Mechanical assessment of defects in welded joints: morphological classification and data augmentation

Journal of Mathematics in Industry

François Willot¹  Hugo Launay²  David Ryckelynck²  Jacques Besson² 

[1] Mines Paris, PSL Research University, Centre de Morphologie Mathématique, 35 rue St Honoré, 77300, Fontainebleau, France;Mines Paris, PSL Research University, Centre des Matériaux, CNRS UMR 7633, 63-65 rue Henri-Auguste Desbruères, BP 87, 91003, Évry, France;

关键词: Model-order reduction;    FFT method;    Data augmentation;    Clustering;    Defects;    Shape space;    74B05;    74S25;    68T99;   

DOI  :  10.1186/s13362-021-00114-7

来源: Springer

【 摘 要 】

We develop a methodology for classifying defects based on their morphology and induced mechanical response. The proposed approach is fairly general and relies on morphological operators (Angulo and Meyer in 9th international symposium on mathematical morphology and its applications to signal and image processing, pp. 226-237, 2009) and spherical harmonic decomposition as a way to characterize the geometry of the pores, and on the Grassman distance evaluated on FFT-based computations (Willot in C. R., Méc. 343(3):232–245, 2015), for the predicted elastic response. We implement and detail our approach on a set of trapped gas pores observed in X-ray tomography of welded joints, that significantly alter the mechanical reliability of these materials (Lacourt et al. in Int. J. Numer. Methods Eng. 121(11):2581–2599, 2020). The space of morphological and mechanical responses is first partitioned into clusters using the “k-medoids” criterion and associated distance functions. Second, we use multiple-layer perceptron neural networks to associate a defect and corresponding morphological representation to its mechanical response. It is found that the method provides accurate mechanical predictions if the training data contains a sufficient number of defects representing each mechanical class. To do so, we supplement the original set of defects by data augmentation techniques. Artificially-generated pore shapes are obtained using the spherical harmonic decomposition and a singular value decomposition performed on the pores signed distance transform. We discuss possible applications of the present method, and how medoids and their associated mechanical response may be used to provide a natural basis for reduced-order models and hyper-reduction techniques, in which the mechanical effects of defects and structures are decorrelated (Ryckelynck et al. in C. R., Méc. 348(10–11):911–935, 2020).

【 授权许可】

CC BY