Data-driven techniques to estimate parameters in a rate-dependent ferromagnetic hysteresis model

The quantification of rate-dependent ferromagnetic hysteresis is important in a range of applications including high speed milling using Terfenol-D actuators. There exist a variety of frameworks for characterizing rate-dependent hysteresis including the magnetic model in Ref. [2], the homogenized energy framework, Preisach formulations that accommodate after-effects, and Prandtl-Ishlinskii models. A critical issue when using any of these models to characterize physical devices concerns the efficient estimation of model parameters through least squares data fits. A crux of this issue is the determination of initial parameter estimates based on easily measured attributes of the data. In this paper, we present data-driven techniques to efficiently and robustly estimate parameters in the homogenized energy model. This framework was chosen due to its physical basis and its applicability to ferroelectric, ferromagnetic and ferroelastic materials.