In recent years the greater emphasis is placed on the renewable energy sources that are environmentally friendly. Demand for renewable energy sources is supported by government incentives, which leads to an increasing pace of investment in this sector. Prices for electricity from renewable energies are far higher than the prices of conventional electricity. If the current trend continues, it is only a matter of time before they meet. According to this fact, PRE Company decided to invest in hydropower. This thesis deals with identifying of potential investment opportunities in small hydropower plants from the PRE point of view and the subsequent evaluation of these variants on the basis of multi-criteria decision making.

Optimization is a very important field with diverse applications in physical, social and biological sciences and in various areas of engineering. It appears widely in ma-chine learning, information retrieval, regression, estimation, operations research and a wide variety of computing domains. The subject is being deeply studied both theoretically and experimentally and several algorithms are available in the literature. These algorithms which can be executed (sequentially or concurrently) on a computing machine explore the space of input parameters to seek high quality solutions to the optimization problem with the search mostly guided by certain structural properties of the objective function. In certain situations, the setting might additionally demand for “absolute optimum” or solutions close to it, which makes the task even more challenging. In this thesis, we propose an optimization algorithm which is “gradient-free”, i.e., does not employ any knowledge of the gradient or higher order derivatives of the objective function, rather utilizes objective function values themselves to steer the search. The proposed algorithm is particularly effective in a black-box setting, where a closed-form expression of the objective function is unavailable and gradient or higher-order derivatives are hard to compute or estimate. Our algorithm is inspired by the well known cross entropy (CE) method. The CE method is a model based search method to solve continuous/discrete multi-extremal optimization problems, where the objective function has minimal structure. The proposed method seeks, in the statistical manifold of the parameters which identify the probability distribution/model defined over the input space to find the degenerate distribution concentrated on the global optima (assumed to be finite in quantity). In the early part of the thesis, we propose a novel stochastic approximation version of the CE method to the unconstrained optimization problem, where the objective function is real-valued and deterministic. The basis of the algorithm is a stochastic process of model parameters which is probabilistically dependent on the past history, where we reuse all the previous samples obtained in the process till the current instant based on discounted averaging. This approach can save the overall computational and storage cost. Our algorithm is incremental in nature and possesses attractive features such as stability, computational and storage efficiency and better accuracy. We further investigate, both theoretically and empirically, the asymptotic behaviour of the algorithm and find that the proposed algorithm exhibits global optimum convergence for a particular class of objective functions. Further, we extend the algorithm to solve the simulation/stochastic optimization problem. In stochastic optimization, the objective function possesses a stochastic characteristic, where the underlying probability distribution in most cases is hard to comprehend and quantify. This begets a more challenging optimization problem, where the ostentatious nature is primarily due to the hardness in computing the objective function values for various input parameters with absolute certainty. In this case, one can only hope to obtain noise corrupted objective function values for various input parameters. Settings of this kind can be found in scenarios where the objective function is evaluated using a continuously evolving dynamical system or through a simulation. We propose a multi-timescale stochastic approximation algorithm, where we integrate an additional timescale to accommodate the noisy measurements and decimate the effects of the gratuitous noise asymptotically. We found that if the objective function and the noise involved in the measurements are well behaved and the timescales are compatible, then our algorithm can generate high quality solutions. In the later part of the thesis, we propose algorithms for reinforcement learning/Markov decision processes using the optimization techniques we developed in the early stage. MDP can be considered as a generalized framework for modelling planning under uncertainty. We provide a novel algorithm for the problem of prediction in reinforcement learning, i.e., estimating the value function of a given stationary policy of a model free MDP (with large state and action spaces) using the linear function approximation architecture. Here, the value function is defined as the long-run average of the discounted transition costs. The resource requirement of the proposed method in terms of computational and storage cost scales quadratically in the size of the feature set. The algorithm is an adaptation of the multi-timescale variant of the CE method proposed in the earlier part of the thesis for simulation optimization. We also provide both theoretical and empirical evidence to corroborate the credibility and effectiveness of the approach. In the final part of the thesis, we consider a modified version of the control problem in a model free MDP with large state and action spaces. The control problem most commonly addressed in the literature is to find an optimal policy which maximizes the value function, i.e., the long-run average of the discounted transition payoffs. The contemporary methods also presume access to a generative model/simulator of the MDP with the hidden premise that observations of the system behaviour in the form of sample trajectories can be obtained with ease from the model. In this thesis, we consider a modified version, where the cost function to be optimized is a real-valued performance function (possibly non-convex) of the value function. Additionally, one has to seek the optimal policy without presuming access to the generative model. In this thesis, we propose a stochastic approximation algorithm for this peculiar control problem. The only information, we presuppose, available to the algorithm is the sample trajectory generated using a priori chosen behaviour policy. The algorithm is data (sample trajectory) efficient, stable, robust as well as computationally and storage efficient. We provide a proof of convergence of our algorithm to a high performing policy relative to the behaviour policy.

