Littérature scientifique sur le sujet « Probabilité d'événements rares »
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Articles de revues sur le sujet "Probabilité d'événements rares"
Poda, Pasteur, Samir Saoudi, Thierry Chonavel, Frédéric GUILLOUD et Théodore Tapsoba. « Non-parametric kernel-based bit error probability estimation in digital communication systems : An estimator for soft coded QAM BER computation ». Revue Africaine de la Recherche en Informatique et Mathématiques Appliquées Volume 27 - 2017 - Special... (3 août 2018). http://dx.doi.org/10.46298/arima.4348.
Texte intégralThèses sur le sujet "Probabilité d'événements rares"
Estecahandy, Maïder. « Méthodes accélérées de Monte-Carlo pour la simulation d'événements rares. Applications aux Réseaux de Petri ». Thesis, Pau, 2016. http://www.theses.fr/2016PAUU3008/document.
Texte intégralThe dependability analysis of safety instrumented systems is an important industrial concern. To be able to carry out such safety studies, TOTAL develops since the eighties the dependability software GRIF. To take into account the increasing complexity of the operating context of its safety equipment, TOTAL is more frequently led to use the engine MOCA-RP of the GRIF Simulation package. Indeed, MOCA-RP allows to estimate quantities associated with complex aging systems modeled in Petri nets thanks to the standard Monte Carlo (MC) simulation. Nevertheless, deriving accurate estimators, such as the system unavailability, on very reliable systems involves rare event simulation, which requires very long computing times with MC. In order to address this issue, the common fast Monte Carlo methods do not seem to be appropriate. Many of them are originally defined to improve only the estimate of the unreliability and/or well-suited for Markovian processes. Therefore, the work accomplished in this thesis pertains to the development of acceleration methods adapted to the problematic of performing safety studies modeled in Petri nets and estimating in particular the unavailability. More specifically, we propose the Extension of the "Méthode de Conditionnement Temporel" to accelerate the individual failure of the components, and we introduce the Dissociation Method as well as the Truncated Fixed Effort Method to increase the occurrence of their simultaneous failures. Then, we combine the first technique with the two other ones, and we also associate them with the Randomized Quasi-Monte Carlo method. Through different sensitivities studies and benchmark experiments, we assess the performance of the acceleration methods and observe a significant improvement of the results compared with MC. Furthermore, we discuss the choice of the confidence interval method to be used when considering rare event simulation, which is an unfamiliar topic in the field of dependability. Last, an application to an industrial case permits the illustration of the potential of our solution methodology
Krauth, Timothé. « Modèle génératif profond pour l'estimation de probabilité de collision en vol ». Electronic Thesis or Diss., Toulouse, ISAE, 2024. http://www.theses.fr/2024ESAE0018.
Texte intégralIt is essential to calculate the probability of aircraft collisions to optimise air traffic while maintaining high safety standards. This need became more pronounced in the 1960s with the increase in transatlantic commercial air traffic. Initially, analytical models such as those of Reich and Anderson-Hsu were benchmarks for assessing in-flight collision risks, but they proved to be less suited for the complex airspace around airports.Data-driven methods, especially Monte Carlo simulations, have become a promising alternative for collision risk assessment. They offer significant flexibility through simplified assumptions, making them adaptable to various contexts. However, traditional Monte Carlo simulations are inefficient for estimating rare event probabilities, requiring a large number of aircraft trajectories and substantial computational resources. This thesis proposes a collision risk model based on Monte Carlo simulations, using a trajectory generation model to overcome these limitations associated with rare events. These generative methods faithfully reproduce observed trajectory distributions while incorporating uncertainties from external factors. Three main research areas are defined: (i) developing a trajectory generation method, (ii) constructing a Monte Carlo-based collision risk model using synthetic trajectories, and (iii) improving the interpretability of collision risk estimates.Generating synthetic samples involves estimating the distribution of observed data to ensure identical distribution in new samples. This is particularly important for aircraft trajectories, where the model must reflect uncertainty sources causing deviations from standard trajectories. We initially use traditional statistical learning methods to estimate complex two-dimensional aircraft trajectories. Despite reducing the problem's dimensionality, conventional methods struggle with high-dimensional distribution estimation. We then explore the use of variational autoencoders for more refined probability density