Comparison of a quasi Newton method using Broyden’s update formula and an adjoint method for determining local magnetic material properties of electrical steel sheets

Abstract

Purpose

Performing accurate numerical simulations of electrical drives, the precise knowledge of the local magnetic material properties is of utmost importance. Due to the various manufacturing steps, e.g. heat treatment or cutting techniques, the magnetic material properties can strongly vary locally, and the assumption of homogenized global material parameters is no longer feasible. This paper aims to present the general methodology and two different solution strategies for determining the local magnetic material properties using reference and simulation data.

Design/methodology/approach

The general methodology combines methods based on measurement, numerical simulation and solving an inverse problem. Therefore, a sensor-actuator system is used to characterize electrical steel sheets locally. Based on the measurement data and results from the finite element simulation, the inverse problem is solved with two different solution strategies. The first one is a quasi Newton method (QNM) using Broyden's update formula to approximate the Jacobian and the second is an adjoint method. For comparison of both methods regarding convergence and efficiency, an artificial example with a linear material model is considered.

Findings

The QNM and the adjoint method show similar convergence behavior for two different cutting-edge effects. Furthermore, considering a priori information improved the convergence rate. However, no impact on the stability and the remaining error is observed.

Originality/value

The presented methodology enables a fast and simple determination of the local magnetic material properties of electrical steel sheets without the need for a large number of samples or special preparation procedures.