## 3 Results  
### Simulation-Based ART Training Data Generation  
The first step of our application scenario demonstration covered the generation of the ART training data based on simulation techniques (see Figure 1). The training data generation included FEM simulations of connecting rods, but also further partial steps that aimed to enhance the amount of simulation data and to adapt it to measurement data. The geometric dimensions of 5000 virtual training parts were described with random numbers. Contrary to the basic population, uniform distribution was chosen for the virtual training parts. This ensured that no subrange of the training data was more common. The uniform distribution interval borders were set to the mean values plus or minus 4.5 times the standard deviations of the basic population. Since the essential values of the basic population differed by a maximum of three standard deviations from the respective mean values, by 50% increased ranges were assigned for the virtual training parts. This scaling ensured that the training data confidently covered the geometries of the machine-made parts (or of any of the basic population parts subjected to a defect detection). The structure-dependent eigenfrequencies of the virtual training parts with respect to Mode-1 to Mode-18 were calculated by FEM. The simulations were initially performed without any defect. Afterwards, the simulations were repeated three times, assuming again 5000 virtual parts each time with the same individual geometric dimensions as before, but considering a through-hole defect either in one of the two cylinder rings or in the bar area. This entire set featured defective parts with a 2 mm through-hole appearing uniformly, and randomly distributed within the defined defect domains. As an output, we obtained the geometric data and eigenfrequencies of 5000 defect-free virtual trainings parts and the corresponding data for the geometrically same parts, but with a randomly positioned 2 mm defect within one of the cylinder rings or the bar area. To achieve a suitable ART defect detection, the training data generation had to take into account that the eigenfrequencies of a defective part depend, in a nearly quadratic manner, on the defect diameter. However, performing further FEM simulations assuming many other defect sizes would have resulted in a large computational effort. To counteract this and to enhance the data effectively, we took advantage of the recognized defect size behavior and the fact that the geometric dimensions of the defect-free training parts were used again for the FEM simulations including a 2 mm defect. The eigenfrequency deviations from the defective to the good parts were calculated. These deviations can be seen as the isolated impacts of a randomly positioned 2 mm defect in each case. We scaled these defect impacts by using the quadratic dependence from the defect diameter. For example, a 1 mm defect causes approx. one quarter of the impact of a 2 mm defect at the same position. In this way, the defect impacts from 0.8 mm to 3.6 mm with an increment of 0.1 mm were derived (since the aim is the detection of any defects from 1 mm to 3 mm in size, 20% smaller or larger values were chosen). Finally, the impacts of the scaled defects were added to the eigenfrequencies of the 5000 defect-free parts for each defect size, resulting in a much more extensive data set. If we had generated all of the data directly with FEM and not enhanced them, we would have had to perform 440,000 calculations instead of 20,000 FEM calculations (5000 good parts + 3 \(\times\) 5000 defective parts \(\times\) 29 defect sizes). Since the simulation-based data differed from the measured data due to many simplifications or inaccurate assumptions, as discussed extensively within our previous publication, the synthetic data set had to be adapted to the measurement data. The five machine-madereference parts were taken into account for this. Their associated FEM-calculated eigenfrequencies were evaluated versus the frequencies that were measured by ART.