## 1 Introduction
There are many of basic studies regarding simple bodies and their natural vibrations in case of more or less strongly idealized structural defects or the inverse defect detection, for example, References [24; 25; 26]. Other works deal with the inverse quantitative conclusion on the material properties of geometrically defined samples by analyzing their natural vibration characteristics, for example, References [19; 27; 28]. However, practical effects like random component variations or metrological relevant perturbations are usually ignored and only simple geometries are considered. In contrast to other studies, the presented work understands ART as a NDT procedure for geometrically more complicated and practice-relevant serial parts and therefore takes aspects like tolerable component variations into account. Finite element method (FEM) as a widespread simulation technique can help with general understanding and evaluation of a components natural vibration behavior, for performing sensitivity analyses regarding geometry or material properties, or to analyze the influences caused by defects [8; 21]. A quantitative good match of FEM results compared to ART measured frequencies can, in principle, be reached by FEM calculations if the component's geometry and material properties are sufficiently known [20]. A few publications deal with the effects to the resonance spectra caused by defects or due to small tolerable component variations [22; 29]. Some ideas for the algorithmic differentiation between those effects are described. FEM data were used for demonstration. Some further publications deal with the influences caused by structural defects or stiffness changes as a function of the position. Corresponding correlations represented by FEM data were used to draw conclusions about the type and position of a defect on the basis of a given set of eigenfrequencies [30; 31; 32]. Within these studies, exclusively numerically calculated frequencies were used for the investigations. This study focuses on the simulation-based generation of representative and valid ART training data. This means that the work counteracts the challenges connected with the conventional and purely experimental generation of ART training data, as mentioned in several publications like References [20; 30; 31; 32] and which is a limiting factor for the method. The benefit of FEM for estimating the effects of component variations and defects even in a quantitative satisfying manner, as noted in References [8; 20; 21], indicates the principle possibility of a simulation-based generation of synthetic ART training data. Aspects like the distinction between the influences of defects from those of tolerable variations, which is addressed in References [22; 29], or the inverse detection of defects including different positions, which is mentioned in References [30; 31; 32], are relevant points. They could also be considered within a generation of synthetic ART training data if necessary for a specific application. However, the mentioned works from other authors used simulation data for demonstrating their approaches and the authors point out that further research is needed, for example, regarding effects like random part variations, the purposeful use of simulation data, and other practice-relevant effects. Therefore, our approach is not only described in detail or discussed theoretically. It is also verified by means of manufactured parts and measured data, as there is no concept or demonstration of a simulation-based ART training data generation within literature. Regarding our idea in general, ART training data have to be representative and valid to reach meaningful and trustful ART results. This means that the data should represent the natural vibration behavior for a considered part type in a quantitative, realistic way. The data should reflect effects like random geometric or material variations, which occur from part to part within a series production. Furthermore, a synthetic data set should cover reality precisely without gaps.