Potentially damaging submerged invasive freshwater macrophytes have been identified in South African freshwater systems, but have received less attention than their floating counterparts. To ascertain the changes and effects that these species may have on macrophyte ecology, an understanding of the drivers of macrophyte assemblages is essential. The aims of this thesis were to investigate select abiotic and biotic factors driving introduction, establishment and spread of submerged macrophytes in South Africa. Surveys on the status of submerged plant species in South Africa were conducted to find out the distribution and diversity of the species present, imported to, and traded in South Africa. Numerous submerged indigenous and invasive macrophyte locality records were collected during field surveys, of which many were first time records. Pet stores and aquarist trading activities were identified as potential vectors for the spread of submerged macrophytes through online surveys and personal interviews. These results highlighted the potential these species have for continuing to enter, and spread within South African water bodies. Maximum Entropy (MAXENT) is a general-purpose method used to predict or infer distributions from incomplete information, and was used here to predict areas suitable for the establishment of five of these invasive macrophytes. Many systems throughout South Africa, particularly those in the subtropical coastal regions, were found to be climatically suitable for the establishment of Elodea canadensis Michx., Egeria densa Planch., Hydrilla verticillata (L.f.) Royle (all Hydrocharitaceae), Myriophyllum spicatum L. (Haloragaceae), and Cabomba caroliniana Gray (Cabombaceae). Despite the high probability of invasion, facilitated by vectors and suitable climate, South Africa’s rich indigenous submerged aquatic flora may be preventing the establishment of these submerged invasive species. Studies on the competitive interactions between a common indigenous submerged macrophytes, Lagarosiphon major (Roxb.) (Hydrocharitaceae) and M.spicatum, an invasive native to Eurasia, were conducted to ascertain which conditions influence competitive superiority. High sediment nutrient conditions significantly increased the growth rate and competitive ability of both species, while clay sediments significantly increased the competitive ability of L. major over M. spicatum, but sandy sediments improved the competitive ability of M. spicatum. These results highlighted the dynamic changes in competition between submerged species driven by abiotic factors, but did not take into consideration the effect that herbivory, a biotic factor, could have on competition between the two species. The effect of herbivory by phytophagous insects of submerged plant species has been regarded as negligible. To find out what this effect is, multiple field surveys were undertaken throughout South Africa to find natural enemies of indigenous Lagarosiphon species with the aim of identifying such species, and quantifying their influence on plant growth dynamics. Several new phytophagous species were recorded for the first time. An ephydrid fly, Hydrellia lagarosiphon Deeming (Diptera: Ephydridae) was ascertained to be the most ubiquitous and abundant species associated with L. major in South Africa. The influence of herbivory by this fly on the competitive ability of L. major in the presence of M. spicatum was investigated using an inverse linear model, which showed that herbivory by H. lagarosiphon reduced the competitive ability of L. major by approximately five times in favour of M. spicatum. This study served to highlight the importance of herbivory as a driver of submerged aquatic plant dynamics. Current ecological theory emphasises the importance of investigating beyond plant-herbivore interactions, by including multitrophic interactions in community dynamics. Therefore, the potential of parasitism by a parasitoid wasp, Chaenusa luteostigma sp. n. Achterberg (Hymenoptera: Braconidae: Alysiinae) on H. lagarosiphon to shift the competitive interactions between the two plant species was also examined. The addition of the parasitoid reduced the effect of herbivory by the fly on L. major by half, thereby shifting the competitive balance in favour of L. major over M. spicatum. This study provides valuable insight into a selection of drivers of submerged macrophyte assemblages of South Africa. It highlights the precarious position of South African freshwater systems with regard to the potential invasion by damaging submerged invasive species. It also provides interesting insights into the effect of competition, herbivory and parasitism on the establishment and spread of species within submerged freshwater systems. Understanding the different influences could assist managers and policy makers to make validated decisions ensuring the integrity of South African freshwater systems.

