## 2 Materials and Methods
### Overview and Further Specifications for the Application Scenario  
The application scenario is focused on the detection of defective connecting rods via ART, under the additional boundary condition that the parts also vary randomly in their geometric dimensions. As the defect to detect, a through-hole with a size between 1 mm and 3 mm was chosen, whereby a part features exactly one single through-hole or none. Multiple holes or other defect types were not allowed. Material variations were avoided as far as possible. A set of 18 eigenfrequencies, being used as the mandatory classification input, and either four or all of the eight geometric dimensions per part, being used as an optional input, formed the basis for each test decision with respect to a defect. To design the application scenario unambiguously and to achieve an appropriate optimization of the classification problem, the scoring of any misclassification, as well as the probabilities of occurrence for the undamaged and defective parts, also had to be taken into account.  
Within a real series production, whether a defective part is overlooked or a good part is mistakenly rejected will usually have different degrees of severity. This can have safety-critical or economic reasons. Our application scenario is fictive and only serves for demonstration. Therefore, we did not specify any additional constraints and remained neutral with regard to the scoring of misclassifications. Any mixing up of the good parts with the defective parts or vice versa by a classification model was seen critically in the same way during the data evaluation. Furthermore, good parts are usually more frequent in a series production. Some of the possible defect types, positions or sizes can also be more likely than others. However, defining specific constraints would have been speculative, especially because finding an allover optimizing classification rule can highly depend on the assumed probabilities of occurrence. Therefore, we once again remained neutral to ensure a balanced quality evaluation. This means that we assumed that the good parts and defective parts would occur with an equal fifty-fifty chance. In the case of damage, each of the defined defect domains should occur with a probability of 1/3. Additionally, within each of these domains, the defect specifications are random and uniformly distributed, with no subdomain being more likely.  
In the end, the application scenario aims at the discrimination of the good parts and the defective ones. For the classification models with multiple defect classes, the assigned defect size or defect position of a classified part was only considered secondarily. Rather, it was primarily evaluated whether a part had been correctly or incorrectly assigned to the good class, or to any defect class at all. In other words, the decisions were mostly retrospectively reduced to a two-class system (good/defective) and then evaluated. The evaluation was completed with the help of TPR (true positive rate) and TNR (true negative rate) [37]. These metrics represent the proportion of the defective parts that are also classified as damaged (TPR) or the proportion of good parts that are also classified as (TNR).