## 4 Discussion  
The demonstration of our defect detection strategy, using synthetic ART training data based on simulation techniques, led to very satisfying results. For the presented application scenario aiming to detect a through-hole defect within two dozen machine-made parts by ART, a detection limit between \(1.5\) mm and \(2.5\) mm was achieved. The results depend on the implemented classification model predictor variables. In addition, three parts with an unexpected and systematical behavior, most likely caused by an unknown structural anomaly, were rejected. This also indicates a strong classification performance. A model part type with a parameterizable geometry, a well-finished surface, and a homogeneous material was examined. It was possible to control and to preset these and other application features, such as the geometric scatter or the defect type. As is typical for research works, we had extensive methods as well as plenty of time and equipment. This is all the more challenging for a series application, as complicated geometries, difficult material structures, or rough surface textures can occur. The time and methods are also limited in practice. The application of this work to a series application requires, of course, a part and a defect type of interest both being suitable for an application of ART. The derived findings are, moreover, particularly useful if significant variations in the tolerable parts' eigenfrequencies occur. Thereby, the eigenfrequency variations can be caused by geometry or material. There is also a minimal requirement for a series-integrated ART rig, as well as having a simulation tool for the generation of synthetic ART training data. It is noted that the general idea of our strategy may be suitable for any ART sorting tasks, besides structural defect detection. This covers applications regarding potential material mix-ups, the identification of invalid geometry shapes, or the detection of microstructural anomalies. Figure 14: Overview of the classification results for machine-made connecting rods being either undamaged or featuring a defect anywhere in the part with a size between \(1\) mm and \(3\) mm, based on various classification models derived from training datasets with different noise levels. Our main approach to separate between the good parts and the defective ones is based on a classification model trained with synthetic data, covering both the good and the defective parts. This can allow a classification using eigenfrequencies alone. Additional geometric or material a priori information about each specific part may help to improve the classification power, but this is optional and even isolated information about the part structure may add extra value. However, the application of the simulation-based ART training data is not straightforward for real series parts. The synthetic training data have to be representative. This means that they have to cover tolerable and random part variations in geometry or materials, as well as possible defect types or other unacceptable structural conditions, in a realistic manner. This is challenging towards a simulation modeling from a physical view, especially regarding the modeling of real defects. For example, cracks may not only cause a local stiffness reduction, but also result in nonlinear effects. The real defects may also be complicated in their shape and more than one defect per part can occur. We assumed only variations in geometry in this study, but the material properties can also vary from part to part. In this case, the variable material properties must also be considered during the data generation procedure. Moreover, the part-to-part variations or the defect specifications appearing within a series production, including all of the relevant probability distributions, need to be quantitatively known. This is connected with many experimental analyses, if the information is not already known.