Ce travail de thèse se situe dans la thématique des oxydes dérivés de la pérovskite ayant des propriétés de conduction mixte tels que les structures de type K2NiF4, les pérovskites doubles et la brownmillérite. Cette aptitude à conduire à la fois l'oxygène et les électrons présente un intérêt pour des dispositifs électrochimiques fonctionnant à haute température et notamment en tant qu'électrode pour les piles à combustible à oxyde solide. Plus précisément, cette thèse concerne la synthèse et l'étude cristallochimique avancée de la réactivité de ces matériaux essentiellement par les grands instruments par le biais de la diffraction de neutrons (NPD) et des rayons X synchrotron. Le travail préliminaire à ces études implique de la synthèse inorganique par voie solide ou par voie sol-gel, l'analyse thermogravimétrique et la titration iodométrique. Des cellules de réactivité originales ont été développées spécialement à l'ISCR pour l'étude in situ du comportement redox sous différents flux gazeux et en fonction de la température à la fois dans le cadre de la diffraction des neutrons et rayons X synchrotron. L'étude in situ par NPD des composés La2-xSrxMnO4±δ où x = 2,0 et x = 0,8 qui dérivent du composé de cathode de référence La1-xSrxMnO3 a permis de suivre l'évolution structurale en fonction du δ en conditions réductrices pour x = 2,0 et en conditions oxydantes pour x = 0,8. L'étude DRX synchrotron de Pr2NiO4,22 a permis de mettre en évidence la symétrie monoclinique à température ambiante alors que les études précédentes annonçaient une symétrie orthorhombique. Les variations structurales notamment la transition vers la phase HTT sont accompagnées d'une modulation incommensurable qui persiste jusqu'à au moins 900 °C. L'étude des pérovskites doubles NdBaCo2−xMnxO5+δ où 0 ≤ x ≤ 2 a permis de montrer que ces matériaux présentent des conductivités électriques totales très prometteuses pour des applications en tant que cathode de SOFC. De plus, la confrontation de la dynamique moléculaire et de la NPD combinée à la MEM pour le composé x = 0 a permis d'élucider le mécanisme de diffusion de l'oxygène dans cette famille de composés. L'étude par NPD de la réduction de LaSrFeCoO6 vers LaSrFeCoO5 de structure brownmillérite a permis de mettre en évidence que la structure réduite persiste à haute température et l'évolution de la mise en ordre des moments magnétiques lors du refroidissement de LaSrFeCoO5. / This thesis is focused on oxides related to perovskite such as K2NiF4 structure-type, double perovskite and brownmillerite with mixed conduction properties. This ability to conduct both oxygen ions and electrons is relevant for electrochemical devices operating at high temperature, particularly as an electrode for solid oxide fuel cell. Specifically, this thesis deals with the synthesis and advanced crystal structure characterization of the reactivity of these materials mainly through large scale facilities by means of neutron powder diffraction (NPD) and X-ray synchrotron. Preliminary work in these studies involves inorganic synthesis by solid-state or by sol-gel route, thermogravimetric analysis and the iodometric titration. Original reactivity cells have been developed at the ISCR to study redox behavior under different gas flow and as a function of temperature for both neutron diffraction and X-ray synchrotron experiment. In situ study by NPD of La2-xSrxMnO4 ± δ compounds where x = 2.0 and x = 0.8 which derived from the compound cathode reference La1-xSrxMnO3 allowed to follow the structural evolution as a function of δ in reducing conditions for x = 