SHM via topological derivative

This paper deals with the use of the topological derivative as an analysis tool for structural health monitoring, to locate the presence of ?aws in a homogeneous material plate that is subject to guided elastic waves excitation. Using a numerical solver to compute the response of the system and de?ning a scalar objective function that measures the least squares difference between the measured and calculated signals, the topological derivative somehow describes the sensitivity of the objective function to localized perturbations of the material properties due to the presence of defects. Thus, defects are guessed to be located near the topological derivative peaks. This is somehow related to theminimizationof theobjectivefunctionandusesthewholephysics ofthe problem (to computethe objectivefunction),insteadofasmalleramountofphysicalinformation,asconventionalmethodsdo. Here, we reconstruct small defects via the topological derivative by using multi-frequency synthetic data, for several representative con?gurations of the actuators and sensors, and several defect locations. Among these, some fairly demanding con?gurations are considered that are not accessible to conventional methods, such as actuators and sensors located very close to the plate boundary, and defects located beyond both elongated through-slits and elongated inclusions of a different material.