Inversion scheme based on optimization for 3-D Eddy current flaw reconstruction problems

An inversion scheme based on first-order optimization is developed for eddy current flaw reconstruction problems with arbitrary specimen, probe and defect shapes. As an essential component of this scheme, a new 3-D forward solver is introduced for the purpose of rapid flaw signal prediction in the inversion loop. This forward solver, whose numerical formulation is basically a discrete reaction variational technique, relies on a reaction data set in the form of an equation system, constructed before entering the inversion loop by a finite element electromagnetic field simulator. The anomalous region is subdivided into small subregions, called flaw cells, and a flaw is represented by a complete set of current dipole density pulses defined in these flaw cells. The coefficient matrix of the equation system consists of reactions between the dipole current density pulses while the elements of the right-hand-side vector are reactions between the pulses and the probe coils. The gradient of the error function, which represents the sensitivity with respect to the flaw parameters, can also be computed quickly from the same pre-calculated reaction dataset, thereby ensuring the efficient implementation of a first-order optimization algorithm. In order to avoid being trapped in a local minimum of the error function, good initial flaw estimates are generated by a neural network signal processing system developed recently by the authors. Various reconstruction examples demonstrate the efficiency of the reconstruction system.