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Parametric Curves Metamodelling Based on Data Clustering, Data Alignment, POD-Based Modes Extraction and PGD-Based Nonlinear Regressions

Article dans une revue avec comité de lecture
Article dans une revue avec comité de lecture
Author
ccCHAMPANEY, Victor
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
PASQUALE, Angelo
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
ccAMMAR, Amine
211916 Laboratoire Angevin de Mécanique, Procédés et InnovAtion [LAMPA]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/22377
DOI
10.3389/fmats.2022.904707
Date
2022-06
Journal
Frontiers in Materials

Abstract

In the context of parametric surrogates, several nontrivial issues arise when a whole curve shall be predicted from given input features. For instance, different sampling or ending points lead to non-aligned curves. This also happens when the curves exhibit a common pattern characterized by critical points at shifted locations (e.g., in mechanics, the elasticplastic transition or the rupture point for a material). In such cases, classical interpolation methods fail in giving physics-consistent results and appropriate pre-processing steps are required. Moreover, when bifurcations occur into the parametric space, to enhance the accuracy of the surrogate, a coupling with clustering and classification algorithms is needed. In this work we present several methodologies to overcome these issues. We also exploit such surrogates to quantify and propagate uncertainty, furnishing parametric stastistical bounds for the predicted curves. The procedures are exemplified over two problems in Computational Mechanics.

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