Reconstructing the conductivity profile of a graphite block using inductance spectroscopy with data-driven techniques

Abstract

The radial depth profile of the electrical conductivity of the graphite channels in the UK's advanced gas-cooled reactors (AGRs) can be reconstructed and estimated by solving a non-linear optimisation problem using the mutual inductance spectra of a set of coils. This process is slow, as it requires many iterations of a forward solver. Alternatively, a data-driven approach can be used to provide an initial estimate for the optimisation algorithm, reducing the amount of time it takes to solve the ill-posed inverse problem. Two data-driven approaches are compared: multi-variable polynomial regression (MVPR) and a convolutional neural network (CNN). The training data are generated using a finite element (FE) model and superimposed on a noise floor in the interval [20, 60] dB of the weakest amplitude point in the corresponding spectrum. A total of 5000 simulated datasets are generated for training. The results on smoothed test data show that the two models have a comparable mean percentage error norm of 17.8% for the convolutional neural network and 17.3% for multivariable polynomial regression. A further 500 unsmoothed profiles are tested in order to assess the performance of each algorithm on conductivity distributions where the conductivity of each layer is independent of another. The performance of both algorithms is then assessed on reactor-type test data. The results show that the two data-driven algorithms have a comparable performance when estimating the electrical conductivity depth profile of a typical reactor-type distribution, as well as vast deviations. More generally, it is thought that data-driven approaches for depth profiling of some electromagnetic quantity have the potential to be applied to other ill-posed inverse problems where speed is a priority.