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Flaw characterization in eddy current testing usually requires to solve a non-linear inverse problem. Due to high computational cost, Markov Chain Monte Carlo (MCMC) methods are hardly employed since often needing many forward evaluations. However, they have good potential in dealing with complicated forward models and they do not reduce to only providing the parameters sought. Here, we introduce a computationally-cheap surrogate forward model into a MCMC algorithm for eddy current flaw characterization. Due to the use of a database trained off-line, we benefit from the MCMC algorithm for getting more information and we do not suffer from the computational burden. Numerous experiments are carried out to validate the approach. The results include not only the estimated parameters, but also standard deviations, marginal densities and correlation coefficients between two parameters of interest. [ABSTRACT FROM AUTHOR]

In non-destructive testing, model selection is a common problem, e.g., to determine the number of defects present in the inspected workpiece. Statistical model selection requires to approximate the marginal likelihood also called model evidence. Its numerical approximation is usually computationally expensive. Nested sampling (NS) offers a good compromise between estimation accuracy and computational cost. But, it requires to evaluate the forward model many times. Here, we first propose a general framework where data-fitting surrogate models are used to accelerate the computation. Then, improvements benefiting from surrogate modeling are introduced into the traditional NS algorithm to further reduce the computational cost. These improvements include the use of a sparse-grid surrogate model to deal with the “curse-of-dimensionality” in large dimensional problems and of the preestimated posterior space to save warming-up time. Based on eddy-current simulations, we show that this improved model selection approach has high model selection ability and can jointly perform model selection and parameter inversion. [ABSTRACT FROM AUTHOR]