Fast Identification of the Jiles–Atherton Model Parameters and the Electrical Conductivity Based on Gaussian Process Regression

Various approaches already exist for identifying the Jiles-Atherton (JA) hysteresis model, typically using optimization algorithms that minimize the deviation of hysteresis curves from a reference trajectory to approximate suitable parameters. However, depending on the implementation of the JA model and the optimization algorithm, this approach can be computationally intensive. Therefore, a data-driven approach based on the Gaussian process regression (GPR) is investigated. Using numerical simulations, B(H) curves of toroidal core samples are initially generated. Hysteresis and eddy current effects are considered through the use of electromagnetically coupled Maxwell equations and the JA model. By varying JA parameters, core geometry, and electrical excitation, a dataset of B(H) loops for different materials and different test configurations is created. The resulting dataset serves as input for GPR models which predict JA parameters and electrical conductivity based on hysteresis curves and boundary conditions. The GPR models achieves strong regression performance with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$R^{2}$ </tex-math></inline-formula> values of up to 0.999. Overall, this approach can reliably estimate the JA parameters and the conductivity of the material based on the hysteresis curve as well as the geometrical and electrical boundary conditions. The estimation of the parameters occurs with minimal temporal delay and is universally applicable.