Data-Driven Update of B(H) Curves of Iron Yokes in Normal Conducting Accelerator Magnets

TL;DR

This paper presents a data-driven method to update the B(H) curve of iron yokes in accelerator magnets by solving a regularized inverse problem, improving the predictive accuracy of electromagnetic simulations.

Contribution

It introduces a novel inverse problem approach using Karhunen Loeve expansion to update B(H) curves based on observed data, enhancing modeling accuracy.

Findings

Successfully retrieves the ground truth B(H) curve.

Improves model predictions for unseen excitation currents.

Demonstrates effectiveness of stochastic function space regularization.

Abstract

Constitutive equations are used in electromagnetic field simulations to model a material response to applied fields or forces. The $B(H)$ characteristic of iron laminations depends on thermal and mechanical stresses that may have occurred during the manufacturing process. Data-driven modelling and updating of the $B(H)$ characteristic are therefore well known necessities. In this work the $B(H)$ curve of an iron yoke of an accelerator magnet is updated based on observed magnetic flux density data by solving a non-linear inverse problem. The inverse problem is regularized by restricting the solution to the function space that is spanned by the truncated Karhunen Loeve expansion of a stochastic $B(H)$-curve model based on material measurements. It is shown that this method is able to retrieve a previously selected ground truth $B(H)$-curve. With the update of the $B(H)$ characteristic, the numerical model gains predictive capacities for excitation currents that were not included in the data.