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Comptes Rendus. Mécanique

Mechanical dissimilarity of defects in welded joints via Grassmann manifold and machine learning
Comptes Rendus. Mécanique, Tome 348 (2020) no. 10-11, pp. 911-935.

Article du numéro thématique : Contributions in mechanics of materials

L’évaluation de la nocivité des défauts à partir d’images est de plus en plus courante dans l’industrie. Aujourd’hui, ces défauts peuvent être insérés dans des jumeaux numériques qui visent à reproduire dans un modèle mécanique ce qui est observé sur un composant. Ainsi, un diagnostic à partir d’image peut être mis en place. Mais la variété des défauts, la complexité de leur forme et la complexité de calcul des modèles d’éléments finis liés à leur jumeau numérique, rendent ce type de diagnostic trop lent pour toute application pratique. Nous montrons dans cet article qu’une classification des défauts observés permet de définir un dictionnaire des jumeaux numériques. Ces jumeaux numériques se révèlent représentatifs pour la réduction de modèle, tout en conservant une précision acceptable pour la prévision des contraintes. Un apprentissage automatique non supervisé est utilisé à la fois pour la question de la classification et pour la construction de jumeaux numériques réduits. Les éléments du dictionnaire sont des médoïdes trouvés par l’algorithme de partitionnement k-médoïdes. Les médoïdes sont censés être bien répartis dans l’ensemble des données d’entraînement, selon une métrique ou une mesure de dissimilitude. Dans cet article, nous proposons une nouvelle mesure de dissimilitude entre les défauts. Elle est fondée théoriquement sur les erreurs d’approximation des prévisions hyperréduites. Ce faisant, les classes de défauts sont définies en fonction de leur effet mécanique et non directement en fonction de leur morphologie. En pratique, chaque défaut de l’ensemble de données d’entraînement est encodé comme un point sur une variété de Grassmann. Cette méthodologie est évaluée au moyen d’un ensemble de défauts tests totalement différents de l’ensemble de données d’apprentissage utilisé pour calculer le dictionnaire des jumeaux numériques. L’élément le plus approprié du dictionnaire, pour la réduction du modèle, est sélectionné en fonction d’un indicateur d’erreur lié à la prévision hyperréduite des contraintes. Aucun effet de plasticité n’est considéré ici (simplement des matériaux élastiques isotropes), ce qui est une hypothèse forte mais qui n’est pas critique pour l’objectif de ce travail. Malgré la grande variété de défauts, nous montrons des prévisions précises des contraintes pour la plupart des défauts de l’ensemble de test.

Assessing the harmfulness of defects based on images is becoming more and more common in industry. At present, these defects can be inserted in digital twins that aim to replicate in a mechanical model what is observed on a component so that an image-based diagnosis can be further conducted. However, the variety of defects, the complexity of their shape, and the computational complexity of finite element models related to their digital twin make this kind of diagnosis too slow for any practical application. We show that a classification of observed defects enables the definition of a dictionary of digital twins. These digital twins prove to be representative of model-reduction purposes while preserving an acceptable accuracy for stress prediction. Nonsupervised machine learning is used for both the classification issue and the construction of reduced digital twins. The dictionary items are medoids found by a k-medoids clustering algorithm. Medoids are assumed to be well distributed in the training dataset according to a metric or a dissimilarity measurement. In this paper, we propose a new dissimilarity measurement between defects. It is theoretically founded according to approximation errors in hyper-reduced predictions. In doing so, defect classes are defined according to their mechanical effect and not directly according to their morphology. In practice, each defect in the training dataset is encoded as a point on a Grassmann manifold. This methodology is evaluated through a test set of observed defects totally different from the training dataset of defects used to compute the dictionary of digital twins. The most appropriate item in the dictionary for model reduction is selected according to an error indicator related to the hyper-reduced prediction of stresses. No plasticity effect is considered here (merely isotropic elastic materials), which is a strong assumption but which is not critical for the purpose of this work. In spite of the large variety of defects, we provide accurate predictions of stresses for most of defects in the test set.

Première publication : 2020-11-18
Publié le : 2021-01-13
DOI : https://doi.org/10.5802/crmeca.51
Mots clés : Encodage de données, Hyper-réduction, Réduction d’ordre de modèles, ROM-net, Taxonomie de défauts, Vision par ordinateur
@article{CRMECA_2020__348_10-11_911_0,
     author = {David Ryckelynck and Thibault Goessel and Franck Nguyen},
     title = {Mechanical dissimilarity of defects in welded joints via Grassmann manifold and machine learning},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {911--935},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {10-11},
     year = {2020},
     doi = {10.5802/crmeca.51},
     language = {en},
     url = {comptes-rendus.academie-sciences.fr/mecanique/item/CRMECA_2020__348_10-11_911_0/}
}
David Ryckelynck; Thibault Goessel; Franck Nguyen. Mechanical dissimilarity of defects in welded joints via Grassmann manifold and machine learning. Comptes Rendus. Mécanique, Tome 348 (2020) no. 10-11, pp. 911-935. doi : 10.5802/crmeca.51. https://comptes-rendus.academie-sciences.fr/mecanique/item/CRMECA_2020__348_10-11_911_0/

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