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kPCA-Based Parametric Solutions Within the PGD Framework

Article dans une revue avec comité de lecture
Author
GONZÁLEZ, David
95355 Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
AGUADO, José Vicente
ccABISSET-CHAVANNE, Emmanuelle
10921 Institut de Recherche en Génie Civil et Mécanique [GeM]
ccCHINESTA SORIA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]

URI
http://hdl.handle.net/10985/18681
DOI
10.1007/s11831-016-9173-4
Date
2018
Journal
Archives of Computational Methods in Engineering

Abstract

Parametric solutions make possible fast and reliable real-time simulations which, in turn allow real time optimization, simulation-based control and uncertainty propagation. This opens unprecedented possibilities for robust and efficient design and real-time decision making. The construction of such parametric solutions was addressed in our former works in the context of models whose parameters were easily identified and known in advance. In this work we address more complex scenarios in which the parameters do not appear explicitly in the model—complex microstructures, for instance. In these circumstances the parametric model solution requires combining a technique to find the relevant model parameters and a solution procedure able to cope with high-dimensional models, avoiding the well-known curse of dimensionality. In this work, kPCA (kernel Principal Component Analysis) is used for extracting the hidden model parameters, whereas the PGD (Proper Generalized Decomposition) is used for calculating the resulting parametric solution.

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