## 2 Materials and Methods  
### Part Type and Random Geometric Part-to-Part Variations  
Connecting rods were selected as the exemplary parts. Figure 2 visualizes the geometry of this model-like part type. Since each part is symmetrical with respect to the \(x\)-\(y\)-plane and the \(x\)-\(z\)-plane, the geometry can essentially be quantified with eight geometric parameters. The parameters \(d_{\text{R1}}\) and \(d_{\text{R2}}\) or \(D_{\text{R1}}\) and \(D_{\text{R2}}\) describe the inner or the outer diameters of the rotationally symmetrical cylinder rings, respectively. The two cylinder ring heights are  
Figure 1: Overview of our strategy including a simulation-based ART training data generation and the subsequent training procedure aiming to build a specific ART sorting algorithm.  
identical and indicated with \(h_{\text{R}}\). The bar area has a cuboidal shape with the width \(w_{\text{B}}\) and the height \(h_{\text{B}}\). The bar length is set via \(l_{\text{R}}\), which is the distance between the cylinder ring axes. There are additional edge fillets with a constant radius of 3 mm.  
Random part-to-part variations in geometry are relevant when using ART. To describe such variations, normal distribution was chosen. Each of the eight geometric parameters was connected with a stochastically independent normally distributed random variable, which itself is quantified by a mean value and a standard deviation. The defined mean values and standard deviations are also shown in Figure 2. We use the term _basic population_ in this manuscript to indicate a random population of connecting rods, whose geometry varies normally distributed with respect to the values given in Figure 2.  
Approximately 99.73%, and thus almost all of the possible values, of a normally distributed random variable deviate no more than three standard deviations from the mean value. Having regard to this, the essential geometric ranges of the basic population are covered by the accuracy class \(c\) (_coarse_) or at least \(v\) (_very coarse_) of the general tolerances, according to DIN ISO 2768, see [35]. This means that such variations are large, but still realistic, especially for unfinished blanks produced with a forging or casting process.  
Besides the basic population, some populations with other probability distributions (scaled normal distributions, uniform distributions) were defined. All of the random parts, either virtual parts that only exist as computer models or machine-made parts that are produced according to given nominal dimensions, were specified with independent random numbers. These numbers were created with the MATLAB(r) functions normrnd (normal distribution) and unifrnd (uniform distribution). Often, the same sets of random numbers were used multiple times, for example, to achieve batches of parts with identical geometries, but different defect specifications. This was realized by controlling the random number generator via the function rng, in combination with specific seed values.  
In addition to the parts with random dimensions, a geometrically non-random connecting rod, called _geometrically mean part_, was defined as a reference. The geometric dimensions of this part are the mean values shown in Figure 2.  
The connecting rod material was chosen to be homogeneous and constant with isotropic elastic properties, as far as technically possible for the machine-made parts.