A dual-stage dimensionless method for simultaneous estimation of electrical conductivity, lift-off, and thickness in eddy current testing

This paper presents a dual-stage method for simultaneously estimating electrical conductivity, lift-off, and thickness in conductive samples using Eddy Current Testing (ECT) and dimensional analysis. The approach takes advantage of Buckingham's π theorem to reformulate the physical model in a reduced set of dimensionless variables, allowing for a computationally efficient and geometrically intuitive inversion based on intersections of level curves. The proposed method integrates these principles into a two-step estimation process that requires only one high-frequency and one low-frequency measurement. In the first stage, a high-frequency thickness-independent measurement is used for the simultaneous estimation of electrical conductivity and lift-off. In the second stage, a low-frequency measurement is used to recover the remaining thickness through one of the three proposed strategies, depending on which parameters of Stage 1 are retained. The method was experimentally validated on six conductive samples under five lift-off conditions. The results show high accuracy, with relative errors below 2.5% for both electrical conductivity and lift-off, and 3.2% for thickness, and excellent repeatability with standard deviations generally lower than 1%. The observed repeatability in both stages supports implementation in either a multi-frequency or a single-frequency configuration, enabling simplified hardware, reduced measurement time, and real-time applicability. Overall, the methodology represents a practical and flexible framework suitable for integration into modern industrial ECT systems and Industry 4.0 quality-control environments.