Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization

This work focuses on the characterization of narrow vertical cracks of nite size using optically excited lock-in thermography (OLT). To characterize these cracks, we need to solve an ill-posed inverse problem. As a previous step to the solution of this inverse problem, we propose a sensitivity analy...

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Detalles Bibliográficos
Autores: Omella, A. J., Celorrio, R., Pardo, D.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2020
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1204
Acceso en línea:http://hdl.handle.net/20.500.11824/1204
Access Level:acceso abierto
Palabra clave:Crack characterization
Discontinuous Galerkin Method
Finite Element Method
Lock-in thermography
Sensitivity analysis
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spelling Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack CharacterizationOmella, A. J.Celorrio, R.Pardo, D.Crack characterizationDiscontinuous Galerkin MethodFinite Element MethodLock-in thermographySensitivity analysisThis work focuses on the characterization of narrow vertical cracks of nite size using optically excited lock-in thermography (OLT). To characterize these cracks, we need to solve an ill-posed inverse problem. As a previous step to the solution of this inverse problem, we propose a sensitivity analysis to quantify the influence that the parameters involved in the model have on the surface temperature. Some of these parameters are estimated at the laboratory and they incorporate uncertainty that may severely aff ect the reconstruction of thin cracks. For this reason, we design a calibration criterion based on the sensitivity analysis to determine which parameters we need to include as unknowns of the inverse problem. We perform this analysis using a numerical discontinuous Galerkin method. Additionally, we propose a theoretical noise model for the thermograms. Then, we use a weighted least square method (WLS) to determine the parameters from the experimental thermograms. We also obtain a theoretical uncertainty of the reconstructed parameters in OLT-WLS fi tting according to the used surface temperature dataset. Finally, we perform a numerical experiment with a 2.4 m-thick vertical crack to show the sensitivities of the surface temperature with respect to the model parameters. We also determine the uncertainty of the parameters under di fferent datasets with known noise characteristics.202020202020info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1204reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/pii/S0045782520307088info:eu-repo/grantAgreement/EC/H2020/777778info:eu-repo/grantAgreement/MINECO//SEV-2017-0718info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/12042026-06-19T12:47:47Z
dc.title.none.fl_str_mv Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
title Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
spellingShingle Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
Omella, A. J.
Crack characterization
Discontinuous Galerkin Method
Finite Element Method
Lock-in thermography
Sensitivity analysis
title_short Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
title_full Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
title_fullStr Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
title_full_unstemmed Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
title_sort Sensitivity and Uncertainty Analysis by Discontinuous Galerkin of Lock-in Thermography for Crack Characterization
dc.creator.none.fl_str_mv Omella, A. J.
Celorrio, R.
Pardo, D.
author Omella, A. J.
author_facet Omella, A. J.
Celorrio, R.
Pardo, D.
author_role author
author2 Celorrio, R.
Pardo, D.
author2_role author
author
dc.subject.none.fl_str_mv Crack characterization
Discontinuous Galerkin Method
Finite Element Method
Lock-in thermography
Sensitivity analysis
topic Crack characterization
Discontinuous Galerkin Method
Finite Element Method
Lock-in thermography
Sensitivity analysis
description This work focuses on the characterization of narrow vertical cracks of nite size using optically excited lock-in thermography (OLT). To characterize these cracks, we need to solve an ill-posed inverse problem. As a previous step to the solution of this inverse problem, we propose a sensitivity analysis to quantify the influence that the parameters involved in the model have on the surface temperature. Some of these parameters are estimated at the laboratory and they incorporate uncertainty that may severely aff ect the reconstruction of thin cracks. For this reason, we design a calibration criterion based on the sensitivity analysis to determine which parameters we need to include as unknowns of the inverse problem. We perform this analysis using a numerical discontinuous Galerkin method. Additionally, we propose a theoretical noise model for the thermograms. Then, we use a weighted least square method (WLS) to determine the parameters from the experimental thermograms. We also obtain a theoretical uncertainty of the reconstructed parameters in OLT-WLS fi tting according to the used surface temperature dataset. Finally, we perform a numerical experiment with a 2.4 m-thick vertical crack to show the sensitivities of the surface temperature with respect to the model parameters. We also determine the uncertainty of the parameters under di fferent datasets with known noise characteristics.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020
2020
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1204
url http://hdl.handle.net/20.500.11824/1204
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S0045782520307088
info:eu-repo/grantAgreement/EC/H2020/777778
info:eu-repo/grantAgreement/MINECO//SEV-2017-0718
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-108111RB-I00
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2018-2021
info:eu-repo/grantAgreement/Gobierno Vasco/ELKARTEK/
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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