Sensitivity analysis of inverse problems in EM non-destructive testing

The inverse problem of electromagnetic (EM) non-destructive testing (NdT) consists of reconstructing material defect parameters invoking EM field measurements. Uncertainties of the configuration (e.g. imprecise constitutive and geometrical parameters) are inevitably present; hence, the reconstructed defect parameters are also uncertain. In this study, the different sources of uncertainty are ranked by means of sensitivity analysis. The model-based inversion (involving EM simulation) is computationally demanding; moreover, sensitivity analysis usually requires a vast number of repeated runs of the inversion. To overcome the computational complexity, surrogate models are applied at different levels. Interpolation on a sparse grid is used as a surrogate model of the EM simulation. The sensitivity of the reconstructed defect parameters concerning configuration uncertainties is characterised by means of Sobol indices. The Sobol indices are obtained from a polynomial chaos expansion surrogate model of the entire inversion scheme. A numerical example drawn from eddy-current NdT is thoroughly analysed to illustrate the proposed methodology and to demonstrate its performance.