Non-Destructive Testing of metallic structures based on electromagnetic computational methods

This thesis explores research published between 2018 to 2021 and focuses on electromagnetic (EM) computational methods in the field of non-destructive testing (NDT). Conductive samples affect the electromagnetic field generated by coils with alternating induced currents. Referring to eddy current effects, materials with different properties (magnetic permeability, electrical conductivity, thickness) result in different secondary electromagnetic fields (influenced by the eddy current) and induced voltages on coils. Based on this fact, various methods have been developed to interrogate conductive samples (particularly for steels) using electromagnetic eddy current sensors. Compared to other NDT techniques that evaluate samples, the EM eddy current technique is employed to test good conductors such as steel. This research places an emphasis on the efficient and accurate EM computational methods for the EM field simulation (or the computation of impedance or voltage on coils) and retrieval of conductivity, permeability, and thickness for both nonferromagnetic and ferromagnetic steels. For the EM simulation, a robust acceleration method was developed to hasten the edge-element finite element method (FEM). The main objective of the EM simulation is the development of a novel forward solver that can efficiently simulate how the EM properties (magnetic permeability, electrical conductivity, thickness, and lift-off) affect the detected signal (voltage or impedance) under different frequencies. The solver exploited an optimised initial guess to accelerate the EM eddy current computation for probes scanning (over a metallic plate) process. The bi-conjugate gradients stabilised (BICGS) method was utilised in solving the equation of finite-element sparse matrices - matrices forms of the Galerkin’s equations (i.e., the fundamental formulas of EM FEM). Conventional methods start iterations with an initial guess of the vector potential (and electric scalar potential) at the default value (a zero vector). Based on the fact that the eddy current (or electromagnetic field) solutions under the adjacent position steps of the probe (for the scanning process) are very similar, the solution from the previous position step of the probe was assigned to be an initial guess for the next position step of the probe. As a result, the iterations in each solving process start from an optimised guess and smaller residuals (hasten the convergence) and thus nearly 40 % of the computation time were reduced. Simplified algorithms (embedded in the system) were introduced for the retrieval of conductivity, permeability, and thickness of steels. The simplified formulation has its merits of high computation speed, and solving the lift-off effect on the property retrieval in the production process of steels when using custom-designed EM sensors. Both the swept-frequency (or multi-frequency) and single-frequency impedance were used for the sensitivity analysis of spectrum and real-time retrieval of EM properties. Various features, retrieval strategies, and EM eddy current sensors were used for different conditions on the property retrieval. Firstly, a new permeability Invariance Phenomenon was discovered and investigated in the Dodd-Deeds method (analytical formulas of the impedance for circular coils horizontally deployed above the steel plate) when using a custom-built sensor (driving-pickup sensor, i.e., transmitter and receiver are horizontally spaced on the same height), which tackled the solution uniqueness problem due to the coupling impact of the sample’s electrical conductivity and magnetic permeability. Based on this phenomenon, the electrical conductivity of ferromagnetic samples was measured without knowing its permeability. Secondly, several novel sensors were designed to reduce the lift-off effect on the property retrievals. By combining the measurement of different sensing pairs (considering sensitivities to lift-offs and test pieces), the thickness of the non-magnetic samples and the parameters of ferromagnetic slabs were retrieved using the simplified formulas. The error of the retrieved thickness (of non-ferromagnetic laminates) is 1.4 % for lift-offs up to 15 mm when using the triple-coil sensor, and 5.4 % for lift-offs up to 12 mm when using the single transmitter-receiver sensor.