Ultrasonic inspection of welding joints using the topological derivative as damage indicator

This work addresses the ultrasonic inspection of welding joints for detecting internal defects that may compromise the structural integrity of critical components. We propose a non-destructive evaluation methodology based on the topological derivative, applied to ultrasonic wavefield data. To generate synthetic measurements, we employ two elastic wave propagation models: a simplified two-dimensional model for initial proof of concept assessment and a full three-dimensional model that captures the complexity of realistic welded structures. The method is tested in several challenging scenarios, including the detection of small-scale defects, the identification of different defect types, and adverse conditions such as measurement noise, model mismatches, attenuation effects, and limited data availability. Numerical results demonstrate the robustness and effectiveness of the topological derivative-based strategy for ultrasonic imaging and defect characterization in welded components.