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Data Completion, Model Correction and Enrichment Based on Sparse Identification and Data Assimilation

Article dans une revue avec comité de lecture
Author
DI LORENZO, Daniele
564849 ESI Group [ESI Group]
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
CHAMPANEY, Victor
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
564849 ESI Group [ESI Group]
GERMOSO, Claudia
580476 Instituto Tecnológico de Santo Domingo [INTEC [República Dominicana]]
CUETO, Elias
95355 University of Zaragoza - Universidad de Zaragoza [Zaragoza]
161327 Aragón Institute of Engineering Research [Zaragoza] [I3A]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
564849 ESI Group [ESI Group]

URI
http://hdl.handle.net/10985/23041
DOI
10.3390/app12157458
Date
2022-07
Journal
Applied Sciences

Abstract

Many models assumed to be able to predict the response of structural systems fail to efficiently accomplish that purpose because of two main reasons. First, some structures in operation undergo localized damage that degrades their mechanical performances. To reflect this local loss of performance, the stiffness matrix associated with the structure should be locally corrected. Second, the nominal model is sometimes too coarse grained for reflecting all structural details, and consequently, the predictions are expected to deviate from the measurements. In that case, there is no small region of the model that needs to be repaired, but the entire domain needs to be repaired; therefore, the entire structure-stiffness matrix should be corrected. In the present work, we propose a methodology for locally correcting or globally enriching the models from collected data, which is, upon its turn, completed beyond the sensor’s location. The proposed techniques consist in the first case of an L1-minimization procedure that, with the support of data, aims at the same time period to detect the damaged zone in the structure and to predict the correct solution. For the global enrichment, instead, the methodology consists of an L2-minimization procedure with the support of measurements. The results obtained showed, for the local problem, a correction up to 90% with respect to the initially incorrectly predicted displacement of the structure, and for the global one, a correction up to 60% was observed (this results concern the problems considered in the present study, but they depend on different factors, such as the number of data used, the geometry or the intensity of the damage). The benefits and potential of such techniques are illustrated on four different problems, showing the large generality and adaptability of the methodology.

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