2.0 and oxidizing conditions for x = 0.8. The synchrotron study of Pr2NiO4.22 helped to highlight the monoclinic symmetry at room temperature while previous studies announced an orthorhombic symmetry. Besides, structural changes including the transition to the HTT phase are accompanied by an incommensurable modulation that persists at least up to 900 °C. The study of double perovskites NdBaCo2-xMnxO5+δ where 0 ≤ x ≤ 2 showed that these materials exhibit a promising electrical conductivities for SOFC applications as cathode. In addition, the comparison of the molecular dynamics and NDP combined with MEM for x = 0 compound has elucidated the oxygen diffusion mechanism in these compounds. The study by NPD in reducing condition of LaSrFeCoO6 to the brownmillerite LaSrFeCoO5 has showed that the reduced structure persists at high temperatures and allowed to follow the evolution in the ordering of the magnetic moments while cooling LaSrFeCoO5.

Dans cette thèse nous étudions l'influence de l'environnement sur le comportement d'une cellule dans deux situations différentes. Dans chacune de ces deux situations, apparaît un couplage non-linéaire sur le champ d'advection lié à un terme non-local provenant du bord du domaine. Dans une première partie, nous modélisons la polarisation cellulaire durant la conjugaison de la cellule de levure. Nous utilisons un modèle de type convection-diffusion avec un terme de convection non-linéaire et non-local. Ce modèle présente des similarités avec le modèle de Keller-Segel, la source du potentiel attractif étant sur le bord du domaine. Nous étudions le cas de la dimension un en utilisant des inégalités de Sobolev logarithmiques et HWI. En nous appuyant sur un raisonnement heuristique, nous ramenons l'étude de notre modèle en dimension deux au bord du domaine. Nous validons le modèle à l'aide des résultats expérimentaux obtenus par M. Piel en utilisant un bruit dynamique dans nos simulations numériques. Nous étudions ensuite le problème du dialogue cellulaire entre cellules de levure de sexe opposé. Dans une seconde partie, nous étudions la réaction immunitaire durant l'athérosclérose. Nous construisons puis développons un modèle structuré en âge pour décrire l'inflammation. Pour des paramètres particuliers, nous déterminons le comportement en temps long de notre système en utilisant une fonctionnelle de Lyapunov. / We investigate the influence of the environment on the behaviour of a cell in two different situations. In each of these situations, there is a non-linear coupling of the drift due to a non-local term coming from the boundary of the domain.The first part focuses on the modeling of cell polarisation during the mating of yeast. We use a convection-diffusion model with a non-linear and non-local drift. This model is similar to the Keller-Segel model, the source of the attractive potential comes from the boundary of the domain. We study the long time behaviour of the one-dimensional case by using logarithmic Sobolev and HWI inequalities.By relying on a heuristic, we reduce the study of our model in the two-dimensional case to the boundary of the domain. We validate the model with data provided by M. Piel. This validation requires adding a dynamical noise in our numerical simulations. We study then the cell discussion between yeast of opposite gender. In the second part we study the immune response in atherosclerosis. We build and then develop an age structured model in order to describe the inflammation. For specific parameters, we investigate the long time behaviour of our system by using a Lyapunov functional.

