Abstract

International audience; In air transportation, especially in airport safety, radar tracks are continuously recorded and may be used for detecting incidents on airport surface. However, all known statistical algorithms, even those based on functional data, are unable to distinguish between a safety critical flight and another one departing from standard behavior, but otherwise safe. In this work, we propose a change of paradigm by representing curves as points in a shape manifold. In this framework, it is possible to use Finsler distances between shapes that explicitly take into account the second derivative and can be able to 1 correctly detect skid situations from deviant trajectories that cannot be considered as a slipped trajectory. This metric is next used in curve clustering for detecting bad runway conditions. Some results on datasets of synthetic and real trajectories are presented, as well as a comparison of existing metrics.; Sur la plupart des plateformes aéroportuaires, les déplacements des aéronefs sont enregistrés en continu par des radars de surveillance et les trajectoires ainsi obtenues peuvent être utilisées pour détecter ou prévenir des incidents lors du roulage, en particu-lier des dérapages. Cependant, l'exploitation de ces données est rendue difficile par le fait que les algorithmes statistiques connus, même ceux basés sur des données fonctionnelles, ne sont pas capables de distinguer les situations réellement dangereuses des déviations au comportement standard qui sont sans gravité. Dans cette étude, nous proposons un chan-gement de paradigme en représentant les trajectoires comme des points dans un espace de formes. Dans ce nouveau cadre, il est possible de construire des distances de type Fins-ler, prenant explicitement en compte les dérivées secondes des trajectoires, et qui sont en mesure de bien séparer les trajectoires présentant un dérapage de celles dont la déviation par rapport au comportement nominal n'est pas due à un manque d'adhérence. Cette métrique est ensuite utilisée dans des méthodes de clustering pour détecter un mauvais état de la piste d'atterrissage. Des résultats sur des jeux de données de trajectoires syn-thétiques et réelles sont présentés ainsi qu'une comparaison avec des métriques existantes. Mots-clés. Similarité entre courbes, espace de formes, données fonctionnelles, classification non supervisée de courbes, sécurité aéroportuaire.

Abstract

The degree of similarity between damage patterns often correlates with the likelihood of having similar damage causes. Therefore, deciding whether crack patterns are similar is one of the key steps in assessing the conditions of masonry structures. To our knowledge, no literature has been published regarding masonry crack pattern similarity measures that would correlate well with assessment by structural engineers. Hence, currently, similarity assessments are solely performed by experts and require considerable time and effort. Moreover, it is expensive, limited by the availability of experts, and yields only qualitative answers. In this work, we propose an automated approach that has the potential to overcome the above shortcomings and perform comparably with experts. At its core is a deep neural network embedding that can be used to calculate a numerical distance between crack patterns on comparable façades. The embedding is obtained from fitting a deep neural network to perform a classification task; i.e., to predict the crack pattern archetype label from a crack pattern image. The network is fitted to synthetic crack patterns simulated using a statistics-based approach proposed in this work. The simulation process can account for important crack pattern characteristics such as crack location, orientation, and length. The embedding transforms a crack pattern (raster image) into a 64-dimensional real-valued vector space where the closeness between two vectors is calculated as the cosine of their angle. The proposed approach is tested on 2D façades with and without openings, and with synthetic crack patterns that consist of a single crack and multiple cracks.