Loi de probabilité | EPFL Graph Search

thumb|400px 3 répartitions.png En théorie des probabilités et en statistique, une loi de probabilité décrit le comportement aléatoire d'un phénomène dépendant du hasard. L'étude des phénomènes aléatoires a commencé avec l'étude des jeux de hasard. Jeux de dés, tirage de boules dans des urnes et jeu de pile ou face ont été des motivations pour comprendre et prévoir les expériences aléatoires. Ces premières approches sont des phénomènes discrets, c'est-à-dire dont le nombre de résultats possibles est fini ou infini dénombrable. Certaines questions ont cependant fait apparaître des lois à support infini non dénombrable ; par exemple, lorsque le nombre de tirages de pile ou face effectués tend vers l'infini, la distribution des fréquences avec lesquelles le côté pile apparaît s'approche d'une loi normale. Des fluctuations ou de la variabilité sont présentes dans presque toute valeur qui peut être mesurée lors de l'observation d'un phénomène, quelle que soit sa nature ; de plus, presque

Updated braking forces for the assessment of road bridges

João Miguel De Oliveira Durães Alves Martins

Safety assessments of road bridges to braking events combine the braking force, acting along the longitudinal axis of the deck, with a vertical load that accounts for the vertical component of the traffic action. In modern design standards the vertical load models result from probabilistic calibration procedures targeting predefined return periods. On the contrary, the braking force was derived from a deterministic characterization of the vehicle configurations and of the braking process. Therefore, the return period of the braking force is unclear and may not be consistent with that of the vertical load model. Significant deviations from the target return period might lead to either uneconomical decisions, e.g. uncalled-for retrofitting interventions, or to inaccurate structural safety verifications. This thesis presents an original stochastic model to compute site-specific values of the braking force as a function of the return period. The developed stochastic model takes into account the length of the bridge deck and its dynamic properties for vibrations in the longitudinal direction, as well as different sources of randomness related to braking events, all of which comply with real-world measurements, including: - vehicle configurations, resorting to a time-history of crossing vehicles; - driver response times, randomly generated from probability distributions defined in the scope of this project; - deceleration profiles of the vehicles, resampled from catalogues of realistic deceleration profiles. The stochastic model uses Monte Carlo simulation of braking events and computes the maximum of the dynamic response of the bridge to each event. The computed maxima are collected in an empirical distribution function of the braking force. In the end, the model returns the quantile of this distribution that is suitable for safety assessments. This value of braking force is specific to the bridge given properties, to the traffic characteristics, and to the target return period. An additional novelty of this research work is the estimation of a rate of occurrence on motorways of braking events per vehicle-distance travelled. This parameter enables the estimation of the period of time covered by the simulations of braking events as a function of traffic flow and of the total number of braking events simulated. This step is fundamental to determine the value of the braking force that has a given return period. The braking forces returned by the stochastic model show significant dependence on the bridge length, the natural vibration period of the deck in the longitudinal direction, and the number of directions of traffic on the deck. On the contrary, damping ratio, traffic on the fast-lane or on weekends, and an augmentation of traffic in 20% show no substantial influence on the braking force. Moreover, the two motorway locations considered as sources of traffic data, Denges and Monte Ceneri, both in Switzerland, yielded braking forces with similar magnitudes, despite the significant differences in traffic characteristics. Finally, the results compiled served to calibrate an updated braking force that depends explicitly on the parameters found relevant, as well as on the return period so that it can be adopted by different standards even if they enforce different safety targets. This updated expression evidences that the braking forces of current codes tend to be conservative and, hence, can be improved based on the findings of this project.

EPFL2016

Erdos Goes Neural: an Unsupervised Learning Framework for Combinatorial Optimization on Graphs

Nikolaos Karalias, Andreas Loukas

Combinatorial optimization (CO) problems are notoriously challenging for neural networks, especially in the absence of labeled instances. This work proposes an unsupervised learning framework for CO problems on graphs that can provide integral solutions of certified quality. Inspired by Erdos' probabilistic method, we use a neural network to parametrize a probability distribution over sets. Crucially, we show that when the network is optimized w.r.t. a suitably chosen loss, the learned distribution contains, with controlled probability, a low-cost integral solution that obeys the constraints of the combinatorial problem. The probabilistic proof of existence is then derandomized to decode the desired solutions. We demonstrate the efficacy of this approach to obtain valid solutions to the maximum clique problem and to perform local graph clustering. Our method achieves competitive results on both real datasets and synthetic hard instances.

2020

Progressive Correspondence Pruning by Consensus Learning

Hongwei Li, Mathieu Salzmann, Rui Zhao, Chen Zhao

Correspondence pruning aims to correctly remove false matches (outliers) from an initial set of putative correspondences. The pruning process is challenging since putative matches are typically extremely unbalanced, largely dominated by outliers, and the random distribution of such outliers further complicates the learning process for learning-based methods. To address this issue, we propose to progressively prune the correspondences via a local-to-global consensus learning procedure. We introduce a "pruning" block that lets us identify reliable candidates among the initial matches according to consensus scores estimated using local-to-global dynamic graphs. We then achieve progressive pruning by stacking multiple pruning blocks sequentially. Our method outperforms state-of-the-arts on robust line fitting, camera pose estimation and retrieval-based image localization benchmarks by significant margins and shows promising generalization ability to different datasets and detector/descriptor combinations.

IEEE2021

Updated braking forces for the assessment of road bridges

João Miguel De Oliveira Durães Alves Martins

EPFL2016