A numerical optimisation method for obtaining technically smooth magnetisation characteristics

Abstract

In general, if measurements can be repeated several times assuming the same conditions, the measurement error can significantly be decreased by statistically evaluating the measurements. However, an uncertainty band always remains. Non-linear numerical simulations based on e.g. the Newton-Raphson method may establish a poor convergence if they are provided directly with measured data. Therefore, data pre-processing is required. Here, a neural network approach is employed. A two-layer perceptron is fitted on a measured magnetisation curve, thereby restricting the solution to be technically feasible while accepting the statistical nature of the data. By using a perceptron, an analytical expression of the magnetisation curve is obtained and expressions for its derivatives can easily be computed. The standard Newton iteration scheme to solve a non-linear system of equations obtained from the finite element method is based on the updating of the field dependent element reluctivity and its derivative. Usually, the manufacturer of the ferromagnetic material provides a BH-characteristic as diagram or in the form of a table of data samples. The influence of the material properties, in particular their accurate numerical representation, is significant for the rate of convergence during the Newton iterations. Here, a numerical optimization aiming at a technically smooth non-linear characteristic is performed to obtain a higher rate of convergence of the Newton iteration scheme. The neural network approach is adopted for representing the magnetisation curve.