Identification of B(H) Curves Using the Karhunen Loève Expansion

Constitutive equations are required in electromagnetic field simulations to model a material response to applied fields or forces. Series measurements of iron specimens have shown significant variations of the observed
$(B, H)$
data between the samples that may occur due to material impurities, mechanical stresses, or aging. Data-driven modeling and updating of
$B(H)$
curves are, therefore, well-known necessities. To update the
$B(H)$
curve in a numerical model given observations of the magnetic flux density, an inverse problem has to be solved. This problem has to be regularized e.g. by finite-dimensional approximation. In this article, we propose using a stochastic model that is based on material measurements and the Karhunen Loève expansion. The parameters of this model are determined by optimization. It is shown that this approach can retrieve a previously selected ground truth
$B(H)$
curve. With the update of the
$B(H)$
curve, the numerical model gains predictive capacities with relative errors of less than 1 unit in 10000 for excitation currents that were not included in the data.