estimation. Suitably adapted for multivariate time-series applications, variational autoencoders prove effective for estimating the distribution of complex aircraft trajectories.Using the developed generation method, we estimate the risk of loss of separation induced by the departure and approach procedures of Paris-Orly Airport using Monte Carlo simulations. The use of a trajectory generation method proves promising, allowing the creation of the equivalent of 20 years of air traffic trajectories from only two months of observations. However, this direct method has limitations for estimating extremely low collision probabilities, requiring the use of one variational autoencoder per flight procedure considered in the studied scenario. The processes of trajectory generation and collision risk evaluation are distinctly separated. Consequently, the inherent constraints of classical Monte Carlo methods are not truly overcome but merely postponed by the production of a set of arbitrarily large trajectories.The thesis's final work unifies the frameworks of variational autoencoders and uncertainty quantification. It demonstrates how variational autoencoders can build suitable input distributions for uncertainty quantification algorithms, enhancing the reliability of Monte Carlo simulations through subset simulation and the explainability of mid-air collision probability estimation through sensitivity analysis. More broadly, we show that the variational autoencoder represents a promising tool to be associated with uncertainty quantification problems
Shao, Jun. « Calcul de probabilités d'événements rares liés aux maxima en horizon fini de processus stochastiques ». Thesis, Clermont-Ferrand 2, 2016. http://www.theses.fr/2016CLF22771/document.
Texte intégralInitiated within the framework of an ANR project (the MODNAT project) targeted on the stochastic modeling of natural hazards and the probabilistic quantification of their dynamic effects on mechanical and structural systems, this thesis aims at the calculation of probabilities of rare events related to the maxima of stochastic processes over a finite time interval, taking into account the following four constraints : (1) the set of considered processes must contain the four main categories of processes encountered in random dynamics, namely stationary Gaussian, non-stationary Gaussian, stationary non-Gaussian and non-stationary non-Gaussian ones ; (2) these processes can be either described by their distributions, or functions of processes described by their distributions, or solutions of stochastic differential equations, or solutions of stochastic differential inclusions ; (3) the events in question are crossings of high thresholds by the maxima of the considered processes over finite time intervals and these events are of very weak occurrence, hence of very small probability, due to the high size of thresholds ; and finally (4) the use of a Monte Carlo approach to perform this type of calculation must be proscribed because it is too time-consuming given the above constraints. To solve such a problem, whose field of interest extends well beyond probabilistic mechanics and structural reliability (it is found in all scientific domains in connection with the extreme values theory, such as financial mathematics or economical sciences), an innovative method is proposed, whose main idea emerged from the analysis of the results of a large-scale statistical study carried out within the MODNAT project. This study, which focuses on analyzing the behavior of the extreme values of elements of a large set of processes, has indeed revealed two germ functions explicitly related to the target probability (the first directly related, the second indirectly via a conditional auxiliary probability which itself depend on the target probability) which possess remarkable and recurring regularity properties for all the processes of the database, and the method is based on the joint exploitation of these properties and a "low level approximation-high level extrapolation" principle. Two versions of this method are first proposed, which are distinguished by the choice of the germ function and in each of which the latter is approximated by a polynomial. A third version has also been developed. It is based on the formalism of the second version but which uses as germ function an approximation of "Pareto survival function" type. The numerous presented numerical results attest to the remarkable effectiveness of the first two versions. They also show that they are of comparable precision. The third version, slightly less efficient than the first two, presents the interest of establishing a direct link with the extreme values theory. In each of its three versions, the proposed method is clearly an improvement compared to current methods dedicated to this type of problem. Thanks to its structure, it also offers the advantage of remaining operational in industrial context
Mattrand, Cécile. « Approche probabiliste de la tolérance aux dommages ». Phd thesis, Université Blaise Pascal - Clermont-Ferrand II, 2011. http://tel.archives-ouvertes.fr/tel-00738947.
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