The inverse problem methodology for the measurement of the permeability of the ferromagnetic materials

The inverse problem methodology is used to evaluate the permeability of the ferromagnetic materials from the measurement of the impedance of a sensor. The linear case is studied by a harmonic A-V formulation of the Maxwell equations. The nonlinear case is elaborated by a first harmonic equivalent permeability. The Nelder-Mead simplex search method is then used to solve the inverse problem. To obtain the best operating frequency of the installation, the sensitivity of the sensor is calculated as a function of the frequency.