Inverse Scheme to Locally Determine Nonlinear Magnetic Material Properties: Numerical Case Study

Manfred Kaltenbacher (), Andreas Gschwentner, Barbara Kaltenbacher, Stefan Ulbrich and Alice Reinbacher-Köstinger
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Manfred Kaltenbacher: Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Inffeldgasse 18, 8010 Graz, Austria
Andreas Gschwentner: Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Inffeldgasse 18, 8010 Graz, Austria
Barbara Kaltenbacher: Department of Mathematics, AAU Klagenfurt, Universitätsstrasse 65-67, 9020 Klagenfurt, Austria
Stefan Ulbrich: Department of Mathematics, TU Darmstadt, Dolivostraße 15, 64293 Darmstadt, Germany
Alice Reinbacher-Köstinger: Institute of Fundamentals and Theory in Electrical Engineering, Graz University of Technology, Inffeldgasse 18, 8010 Graz, Austria

Mathematics, 2024, vol. 12, issue 10, 1-13

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.

Keywords: inverse problems; adjoint method; determination of locally nonlinear magnetic material behaviour (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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