verfügbaren Informationen über das Material stützt, werden probabilistische Modelle, einschließlich der zugehörigen wahrscheinlichkeitsbasierten Unschärfen der Mauerwerkseigenschaften, für die Zuverlässigkeitsstudie zur Verfügung gestellt. Außerdem wurde ein neues experimentelles Verfahren für die Ermittlung der Haftscherfestigkeit und den Reibungsbeiwert eingeführt, um die (epistemische) Unschärfe zu reduzieren. Unbewehrte Mauerwerkswände, die wichtige Tragglieder in typischen Mauerwerksgebäuden sind, wurden für die Zuverlässigkeitsstudie ausgewählt. Verschiedene Nachweismethoden für die Kombination von Scheibenschub und Druckbeanspruchung wurden nach verschiedenen Normen zusammengestellt und deterministische Gleichungen, zur Ermittlung der Tragfähigkeit herausgearbeitet. Um Unschärfe zu identifizieren (Ungenauigkeit der Modelle), werden die beobachtete Tragfähigkeit (experimentelle Ergebnisse) mit rechnerischen Werten verglichen, und daraus relevante Aussagen zur Modellunschärfe abgeleitet. Verschiedene Zuverlässigkeitsanalysen wurden zunächst mit stochastischen Methoden und danach mit einem fuzzy-randomness basierten Vorgehen geführt. Die Auswirkung der Unschärfe auf die bewertete Zuverlässigkeit wird herausgestellt. Zusätzlich wurde der Unterschied zwischen der linearen und nichtlinearen Anwendung zur Bestimmung von Teilsicherheitsfaktoren untersucht. Schließlich wird mithilfe von 3D-Graphen das Zuverlässigkeitsniveau von verschiedenen bemessenen Mauerwerkswänden nach dem letzten deutschen nationalen Anhang, DIN EN 1996-1-1/NA:2012-05, für verschiedene Lastsituationen dargestellt.

Load induced top-down fatigue cracking has been recognized recently as a major distress phenomenon in asphalt pavements. This failure mode has been observed in many parts of the world, and in some regions, it was found to be more prevalent and a primary cause of pavements failure. The main factors which are identified as potential causes of top down fatigue cracking are primarily linked to age hardening, mixtures fracture resistance and unbound layers stiffness. Mechanistic Empirical analytical models, which are based on hot mix asphalt fracture mechanics (HMA-FM) and that could predict crack initiation time and propagation rate, have been developed and shown their capacity in delivering acceptable predictions. However, in these methods, the effect of age hardening and healing is not properly accounted and moreover, these models do not consider the effect of mixture morphology influence on long term pavement performance. Another drawback of these models is, as analysis tools they are not suitable to be used for pavement design purpose. The main objective of this study is to develop a reliability calibrated design framework in load resistance factor design (LRFD) format which could be implemented to design pavement sections against top down fatigue cracking. For this purpose, asphalt mixture morphology based sub-models were developed and incorporated to HMA-FM to characterize the effect of aging and degradation on fracture resistance and healing potential. These sub-models were developed empirically exploiting the observed relation that exist between mixture morphology and fracture resistance. The developed crack initiation prediction model was calibrated and validated using pavement sections that have high quality laboratory data and observed field performance history. As traffic volume was identified in having a dominant influence on predicted performance, two separate model calibration and validation studies were undertaken based on expected traffic volume. The predictions result for both model calibration and validation was found to be in an excellent agreement with the observed performance in the field. A LRFD based design framework was suggested that could be implemented to optimize pavement sections against top-down fatigue cracking. To achieve this objective, pavement sections with various design target reliabilities and functional requirements were analyzed and studied.  A simplified but efficient limit state equation was generated using a central composite design (CCD) based response surface methodology, and FORM based reliability analysis was implemented to compute reliabilities and formulate associated partial safety factors. A design example using the new partial safety factors have clearly illustrated the potential of the new method, which could be used to supplement existing design procedures. / <p>QC 20150427</p>

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This dissertation is a systematic study of electric power distribution system reliability evaluation and improvement. Reliability evaluation of electric power systems has traditionally been an integral part of planning and operation. Changes in the electric utility coupled with aging electric apparatus create a need for more realistic techniques for power system reliability modeling. This work presents a reliability evaluation technique that combines set theory and Graph Trace Analysis (GTA). Unlike the traditional Markov approach, this technique provides a fast solution for large system reliability evaluation by managing computer memory efficiently with iterators, assuming a single failure at a time. A reconfiguration for restoration algorithm is also created to enhance the accuracy of the reliability evaluation, considering multiple concurrent failures. As opposed to most restoration simulation methods used in reliability analysis, which convert restoration problems into mathematical models and only can solve radial systems, this new algorithm seeks the reconfiguration solution from topology characteristics of the network itself. As a result the new reconfiguration algorithm can handle systems with loops. In analyzing system reliability, this research takes into account time-varying load patterns, and seeks approaches that are financially justified. An exhaustive search scheme is used to calculate optimal locations for Distributed Generators (DG) from the reliability point of view. A Discrete Ascent Optimal Programming (DAOP) load shifting approach is proposed to provide low cost, reliability improvement solutions. As weather conditions have an important effect on distribution component failure rates, the influence of different types of storms has been incorporated into this study. Storm outage models are created based on ten years' worth of weather and power outage data. An observer is designed to predict the number of outages for an approaching or on going storm. A circuit corridor model is applied to investigate the relationship between power outages and lightning activity. / Ph. D.

