Metamodel-Based Nested Sampling for Model Selection in Eddy-Current Testing

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.