## 5 Conclusions  
This article addresses a simulation-based generation of synthetic ART training data for the separation of undamaged and defective parts, as well as the subsequent training procedure leading to an ART sorting algorithm. For the development and demonstration, a model-like part type and an application scenario were defined. Tolerable geometric part-to-part variations, constant material properties as far as possible, and an optional through-hole defect at a random position were taken into account. The application aim was to classify whether there is a defect in any of altogether two dozen machine-made parts by means of the measured eigenfrequencies of those parts. The implementation started with FEM eigenfrequency simulations of the required extensive synthetic data, covering many good virtual training parts and defective ones, both featuring geometric scatter. These data were enhanced analytically to a wide range of defect sizes. They were then adapted to measured data via correction factors derived from some additional machine-made reference parts. Using the resulting synthetic ART training data, classification models were created. These models were applied to the measurement data of two dozen machine-made validation parts, some of them featuring a through hole enlarged stepwise. Thereby, a model using the eigenfrequencies alone led to a perfect separation of the undamaged parts and the parts with a through-hole from 2.5 mm in size. More complicated models, involving the half or the full geometric part data in the sense of additional a priori information, showed a defect detection limit of 2 mm or 1.5 mm, respectively. In addition, we described a second defect detection strategy based on the undamaged training parts alone, but requiring the full geometric data of an object. The positive study results indicate that the simulation-based ART training data generation offers extensive potential to overcome the limitations associated with a conventional experimental training data approach. Thus, the developments can add significant value to ART and its application on series parts. Further unsolved research tasks cover a transfer of our strategy to a real ART series application, which is accompanied by practice-relevant challenges. Digital part twins representing comprehensive data from an entire series production may thereby be the basis of generating synthetic ART training data. In addition, the collected twin data may be used directly for a powerful multimodal classification by evaluating the eigenfrequencies together with further part or process data. We see a great opportunity through AI or machine-learning methods for ART. Moreover, the data from this study provide an excellent basis for advanced AI model-building approaches, which require large training data. Conceptualization, M.H., B.V. and U.R. ; methodology, M.H. ; software, M.H. ; validation, M.H., B.V. and U.R. ; formal analysis, M.H. and U.R. ; investigation, M.H. ; resources, M.H. and B.V.; data curation, M.H. ; writing--original draft preparation, M.H. ; writing--review and editing, M.H., B.V. and U.R. ; visualization, M.H., B.V. and U.R. ; supervision, B.V. and U.R. ; project administration, B.V.; funding acquisition, M.H. and B.V. All authors have read and agreed to the published version of the manuscript. Previous work was funded by German Federal Ministry for Education and Research (BMBF) under 03 FH029 PY4 and 13 FH029 PY4. The funding recipient was [PERSON] (University of Applied Sciences, Saarbrucken, Germany). Some of the materials used in this study, such as machine-made parts and specific data sets, and some of the knowledge, originate from these previous research activities. Fraunhofer IZFP did not receive any funding for the presented study. Not applicable. The data presented in this study are available on request from the corresponding author. The data are not publicly available due to the very large amount of simulation models and measurement raw data.