A comparison of non-linear optimisation algorithms for recovering the conductivity depth profile of an electrically conductive block using eddy current inspection

Abstract

This paper compares 15 different non-linear optimisation algorithms for reconstructing the depth profile of electrical conductivity for a conductive block of material using multi-frequency measurements from an eddy current probe. Synthetic data was generated using a finite element model, where the underlying conductivity profile was randomly generated and smoothed, noise was then superimposed on the synthetic data. The compared algorithms were designed such that optimal performance was achieved for each algorithm by using the knowledge of the true underlying conductivity profile used to generate the synthetic data. The most competitive algorithm after ten iterations was determined to be dependent on the a priori estimate and level of noise, where the Broyden–Fletcher–Goldfarb–Shanno, augmented Levenberg-Marquardt and Levenberg-Marquardt are each top of different case studies. The augmented Levenberg-Marquardt and Levenberg-Marquardt were then employed on measured data, where the algorithms used a novel update procedure (in the nuclear graphite application) for the regularisation parameter. The study considers the conductivity profile of graphite blocks of the type used in the nuclear industry.