Prediction of magnetic permeability for soft magnetic materials using a physics-constrained Kalman filter algorithm

The DC initial permeability of sheet materials determines the performance of magnetic shielding devices. However, existing measurement methods often neglect the intrinsic linear relationship between magnetic flux density (B) and magnetic field strength (H) in the initial region, leading to poor repeatability. To address this, a Physics-Constrained Kalman Filter (PCKF) algorithm is proposed. By embedding physical constraints into the state and observation models, this algorithm jointly filters B and H signals to enable stable permeability prediction under low signal-to-noise ratio (SNR) conditions. A dynamic thresholding mechanism is also integrated to release constraints beyond the linear region, ensuring accurate processing of the complete magnetization curve. Experiments demonstrate that the PCKF reduces the coefficient of variation from 12% to 2.6%. Furthermore, comparative analysis between finite element simulations and experimental measurements validates that, unlike the conventional ring-specimen method, the PCKF results accurately characterize the actual shielding performance of magnetic shielding boxes.