Analytical Model for the Extraction of Flaw-Induced Current Interactions for SQUID NDE

Incorporating an analytical approach to simulate the interaction of a series of long cracks and the induced current of a double-D excitation coil, we have developed a model-based method to do precise detection of the positions of the cracks in a metallic structure by using eddy-current superconducting quantum interference device (SQUID) nondestructive evaluation (NDE) measurements. Conventionally, the structure of the defects is found by iteratively solving a numerical forward problem, which is usually based on finite-element, boundary-element, or volume-integral method. This, however, incurs a heavy numerical burden, as every time the forward problem is to be solved, a rigorous numerical model should be inevitably employed to extract the complex distribution pattern of the induced current encountering defects of the structure. In this paper, an analytical approach is used for the modeling of the interaction of the induced current and a series of cracks in the sample. It duly considers the distribution of the induced current in the flawed samples, does not call for extremely high computational resource, and thus permits efficient NDE as the forward problem can be solved within a reasonable time. Here, a high-
${T}_{c}$
first-order radio-frequency SQUID gradiometer is employed as the magnetic sensor of the NDE system to scan the samples with different cracks. The accuracy of the proposed algorithm is verified by having the extracted shape of the defects obtained by applying the proposed algorithm on the SQUID NDE measurements against the actual cracks.