La présente thèse a pour objectif principal de développer des approches déterministes et heuristiques pour résoudre certaines classes de problèmes d'optimisation en Finance, Affectation et Recherche d’Informations. Il s’agit des problèmes d’optimisation non convexe de grande dimension. Nos approches sont basées sur la programmation DC&DCA et la méthode Cross-Entropy (CE). Grâce aux techniques de formulation/reformulation, nous avons donné la formulation DC des problèmes considérés afin d’obtenir leurs solutions en utilisant DCA. En outre, selon la structure des ensembles réalisables de problèmes considérés, nous avons conçu des familles appropriées de distributions pour que la méthode Cross-Entropy puisse être appliquée efficacement. Toutes ces méthodes proposées ont été mises en œuvre avec MATLAB, C/C++ pour confirmer les aspects pratiques et enrichir notre activité de recherche. / In this thesis we focus on developing deterministic and heuristic approaches for solving some classes of optimization problems in Finance, Assignment and Search Information. They are large-scale nonconvex optimization problems. Our approaches are based on DC programming & DCA and the Cross-Entropy method. Due to the techniques of formulation/reformulation, we have given the DC formulation of considered problems such that we can use DCA to obtain their solutions. Also, depending on the structure of feasible sets of considered problems, we have designed appropriate families of distributions such that the Cross-Entropy method could be applied efficiently. All these proposed methods have been implemented with MATLAB, C/C++ to confirm the practical aspects and enrich our research works.

[pt] A avaliação de confiabilidade da capacidade de geração é extremamente útil em diversos estudos de planejamento da expansão, na avaliação dos riscos relacionados ao dimensionamento da reserva operativa e também na programação da manutenção de unidades geradoras. O principal objetivo é avaliar se uma determinada configuração de unidades de geração atende de forma aceitável à carga do sistema, assumindo que os equipamentos de transmissão sejam totalmente confiáveis e sem limitações de capacidade. Na última década, a inserção de fontes renováveis nos sistemas elétricos de potência tem crescido de forma acentuada, na grande maioria dos países desenvolvidos como também em desenvolvimento. As flutuações de suas capacidades de geração se tornaram parte da complexidade do problema de planejamento e operação de redes elétricas, uma vez que dependem das condições ambientais em que foram instaladas. Além disso, representações detalhadas da carga têm se tornado uma preocupação a mais de muitos planejadores, tendo em vista as análises de risco ao atendimento da demanda nessas redes. Novos modelos e ferramentas computacionais devem ser desenvolvidos para tratar dessas variáveis principalmente com dependência espaço-temporal. Esta dissertação apresenta diversos estudos para avaliar a confiabilidade da capacidade de sistemas de geração via simulação Monte Carlo quasi-sequencial (SMC-QS), considerando fontes de geração e carga com forte dependência espaço-temporal. Esta ferramenta é escolhida devido à sua fácil implementação computacional e capacidade de simular eventos cronológicos. A técnica de redução de variância denominada amostragem por importância baseada no método Cross Entropy (CE) foi utilizada em conjunto com a SMC-QS. As simulações terão como base o sistema teste IEEE-RTS 96, o qual é adequada-mente modificado para incluir fontes renováveis eólicas e hídricas. Portanto, o principal objetivo desta dissertação é definir a melhor maneira de lidar com as séries temporais representativas da geração renovável e carga, nos diferentes estágios do método SMC-QS via CE, de modo a maximizar sua eficiência computacional. Vários testes de simulação são realizados com o sistema IEEE-RTS 96 modificado e os resultados obtidos são amplamente discutidos. / [en] The reliability evaluation of the generating capacity is extremely useful in several expansion planning studies, in the assessment of risks related to the requirements of the operating reserve and also in the scheduling of maintenance of generating units. The main objective is to assess whether a given generating configuration meets the system load in an acceptable manner, assuming that the transmission equipment is completely reliable and without capacity limitations. In the last decade, the insertion of renewable sources in electrical power systems has grown markedly, in the vast majority of developed and developing countries. Fluctuations in their generation capacities have become part of the complexity of the problem of planning and operating electrical networks, since they depend on the environmental conditions in which they are installed. In addition, detailed representations of the load have become a concern among many planners, given the risk analyzes to meet demand in these networks. New computational models and tools must be developed to deal with these