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

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.

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DOI : 10.5802/crmeca.51
Keywords: Data encoding, Hyper-reduction, Reduced order model, ROM-net, Taxonomy of defects, Computer vision
Mots clés : Encodage de données, Hyper-réduction, Réduction d’ordre de modèles, ROM-net, Taxonomie de défauts, Vision par ordinateur
David Ryckelynck 1 ; Thibault Goessel 2 ; Franck Nguyen 1

1 Mines ParisTech PSL University, Centre des Matériaux, Evry, France
2 Mines ParisTech PSL University, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     journal = {Comptes Rendus. M\'ecanique},
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David Ryckelynck; Thibault Goessel; Franck Nguyen. Mechanical dissimilarity of defects in welded joints via Grassmann manifold and machine learning. Comptes Rendus. Mécanique, Volume 348 (2020) no. 10-11, pp. 911-935. doi : 10.5802/crmeca.51. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.51/

[1] Z. Li; X. Yan; C. Yuan; Z. Peng; L. Li. Virtual prototype and experimental research on gear multi-fault diagnosis using wavelet-autoregressive model and principal component analysis method, Mech. Syst. Signal Process., Volume 25 (2011), pp. 2589-2607 | DOI

[2] T. Mira-Aguiar; C. Leitão; D. M. Rodrigues Solid-state resistance seam welding of galvanized steel, Int. J. Adv. Manufact. Technol., Volume 86 (2016) no. 5, pp. 1385-1391 | DOI

[3] T. Uwaba; Y. Yano; M. Ito Resistance spot weldability of 11cr-ferritic/martensitic steel sheets, J. Nucl. Mater., Volume 421 (2012) no. 1, pp. 132-139 | DOI

[4] S. K. Dinda; J. M. Warnett; M. A. Williams; G. G. Roy; P. Srirangam 3D imaging and quantification of porosity in electron beam welded dissimilar steel to Fe–Al alloy joints by X-ray tomography, Mater. Des., Volume 96 (2016), pp. 224-231 | DOI

[5] J. D. Madison; L. K. Aagesen Quantitative characterization of porosity in laser welds of stainless steel, Scr. Mater., Volume 67 (2012) no. 9, pp. 783-786 | DOI

[6] A. Haboudou; P. Peyre; A. B. Vannes; G. Peix Reduction of porosity content generated during Nd:YAG laser welding of A356 and AA5083 aluminium alloys, Mater. Sci. Eng. A, Volume 363 (2003) no. 1, pp. 40-52 | DOI

[7] D. Amsallem; C. Farhat An online method for interpolating linear parametric reduced-order models, SIAM J. Sci. Comput., Volume 33 (2011), pp. 2169-2198 | DOI | MR | Zbl

[8] S. Moomkesh; S. A. Mireei; M. Sadeghi; M. Nazeri Early detection of freezing damage in sweet lemons using Vis/SWNIR spectroscopy, Biosys. Eng., Volume 164 (2017), pp. 157-170 | DOI

[9] Y. Le Cun; B. E. Boser; J. S. Denker; D. Henderson; R. E. Howard; W. E. Hubbard; L. D. Jackel Handwritten digit recognition with a back-propagation network, Advances in Neural Information Processing Systems 2 (D. S. Touretzky, ed.), Morgan-Kaufmann, 1990, pp. 396-404 (http://papers.nips.cc/paper/293-handwritten-digit-recognition-with-a-back-propagation-network.pdf)

[10] A. Krizhevsky; I. Sutskever; G. E. Hinton Imagenet classification with deep convolutional neural networks, Adv. Neural Inf. Process. Syst., Volume 2 (2012), pp. 1097-1105 (cited By 33336)

[11] T. Zehelein; T. Hemmert-Pottmann; M. Lienkamp Diagnosing automotive damper defects using convolutional neural networks and electronic stability control sensor signals, Sensor Actuator Networks, Volume 9 (2020), pp. 1-19

[12] L. Xiao; B. Wu; Y. Hu; J. Liu A hierarchical features-based model for freight train defect inspection, IEEE Sens. J., Volume 20 (2020), pp. 2671-2678

[13] S. J. Pan; Q. Yang A survey on transfer learning, IEEE Trans. Knowl. Data Eng., Volume 22 (2010) no. 10, pp. 1345-1359 | DOI

[14] D. Ulrich; B. van Rietbergen; H. Weinans; P. Ruegsegger Finite element analysis of trabecular bone structure: a comparison of image-based meshing techniques, J. Biomech., Volume 31 (1998) no. 12, pp. 1187-1192 | DOI

[15] F. N’Guyen Morphologie mathématique appliquée au développement d’outils de maillage EF automatiques dans le cas de microstructures hétérogènes bi et multiphasées, Ph. D. Thesis, Lille 1 University (2014)

[16] P. Henry; G. Nicolas; F. Samuel; L. Wolfgang Incipient bulk polycrystal plasticity observed by synchrotron in-situ topotomography, Materials, Volume 11 (2018), pp. 1-18

[17] Y. Amani; S. Dancette; P. Delroisse; A. Simar; E. Maire Compression behavior of lattice structures produced by selective laser melting: X-ray tomography based experimental and finite element approaches, Acta Mater., Volume 159 (2018), pp. 395-407 | DOI

[18] A. Madra; P. Breitkopf; A. Rassineux; F. Trochu Image-based model reconstruction and meshing of woven reinforcements in composites, Int. J. Numer. Methods Eng., Volume 112 (2017) no. 9, pp. 1235-1252 | DOI | MR

[19] Y. Huang; Z. Yang; W. Ren; G. Liu; C. Zhang 3d meso-scale fracture modelling and validation of concrete based on in-situ X-ray computed tomography images using damage plasticity model, Int. J. Solids Struct., Volume 67–68 (2015), pp. 340-352 | DOI

