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Numerical methods are used to simulate the mathematical models of a wide range of engineering problems. The precision provided by such simulators is usually fine but at the price of computational cost. In some applications this cost might be crucial. This leads us to consider cheap surrogate models in order to reduce the computation time still meeting the precision requirements. Among all available surrogate models, we deal herein with the generation of an "optimal" database of pre-calculated results combined with a simple interpolator. A database generation approach is investigated which is intending to achieve an optimal sampling. Such databases can be used for the approximate solution of both forward and inverse problems. Their structure carries some meta-information about the involved physical problem. In the case of the inverse problem, an approach for predicting the uncertainty of the solution (due to the applied surrogate model and/or the uncertainty of the measured data) is presented. All methods are based on kriging-a stochastic tool for function approximation. Illustrative examples are drawn from eddy-current nondestructive evaluation.

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PurposeThe purpose of this paper is to provide a new methodology for the characterization of a defect by eddy‐current testing (ECT). The defect is embedded in a conductive non‐magnetic plate and the measured data are the impedance variation of an air‐cored probe coil scanning above the top of the plate.Design/methodology/approachThe inverse problem of defect characterization is solved by an iterative global optimization process. The strategy of the iterations is the kriging‐based expected improvement (EI) global optimization algorithm. The forward problem is solved numerically, using a volume integral approach.FindingsThe proposed method seems to be efficient in the light of the presented numerical results. Further investigation and comparison to other methods are still needed.Originality/valueThis is believed to be the first time when the EI algorithm has been used to solve an inverse problem related to the ECT.

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