variables mainly with space-time dependence. This dissertation presents several studies to evaluate the reliability of the capacity of generation systems via quasi-sequential Monte Carlo simulation (QS-MCS), considering generation and load sources with strong space-time dependence. This tool is chosen due to its easy computational implementation and the ability to simulate chronological events. The variance reduction technique named importance sampling based on the cross-entropy (CE) method is used in conjunction with the QS-MCS. The simulations will be carried out with the IEEE-RTS 96 test system, which is adequately modified to include renewable wind and hydro sources. Therefore, the main objective of this dissertation is to define the best way to deal with the time series representing the renewable generation and load, in the different stages of the SMC-QS method via CE, in order to maximize its computational efficiency. Several simulation tests are performed with the modified IEEE-RTS 96 system and the obtained results are widely discussed.

No description available.

[pt] A reserva girante é a parcela da reserva operativa provida por geradores sincronizados, e interligados à rede de transmissão, aptos a suprir a demanda na ocorrência de falhas de unidades de geração, erros na previsão da demanda, variações de capacidade de fontes renováveis ou qualquer outro fator inesperado. Dada sua característica estocástica, essa parcela da reserva operativa é mais adequadamente avaliada por meio de métodos capazes de representar as incertezas inerentes ao seu dimensionamento e planejamento. Por meio do risco de corte de carga é possível comparar e classificar distintas configurações do sistema elétrico, garantindo a não violação dos requisitos de confiabilidade. Sistemas com elevada penetração de fontes renováveis apresentam comportamento mais complexo devido ao aumento das incertezas envolvidas, à forte dependência de fatores energético-climáticos e às variações de capacidade destas fontes. Para avaliar as correlações temporais e representar a cronologia de ocorrência dos eventos no curto-prazo, um estimador baseado na Simulação Monte Carlo Quase Sequencial é apresentado. Nos estudos de planejamento da operação de curto-prazo o horizonte em análise é de minutos a algumas horas. Nestes casos, a ocorrência de falhas em equipamentos pode apresentar baixa probabilidade e contingências que causam corte de carga podem ser raras. Considerando a raridade destes eventos, as avaliações de risco são baseadas em técnicas de amostragem por importância. Os parâmetros de simulação são obtidos por um processo numérico adaptativo de otimização estocástica, utilizando os conceitos de Entropia Cruzada. Este trabalho apresenta uma metodologia de avaliação dos montantes de reserva girante em sistemas com participação de fontes renováveis, em uma abordagem multiárea. O risco de perda de carga é estimado considerando falhas nos sistemas de geração e transmissão, observando as restrições de transporte e os limites de intercâmbio de potência entre as diversas áreas elétricas. / [en] The spinning reserve is the portion of the operational reserve provided by synchronized generators and connected to the transmission network, capable of supplying the demand considering generating unit failures, errors in load forecasting, capacity intermittency of renewable sources or any other unexpected factor. Given its stochastic characteristic, this portion of the operating reserve is more adequately evaluated through methods capable of modeling the uncertainties inherent in its design and planning. Based on the loss of load risk, it is possible to compare different configurations of the electrical system, ensuring the non-violation of reliability requirements. Systems with high penetration of renewable sources present a more complex behavior due to the number of uncertainties involved, strong dependence of energy-climatic factors and variations in the capacity of these sources. In order to evaluate the temporal correlations and to represent the chronology of occurrence of events in the short term, an estimator based on quasi-sequential Monte Carlo simulation is presented. In short-term operation planning studies, the horizon under analysis is from minutes to a few hours. In these cases, the occurrence of equipment failures may present low probability and contingencies that cause load shedding may be rare. Considering the rarity of these events, risk assessments are based on importance sampling techniques. The simulation parameters are obtained by an adaptive numerical process of stochastic optimization, using the concept of Cross Entropy. This thesis presents a methodology for evaluating the amounts of spinning reserve in systems with high penetration of renewable sources, in a multi-area approach. The risk of loss of load is estimated considering failures in the generation and transmission systems, observing the network restrictions and the power exchange limits between the different electric areas.