Yes / The use of the Advanced Censored Closure (ACC) technique, recently proposed by the authors for predicting the peak response of linear structures vibrating under random processes, is extended to the case of non-linear oscillators driven by stationary white noise. The proposed approach requires the knowledge of mean upcrossing rate and spectral bandwidth of the response process, which in this paper are estimated through the Stochastic Averaging method. Numerical applications to oscillators with non-linear stiffness and damping are included, and the results are compared with those given by Monte Carlo Simulation and by other approximate formulations available in the literature.

Dans de nombreuses applications industrielles, les structures en vibration à dimensionner sont en contact avec un fluide (fluide autour des coques des bateaux, réservoirs, échangeurs de chaleur dans les centrales, l’industrie automobile, etc). Cependant, le comportement dynamique de la structure peut être modifié de façon importante par la présence du fluide. Le dimensionnement doit donc prendre en compte les effets de l’interaction fluide-structure.Ces applications nécessitent un couplage efficace. En outre, l’analyse dynamique des systèmes industriels est souvent coûteuse du point de vue numérique. Pour les modèles éléments finis des problèmes couplés fluide-structure, l’importance de la réduction de la taille devient évidente car les degrés de liberté du fluide seront ajoutés à ceux de la structure. Des méthodes de réduction du modèle seront utilisées pour réduire la taille des matrices obtenues.Traditionnellement, l’étude de ces systèmes couplés est fondée sur une démarche déterministe dans laquelle l’ensemble des paramètres utilisés dans le modèle prennent une valeur fixe.Par contre, il suffit d’avoir procédé à quelques expérimentations pour se rendre compte des limites d’une telle modélisation, d’où la nécessité de la prise en compte des incertitudes sur les paramètres du système couplé.Ce travail de thèse s’articule autour de trois études principales. La première consiste à mener une étude déterministe numérique et analytique des problèmes vibro-acoustiques sans réduction de modèles. Cette dernière est basée sur une formulation non symétrique déplacement/pression et une formulation symétrique déplacement/pression et potentiel des vitesses. Dans la deuxième étude, on propose deux méthodes de réduction du modèle : analyse et synthèse modales pour la résolution des problèmes vibro-acoustiques des grandes tailles des systèmes couplés modélisés par la méthode des éléments finis. La méthode de synthèse modale développée couple une méthode de sous-structuration dynamique de type Craig et Bampton et une méthode de sous domaines acoustiques.Enfin, pour tenir compte des incertitudes sur les paramètres du système couplé, on a développé dans la troisième étude une méthode numérique stochastique de synthèse modale étendue à une étude de fiabilité basée sur les approches FORM et SORM pour la résolution de ces problèmes. Ces démarches vont nous permettre de résoudre les problèmes vibro-acoustiques, sans utiliser les méthodes classiques, qui consistent à faire un calcul modal direct allié à la simulation de Monte Carlo demandant un coup de temps très élevé.Plusieurs exemples académiques et industriels ont été traités pour valider les approches proposées.L’étude numérique est conduite en utilisant un code élaboré sous MATLAB couplé au code commercial ANSYS afin d’évaluer la fiabilité du système couplé. La confrontation des résultats numériques, analytiques et expérimentaux nous permet de valider conjointement le processus de calcul et les méthodes proposées dans le domaine de l’analyse fréquentielle et l’étude fiabiliste des structures immergées. D’un point de vue industriel, ces méthodes visent à promouvoir l’introduction de la culture de l’incertain dans les métiers de la conception et encouragent la construction d’un modèle fiable et robuste pour les problèmes d’interaction fluide-structure. / In several industrial applications, the vibrating structures are in contact with a fluid (fluid around the hulls of a boats, reservoirs, heat exchangers in power plants, ...), but the dynamic behavior of the structure can be significantly modified by the presence of the fluid. The sizing must take into account the effects of fluid-structure interaction. These applications require an effective coupling. In addition, the dynamic analysis of the industrial systems is often expensive from the numerical point of view. For the coupling fluid structure finite elements models, the importance of the size reduction becomes obvious because the fluid’s freedom degrees will be added to those of the structure. A proposed condensation method will be used to reduce the matrixes size. Traditionally, the study of the fluid-structure interaction is based on a deterministic approach where all the parameters used in the model have a fixed value. But it suffices having conducted a few experimentations to realize the limitations of such