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
Article, Bibliographie
This is the latest version of this item.
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.
| Item Type: | Article |
|---|---|
| Erschienen: | 2024 |
| Creators: | Kaltenbacher, Manfred ; Gschwentner, Andreas ; Kaltenbacher, Barbara ; Ulbrich, Stefan ; Reinbacher-Köstinger, Alice |
| Type of entry: | Bibliographie |
| Title: | Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study |
| Language: | English |
| Date: | May 2024 |
| Place of Publication: | Basel |
| Publisher: | MDPI |
| Journal or Publication Title: | Mathematics |
| Volume of the journal: | 12 |
| Issue Number: | 10 |
| Collation: | 13 Seiten |
| DOI: | 10.3390/math12101586 |
| Corresponding Links: | |
| 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. |
| Uncontrolled Keywords: | inverse problems, adjoint method, determination of locally nonlinear magnetic material behaviour |
| Identification Number: | Artikel-ID: 1586 |
| Additional Information: | This article belongs to the Special Issue Numerical Optimization for Electromagnetic Problems MSC: 49M41 |
| Classification DDC: | 500 Science and mathematics > 510 Mathematics 600 Technology, medicine, applied sciences > 620 Engineering and machine engineering |
| Divisions: | 04 Department of Mathematics 04 Department of Mathematics > Optimization 04 Department of Mathematics > Optimization > Nonlinear Optimization |
| Date Deposited: | 19 Sep 2024 07:51 |
| Last Modified: | 19 Sep 2024 07:51 |
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| Suche nach Titel in: | TUfind oder in Google |
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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) [Currently Displayed]
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