Standard and extended finite element methods (FEM/XFEM) have been employed to simulate cracked solids and shells. Cracks were either explicitly meshed in the case of standard FEM, or represented by appropriate enrichment functions in the case of XFEM.
In a first attempt to combine numerical models with data-driven methods, a two step crack detection scheme was developed. The first step relied on a damage index based on mode shape curvatures, a quantity typically used in the SHM literature to provide a rough initial damage localization. In the second step, a numerical model for cracked plates, based on the XFEM, was employed along with an evolutionary optimization algorithm to refine the initial localization and eventually yield an accurate estimate for the crack location, size and orientation. At this stage, operational loads were considered known, while the full order XFEM models were used.
Subsequently, a method for parametrizing models of cracked solids with respect to the damage location and extend was developed, relying on mesh morphing. This in turn, enabled the use of state of the art model order reduction (MOR) techniques to construct parametric reduced order models (pROMs), providing similar accuracy to their full order counterparts, over a wide array of damaged configurations, at a fraction of their numerical cost.
With efficient and accurate parametric ROMs available, two alternative approaches for damage detection were developed. In the first, damage indices that rely on output only quantities, and thus do not require information regarding the applied loading were employed. Then optimization was employed to minimize the difference between the measured values of the damage indices and the ones predicted by the pROMs, leading to the detection of damage.
In the second approach, the time history of the loading as well as the damage location and extent are simultaneously estimated, in an online manner, through the use of particle filters. More specifically, a hierarchical Bayesian filter was developed, the input load was estimated at a first level, while, at a second level, multiple models were generated, selected and updated using evolutionary operations, to yield an estimate for the damage extent and location.
Exploitation and dissemination of the results.
The results of the project were presented in three international conferences, two workshops and a seminar. Additional presentations were planned, however several conferences have been cancelled due to COVID-19. One paper has been published with results from the project, with three more under review and one in preparation.
