This paper presents a hybrid model to estimate the magnetic behaviour of a ferromagnetic structure. The mathematical-physical model has been developed using the Method of Moments combined with a hysteresis model. The mathematical model was derived by a linearisation of the hysteresis curve. The initial magnetic state of a ferromagnetic object is found through inverse computations, including regularisation techniques. The idea of dictionary regularisation is introduced to support the inverse computations with prescribed templates that reflect a priori knowledge of the typical shapes of magnetisation distributions. These templates are extracted from the Method of Moments. Data assimilation is used to update the model in time by means of measurements of the magnetic field near a ferromagnetic structure. The proposed hybrid model is implemented for a typical steel object and verified by means of numerical experiments and measurements in an experimental environment.

The purpose of this article is to estimate the parameters of the Jiles-Atherton hysteresis model, based on minor-loop measurement data in weak applied fields. The well-known hysteresis model by Jiles and Atherton serves as a basis of this article with an extension for the closure of minor loops. In order to represent minor loops correctly, a dissipative factor is introduced. A methodology to obtain the initial magnetization of a specimen is defined, based on an expansion in terms of higher order Gaussian functions. The methodology is implemented within a finite-element method using an interconnection between MATLAB and COMSOL. This interconnection allows the investigation of potentially large ferromagnetic objects to be calibrated to the proposed ferromagnetic model in weak fields. The proposed methodology was verified using an original approach. The approach relies on the use of a sensor array that makes it possible to detect local variations of magnetic properties in steel plates. Material parameters for our test specimen are successfully obtained by means of experimental data, using the shuffled frog leaping optimization algorithm. An analysis of the obtained results shows that the calibrated model is able to represent the measurement data accurately.