Optimal needles placement for the identification of magnetic material properties based on uncertainty analysis in the inverse approach

The measured signals picked up by the needle probe method can be interpreted by a numerical method so to identify the magnetic material properties of an electromagnetic device. However, uncertainties in the numerical method give recovery errors since the needle signals are sensitive to these uncertainties. This paper proposes a stochastic Cramér-Rao bound (sCRB) method for determining the optimal sensor placement in the experimental setup with given uncertain geometrical parameters. We apply the method for the characterization of the magnetic material characteristics of an EI inductor and we determine the optimal needles placement that corresponds with the highest resolution of the inverse solution. Moreover, the presented results are compared with the First Order Perturbation method (FOPM) and the recovered material characteristics are validated with the exact material characteristics. The suggested methodology is independent on the values of the material parameter, so it can be applied before solving the inverse problem as a priori estimation stage, which confirms the importance of the proposed methodology