Classic and inverse compositional Gauss‐Newton in global DIC
Summary Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that...
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| Veröffentlicht in: | International journal for numerical methods in engineering Jg. 119; H. 6; S. 453 - 468 |
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| Sprache: | Englisch |
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Bognor Regis
Wiley Subscription Services, Inc
10.08.2019
Wiley |
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| ISSN: | 0029-5981, 1097-0207 |
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| Abstract | Summary
Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss‐Newton implementation of finite element DIC is proposed as a cost‐effective and mathematically sound alternative to this approximation. |
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| AbstractList | Summary
Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss‐Newton implementation of finite element DIC is proposed as a cost‐effective and mathematically sound alternative to this approximation. Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic finite element (or, more generally, global) DIC solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution, etc) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then, an inverse compositional Gauss‐Newton implementation of finite element DIC is proposed as a cost‐effective and mathematically sound alternative to this approximation. Today, effective implementations of Digital Image Correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the classic Finite Element (or more generally global) DIC (FE-DIC) solver consists in replacing the gradient of the deformed state image with that of the reference image, so as to obtain a constant operator. Different arguments (small strains, small deformations, equality of the two gradients close to the solution...) have been given in the literature to justify this approximation, but none of them are fully accurate. Indeed, the convergence of the optimization algorithm has to be investigated from its ability to produce descent directions. Through such a study, this paper attempts to explain why this approximation works and what is its domain of validity. Then an Inverse Compositional Gauss-Newton (ICGN) implementation of FE-DIC is proposed as a cost effective and mathematically sound alternative to this approximation. |
| Author | Passieux, Jean‐Charles Bouclier, Robin |
| Author_xml | – sequence: 1 givenname: Jean‐Charles orcidid: 0000-0001-8387-4122 surname: Passieux fullname: Passieux, Jean‐Charles email: passieux@insa-toulouse.fr organization: Université de Toulouse, Centre National de la Recherche Scientifique/Institut National des Sciences Appliquées/Université Toulouse III/École des Mines d'Albi/Institut Supérieur de l'Aéronautique et de l'Espace – sequence: 2 givenname: Robin orcidid: 0000-0002-6265-4726 surname: Bouclier fullname: Bouclier, Robin organization: Université de Toulouse, Centre National de la Recherche Scientifique/Université Toulouse 1 Capitole/Université Toulouse—Jean Jaurès/Université Toulouse III/Institut National des Sciences Appliquées |
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| Keywords | inverse compositional Gauss-Newton forward compositional Gauss-Newton global DIC |
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Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea... Today, effective implementations of digital image correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the... Today, effective implementations of Digital Image Correlation (DIC) are based on iterative algorithms with constant linear operators. A relevant idea of the... |
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| SubjectTerms | Approximation Deformation mechanisms Digital imaging Engineering Sciences Finite element method forward compositional Gauss‐Newton global DIC inverse compositional Gauss‐Newton Iterative algorithms Iterative methods Linear operators Mathematical analysis Mechanics Optimization Structural mechanics |
| Title | Classic and inverse compositional Gauss‐Newton in global DIC |
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