Permeability Distribution Reconstruction Method Based on Magnetic Dipole and Demagnetization Effect Theories

Electromagnetic tomography (EMT) based on the tunneling magnetoresistance (TMR) sensor has been developed for imaging permeability distribution in the fluidized beds with the magnetic catalyst. Due to the linear approximation of the forward problem, the reconstruction of the permeability distribution using the conventional sensitivity-based algorithms is inaccurate. To solve this problem, the nonlinear relationship between the boundary measurement data and the permeability distribution is derived and transformed into a new form of the system of linear equations according to the magnetic dipole theory and the demagnetization effect theory. The conventional sensitivity-based algorithm is employed to solve the new system of linear equations, and the calculation results are further processed to obtain the permeability distribution. Compared to the conventional reconstruction algorithms based on a linear approximation, the proposed method in this article is based on a more exact nonlinear relationship between the permeability of a single perturbation and the boundary measurement data to solve for permeability distribution, so the values obtained are more accurate, especially for that between the empty field permeability and the full-field permeability. Besides, the proposed method only adds the processing of the sensitivity matrix and the processing of the final algorithm results to the conventional algorithms, so the calculation process is simple.