Invariants in Eddy Current Testing via dimensional analysis

The Buckingham's $π$, theorem has been recently introduced in the context of Non destructive Testing \& Evaluation (NdT\&E) , giving a theoretical basis for developing simple but effective methods for multi-parameter estimation via dimensional analysis. Dimensional groups, or $π-$groups, allow for the reduction of the number of parameters affecting the dimensionless measured quantities. In many real-world applications, the main interest is in estimating only a subset of the variables affecting the measurements. An example is estimating the thickness and electrical conductivity of a plate from Eddy Current Testing data, regardless of the lift-off of the probe, which may be either uncertain and/or variable. Alternatively, one may seek to estimate thickness and lift-off while neglecting the influence of the electrical conductivity, or to estimate the electrical conductivity and the lift-off, neglecting the thickness. This is where the concept of invariants becomes crucial. An invariant transformation is a mathematical mapping that makes the measured signal independent of one or more of these uncertain parameters. Invariant transformations provide a way to isolate useful signals from uncertain ones, improving the accuracy and reliability of the NdT results. The main contribution of this paper is a systematic method to derive \emph{invariant} transformations for frequency domain Eddy Current Testing data, via dimensional analysis. The proposed method is compatible with real-time and in-line operations. After its theoretical foundation is introduced, the method is validated by means of experimental data, with reference to configurations consisting of plates with different thicknesses, electrical conductivity, and lift-off. The experimental validation proves the effectiveness of the method in achieving excellent accuracy on a wide range of parameters of interest.