En raison de la gravité des accidents liés au phénomène de fatigue-propagation de fissure, les préoccupations de l’industrie aéronautique à assurer l’intégrité des structures soumises à ce mode de sollicitation revêtent un caractère tout à fait essentiel. Les travaux de thèse présentés dans ce mémoire visent à appréhender le problème de sûreté des structures aéronautiques dimensionnées en tolérance aux dommages sous l’angle probabiliste. La formulation et l’application d’une approche fiabiliste menant à des processus de conception et de maintenance fiables des structures aéronautiques en contexte industriel nécessitent cependant de lever un nombre important de verrous scientifiques. Les efforts ont été concentrés au niveau de trois domaines dans ce travail. Une méthodologie a tout d’abord été développée afin de capturer et de retranscrire fidèlement l’aléa du chargement de fatigue à partir de séquences de chargement observées sur des structures en service et monitorées, ce qui constitue une réelle avancée scientifique. Un deuxième axe de recherche a porté sur la sélection d’un modèle mécanique apte à prédire l’évolution de fissure sous chargement d’amplitude variable à coût de calcul modéré. Les travaux se sont ainsi appuyés sur le modèle PREFFAS pour lequel des évolutions ont également été proposées afin de lever l’hypothèse restrictive de périodicité de chargement. Enfin, les analyses probabilistes, produits du couplage entre le modèle mécanique et les modélisations stochastiques préalablement établies, ont entre autre permis de conclure que le chargement est un paramètre qui influe notablement sur la dispersion du phénomène de propagation de fissure. Le dernier objectif de ces travaux a ainsi porté sur la formulation et la résolution du problème de fiabilité en tolérance aux dommages à partir des modèles stochastiques retenus pour le chargement, constituant un réel enjeu scientifique. Une méthode de résolution spécifique du problème de fiabilité a été mise en place afin de répondre aux objectifs fixés et appliquée à des structures jugées représentatives de problèmes réels. / Ensuring the integrity of structural components subjected to fatigue loads remains an increasing concern in the aerospace industry due to the detrimental accidents that might result from fatigue and fracture processes. The research works presented here aim at addressing the question of aircraft safety in the framework of probabilistic fracture mechanics. It should be noticed that a large number of scientific challenges requires to be solved before performing comprehensive probabilistic analyses and assessing the mechanical reliability of components or structures in an industrial context. The contributions made during the PhD are reported here. Efforts are provided on each step of the global probabilistic methodology. The modeling of random fatigue load sequences based on real measured loads, which represents a key and original step in stochastic damage tolerance, is first addressed. The second task consists in choosing a model able to predict the crack growth under variable amplitude loads, i.e. which accounts for load interactions and retardation/acceleration effects, at a moderate computational cost. The PREFFAS crack closure model is selected for this purpose. Modifications are brought in order to circumvent the restrictive assumption of stationary load sequences. Finally, probabilistic analyses resulting from the coupling between the PREFFAS model and the stochastic modeling are carried out. The following conclusion can especially be drawn. Scatter in fatigue loads considerably affects the dispersion of the crack growth phenomenon. Then, it must be taken into account in reliability analyses. The last part of this work focuses on phrasing and solving the reliability problem in damage tolerance according to the selected stochastic loading models, which is a scientific challenge. A dedicated method is established to meet the required objectives and applied to structures representative of real problems.