Towards flaw detection in welding joints via multi-frequency topological derivative methods

Exploring the performance of the topological energy method for object and damage detection from noisy and poor databases

“…In the same figure, we represent the values of the topological energy when processing databases corresponding to different emitter/receiver configurations, marked by black dots in the plots, where N E = 60, 30, 20, 10 and 5 (recall that in A2, N R = N E − 1 since we emit from one sensor and measure the resulting total wave in the remaining ones). Although standard inspection techniques use N E = 60 aligned sensors (see [24]), we observe that the topological energy is a powerful tool, able to correctly identify the presence of flaws even when considering a much-reduced number of sensors. Note also that without knowing their nature, the three flaws are correctly identified.…”

“…The second application (A2) is related to the inspection of welding joints. The simplified acoustic model we will consider here was proposed in [24] to perform a preliminary study on the use of a multi-frequency topological derivative-based method for the detection of air bubbles in welding joints of steel plates in defence vehicles. In the simplest two-dimensional case, the setting is as depicted in figure 1b: the two plates to be welded are represented as grey rectangles, and the welding joints are the two triangles in lavender colour.…”

“…where u inc, t s is the incident wave in both applications, p inc, t s is as defined in equation (3.2) in A1, and as in equation (3.5) in A2. The proof for A1 can be found in [10], while for A2, the result in [10] should be adapted following the derivation in [24] for air bubbles.…”