Iterative identification of hysteresis in Maxwell's equations

Abstract

PurposeIn a model resulting from Maxwell's equations with a constitutive law using Preisach operators for incorporating magnetization hysteresis, this paper aims at identifying the hysteresis operator, i.e. the Preisach weight function, from indirect measurements.Design/methodology/approachDealing with a nonlinear inverse problem, one has to apply iterative methods for its numerical solution. For this purpose several approaches are proposed based on fixed point or Newton type ideas. In the latter case, one has to take into account nondifferentiability of the hysteresis operator. This is done by using differentiable substitutes or quasi‐Newton methods.FindingsNumerical tests with synthetic data show that fixed point methods based on fitting after a full forward sweep (alternating iteration) and Newton type iterations using the hysteresis centerline or commutation curve exhibit a satisfactory convergence behavior, while fixed point iterations based on subdividing the time interval (Kaczmarz) suffer from instability problems and quasi Newton iterations (Broyden) are too slow in some cases.Research limitations/implicationsApplication of the proposed methods to measured data will be the subject of future research work.Practical implicationsThe proposed methodologies allow to determine material parameters in hysteresis models from indirect measurements.Originality/valueTaking into account the full PDE model, one can expect to get accurate and reliable results in this model identification problem. Especially the use of Newton type methods – taking into account nondifferentiability – is new in this context.