[20] L. Lacourt; D. Ryckelynck; S. Forest; V. de Rancourt; S. Flouriot Hyper-reduced direct numerical simulation of voids in welded joints via image-based modeling, Int. J. Numer. Methods Eng., Volume 121 (2020) no. 11, pp. 2581-2599 | DOI | MR

[21] D. Ryckelynck Hyper-reduction of mechanical models involving internal variables, Int. J. Numer. Methods Eng., Volume 77 (2009) no. 1, pp. 75-89 | DOI | MR | Zbl

[22] T. Daniel; F. Casenave; N. Akkari; D. Ryckelynck Model order reduction assisted by deep neural networks (ROM-net), Adv. Model. Simul. Eng. Sci., Volume 7 (2020) no. 1, p. 16 | DOI

[23] J. Lumley The structure of inhomogeneous turbulence, Atmospheric Turbulence and Wave Propagation, Nauka, Moscow, 1967, pp. 166-178

[24] M. Raissi; P. Perdikaris; G. E. Karniadakis Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations, J. Comput. Phys., Volume 378 (2019), pp. 686-707 | DOI | MR | Zbl

[25] F. Nguyen; S. M. Barhli; D. P. Muñoz; D. Ryckelynck Computer vision with error estimation for reduced order modeling of macroscopic mechanical tests, Complexity, Volume 2018 (2018), pp. 1-10 | DOI

[26] L. Lacourt Lifetime assessment of welded structures containing defects, Ph. D. Thesis, Mines ParisTech-PSL University (2019)

[27] H. S. Park; C. H. Jun A simple and fast algorithm for k-medoids clustering, Expert Syst. Appl., Volume 36 (2009), pp. 3336-3341 | DOI

[28] D. Ryckelynck; L. Gallimard; S. Jules Estimation of the validity domain of hyper-reduction approximations in generalized standard elastoviscoplasticity, Adv. Model. Simul. Eng. Sci., Volume 2 (2015), p. 6 | DOI

[29] D. Amsallem; C. Farhat Interpolation method for adapting reduced-order models and application to aeroelasticity, AIAA J., Volume 46 (2008), pp. 1803-1813 | DOI

[30] R. Mosquera; A. Hamdouni; A. El Hamidi; C. Allery Pod basis interpolation via inverse distance weighting on grassmann manifolds, Discrete Contin. Dyn. Syst., Series S, Volume 12 (2018), pp. 1743-1759 | MR | Zbl

[31] K. Ye; L. H. Lim Schubert varieties and distances between subspaces of different dimensions, SIAM J. Matrix Anal. Appl., Volume 37 (2016) no. 3, pp. 1176-1197 | DOI | MR | Zbl

[32] B. Miled; D. Ryckelynck; S. Cantournet A priori hyper-reduction method for coupled viscoelastic-viscoplastic composites, Comput. Struct., Volume 119 (2013), pp. 95-103 (cited By 8) | DOI

[33] M. Horák; D. Ryckelynck; S. Forest Hyper-reduction of generalized continua, Comput. Mech., Volume 59 (2017) no. 5, pp. 753-778 | DOI | MR | Zbl

[34] D. Ryckelynck; K. Lampoh; S. Quilici Hyper-reduced predictions for lifetime assessment of elasto-plastic structures, Meccanica, Volume 51 (2016), pp. 309-317 | DOI | MR

[35] M. Barrault; Y. Maday; N. C. Nguyen; A. T. Patera An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations, C. R. Math., Volume 339 (2004) no. 9, pp. 667-672 | DOI | MR | Zbl

[36] J. Fauque; I. Ramiere; D. Ryckelynck Hybrid hyper-reduced modeling for contact mechanics problems, Int. J. Numer. Methods Eng., Volume 115 (2018) no. 1, pp. 117-139 | DOI | MR

[37] J. Baiges; R. Codina; S. Idelson A domain decomposition strategy for reduced order models. Application to the incompressible Navier-Stokes equations, Comput. Methods in Appl. Mech. Eng., Volume 267 (2013), pp. 23-42 | DOI | MR

[38] P. Kerfriden; J. C. Passieux; S. Bordas Local/global model order reduction strategy for the simulation of quasi-brittle fracture, Int. J. Numer. Methods Eng., Volume 89 (2012) no. 2, pp. 154-179 | DOI | MR | Zbl

[39] P. Kerfriden; J. J. Ródenas; S. P.-A. Bordas Certification of projection-based reduced order modelling in computational homogenisation by the constitutive relation error, Int. J. for Numer. Methods Eng., Volume 97 (2014) no. 6, pp. 395-422 | DOI | MR | Zbl

[40] K. C. Hoang; P. Kerfriden; S. P. A. Bordas A fast, certified and “tuning free” two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems, Comput. Methods Appl. Mech. Eng., Volume 298 (2016), pp. 121-158 | DOI | MR | Zbl

[41] S. Sahyoun; S. M. Djouadi Control of nonlinear pdes based on space vectors clustering reduced order systems, IFAC Proc. Volumes, Volume 47 (2014) no. 3, pp. 5181-5186 (19th IFAC World Congress) | DOI

[42] M. Ghasemi; E. Gildin Localized model reduction in porous media flow, IFAC-PapersOnLine, Volume 48 (2015) no. 6, pp. 242-247 (2nd IFAC Workshop on Automatic Control in Offshore Oil and Gas Production OOGP 2015)

[43] M. Hess; A. Alla; A. Quaini; G. Rozza; M. Gunzburger A localized reduced-order modeling approach for pdes with bifurcating solutions, Comput. Methods Appl. Mech. Eng., Volume 351 (2019), pp. 379-403 | DOI | MR | Zbl

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