Kaltenbacher, Manfred ; Gschwentner, Andreas ; Kaltenbacher, Barbara ; Ulbrich, Stefan ; Reinbacher-Köstinger, Alice (2024)
Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study.
In: Mathematics, 12 (10)
doi: 10.3390/math12101586
Artikel, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2024 |
| Autor(en): | Kaltenbacher, Manfred ; Gschwentner, Andreas ; Kaltenbacher, Barbara ; Ulbrich, Stefan ; Reinbacher-Köstinger, Alice |
| Art des Eintrags: | Bibliographie |
| Titel: | Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study |
| Sprache: | Englisch |
| Publikationsjahr: | Mai 2024 |
| Ort: | Basel |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Mathematics |
| Jahrgang/Volume einer Zeitschrift: | 12 |
| (Heft-)Nummer: | 10 |
| Kollation: | 13 Seiten |
| DOI: | 10.3390/math12101586 |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | We are interested in the determination of the local nonlinear magnetic material behaviour in electrical steel sheets due to cutting and punching effects. For this purpose, the inverse problem has to be solved, where the objective function, which penalises the difference between the measured and the simulated magnetic flux density, has to be minimised under a constraint defined according to the corresponding partial differential equation model. We use the adjoint method to efficiently obtain the gradients of the objective function with respect to the material parameters. The optimisation algorithm is low-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS), the forward and adjoint formulations are solved using the finite element (FE) method and the ill-posedness is handled via Tikhonov regularisation, in combination with the discrepancy principle. Realistic numerical case studies show promising results. |
| Freie Schlagworte: | inverse problems, adjoint method, determination of locally nonlinear magnetic material behaviour |
| ID-Nummer: | Artikel-ID: 1586 |
| Zusätzliche Informationen: | This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems MSC: 49M41 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Optimierung 04 Fachbereich Mathematik > Optimierung > Nonlinear Optimization |
| Hinterlegungsdatum: | 19 Sep 2024 07:51 |
| Letzte Änderung: | 19 Sep 2024 07:51 |
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| Suche nach Titel in: | TUfind oder in Google |
Verfügbare Versionen dieses Eintrags
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Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study. (deposited 18 Sep 2024 11:50)
- Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study. (deposited 19 Sep 2024 07:51) [Gegenwärtig angezeigt]
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