A fast crack profile reconstitution model in nondestructive testing is developed using an arrayed eddy current sensor. The inverse problem is based on an iterative solving of the direct problem using genetic algorithms. In the direct problem, assuming a current excitation, the incident field produced by all the coils of the arrayed sensor is obtained by the translation and superposition of the 2D axisymmetric finite element results obtained for one coil; the impedance variation of each coil, due to the crack, is obtained by the reciprocity principle involving the dyadic Green's function. For the inverse problem, the surface of the crack is subdivided into rectangular cells, and the objective function is expressed only in terms of the depth of each cell. The evaluation of the dyadic Green's function matrix is made independently of the iterative procedure, making the inversion very fast.
Zaoui, A., Menana, H., Feliachi, M., & Berthiau, G. (2010). Inverse problem in nondestructive testing using arrayed eddy current sensors. Sensors, 10(9), 8696–8704. https://doi.org/10.3390/s100908696