modeling. Hence it need to take into accounts the uncertainty on the parameters of mechanical systems. In this thesis, we deal with the simulation of vibro-acoustic problems. The first part presents a numerical and analytical study of deterministic problems without model’s reduction, based on a non-symmetric formulation displacement/pressure and on a symmetric formulation displacement/pressure and velocity potential. In the second part of this work, two methods are proposed to reduce the model : modal analysis and modal synthesis for solving vibro-acoustic problems of large sizes modeled by finite elements method. The developed modal synthesis method is coupling dynamic substructure of Craig and Bampton type and acoustic subdomain based on a pressure formulation. To take into account the parameter’s uncertainties of the coupled system, we have developed a numerical stochastic method of the modal synthesis and modal analysis extended to reliability study, based on the FORM and SORM approaches. These approaches will allow us to solve the vibro-acoustic problems without using classical procedure. It may become prohibitive in terms of computation time. Several academic and industrial examples are studied to validate the proposed methods. The numerical study is performed using a code developed with MATLAB coupled with the commercial code ANSYS in order to evaluate the reliability of systems. The comparison of numerical, analytical and experimental results enables us to jointly validate the calculation process and the proposed methods in the domain of frequency analysis and reliability study of submerged structures. From the industrial point of view, our research work aim is to promote the introduction of the uncertainty’s culture during modeling in the context of design processes.

A APS (Análise Probabilística de Segurança) de instalações industriais é assunto que evoluiu com a complexidade dos sistemas. A princípio, foram desenvolvidas ferramentas e técnicas com o propósito de analisar plantas já instaladas, possibilitando a identificação de fenômenos e mecanismos de falha desconhecidos até então. Com a evolução dos estudos dos acidentes, foram desenvolvidas técnicas aplicáveis às fases pré-operacionais com o propósito de diminuir os riscos na operação. Observa-se, portanto, um bom número de técnicas ideais para analisar projetos prontos ou em fase de conclusão. O mesmo não é observado para a fase de concepção. Apesar disto, cada vez mais especialistas na área de risco propõem que as considerações de segurança são mais eficazes quando ponderadas ao longo de toda a vida dos sistemas críticos. O estudo das APS realizadas no mundo em várias indústrias ajuda a entender o consenso sobre a contribuição potencial destas análises no desenvolvimento de novos sistemas. Para explorar este potencial, é essencial a elaboração de processos e modelos prospectivos que sejam simples, quantitativos, realistas, capazes de alimentar análises no estágio de projeto e que tragam resultados que possam ser interpretados pelos profissionais envolvidos no processo decisório. Estas considerações são extensíveis à ACH (Análise de Confiabilidade Humana), i.e., poucas são as ferramentas que ponderam aspectos operacionais, em especial o desempenho humano, na fase de projeto. A reconhecida contribuição do fator humano em acidentes envolvendo sistemas complexos - por vezes atribuída à falta de ferramentas adequadas para sua consideração na fase de projeto - evidencia ainda mais esta lacuna. Neste contexto, esta tese apresenta o desenvolvimento de uma metodologia e de uma técnica para a consideração precoce da confiabilidade humana na concepção de sistemas complexos, sendo que: 1) o desenvolvimento desta metodologia primou pela facilidade de entendimento de suas etapas e resultados, i.e., procurou-se a inteligibilidade para as pessoas envolvidas no projeto, sendo especialistas em ACH ou não, e; 2) a TECHR (Technique for Early Consideration of Human Reliability) foi concebida com o propósito de desenvolver um modelo prospectivo para o desempenho humano que possa ser explorado na fase de concepção de sistemas, e se baseia no aproveitamento da opinião de especialistas em relação a sistemas que operam ou operaram nos últimos anos para obter estimativas das probabilidades dos diversos tipos de erro humano que podem ocorrer durante a execução de uma ação específica. A metodologia proposta e a TECHR resultam em um procedimento simples e capaz de produzir modelos extremamente úteis na fase de projeto, representando uma contribuição original para o estado da arte da concepção de sistemas baseada em dados incertos. / PSA (Probabilistic Safety Assessment) is an industrial plant issue that has evolved with the complexity of systems. Initially, tools and techniques have been developed with the main purpose of analyzing operational plants, enabling the identification of phenomena and fault mechanisms hitherto not highlighted. With the evolution of accidents studies, some techniques applicable to pre-operational phases were developed in order to reduce the risks in operation. Therefore, a number of techniques adequate to analyze ready or near completion designs can be found. The same is not observed for the early design phase. Despite this, more and more experts in the risk assessment field suggest that safety considerations are most effective when assessed over the whole life of critical systems. Probabilistic safety analyses performed worldwide in various industries help us understand the consensus on the potential contribution of these analyses for developing new systems. To exploit this potential, it is essential to develop processes and prospective models that are simple, quantitative, realistic, able to feed analyses at the design stage and to bring results that can be interpreted by the professionals involved in the decision making process. These considerations are extended to HRA (Human Reliability Analysis), i.e., there are few tools that consider operational aspects, especially human performance, during the design phase. The recognized contribution of the human factor in accidents involving complex systems - sometimes attributed to the lack of suitable tools for its consideration in the design phase - further highlights this gap. In this context, this thesis presents a methodology and a technique developed for the early consideration of human reliability in complex systems design, and: 1) the development of this methodology has prioritized the easy understanding of its steps and results, i.e., its intelligibility for people involved in the system design has been sought, with expertise in HRA or not, and; 2) the technique for early consideration of human reliability (TECHR) was designed for developing a prospective human performance model that can be exploited in the system design phase, and is based on the use of expert opinion in relation to systems that operate or have operated in recent years to obtain estimates of the probabilities of the various types of human error that may occur during the performance of a specific action. The proposed methodology and technique result in a simple procedure capable of producing useful models for the design phase, representing an original contribution to the state of the art of systems conception under uncertainty.

Neste trabalho, são desenvolvidas novas técnicas aproximadas de análise de confiabilidade para grelhas de concreto armado levando-se em consideração as probabilidades de falha de vários modos importantes. Realiza-se um acoplamento entre os métodos de Monte Carlo, elementos finitos e procedimentos de otimização para considerar esses modos de falha importantes e classificá-los. Esse acoplamento também permite a redução do número de chamadas ao modelo de elementos finitos. Os cenários de falha são caracterizados como o encurtamento excessivo do concreto e o alongamento do aço. Estes cenários determinam a capacidade última da estrutura, e podem ser representados por um coeficiente escalar que multiplica todas as ações presentes na estrutura. Para a determinação desses estados estruturais últimos, um procedimento incremental-iterativo é utilizado. A análise de confiabilidade é realizada em diferentes conjuntos de realizações aleatórias das variáveis de projeto. O conjunto de respostas estruturais e de realizações permite a determinação dos coeficientes da superfície de respostas da estrutura. O acoplamento realizado permite também o tratamento com estruturas de concreto com elevado número de modos de falha. Aplicam-se as técnicas em exemplos de grelhas de concreto armado / In this work, new local approaches of reliability analysis applied to reinforced concrete grid structures are developed, taking into account several critical cross-section failure probabilities. Monte Carlo simulations are coupled with finite element analyses and optimization techniques with techniques to take into account the failure in the most important cross-sections, in order to classify the severity of failure modes. The failure scenario is depicted when either a concrete fiber or a steel bar reaches the predefined conventional limit. This scenario gives the structural ultimate capacity, which can be represented by a scalar coefficient multiplying all the loads acting on the structure. To achieve the failure scenario, an incremental and iterative procedure is used. To carry out the reliability analysis, the mechanical analysis has to be performed for different sets of random variable realizations of the mechanical, material and geometrical properties. The set of ultimate coefficients obtained from several mechanical analyses defines the response surface. The coupling between Monte Carlo simulations and response surface techniques applied in this work aims to reduce significantly the number of the finite element model calls, and hence to deal with real, or high-scale, reinforced concrete grids where large number of failure components can be found. The proposed procedure is then applied to reinforced concrete grids in order to show some more complex reinforced concrete examples