## 2 Part Type, Machine-Made Parts and Experimental Characterizations  
For the study, connecting rods were selected. This model-like part type is shown in Figure 1. If symmetrical with respect to the \(x\)-\(y\) as well as the \(x\)-\(z\) plane but without further restrictions, the geometry can be quantified with 10 independent geometric parameters. Both rotationally symmetrical cylinder rings are described with the inner diameter \(d_{\text{R1}}\) or \(d_{\text{R2}}\), the outer diameter \(D_{\text{R1}}\) or \(D_{\text{R2}}\) and the height \(h_{\text{R1}}\) or \(h_{\text{R2}}\), respectively. The cuboidal bar area is defined by the width \(w_{\text{B}}\) and the height \(h_{\text{B}}\). The length of the bar is fixed via \(l_{\text{R}}\), which is the distance between the cylinder rings' axes. There are also four edge fillets, which have the unique radius \(r\). The material is chosen to be homogeneous with linear-elastic behavior. Thus, assuming low damping, each connecting rod is a mechanically deformable, vibrational system, which is characterized by typical vibration modes, that is, eigenmodes, and associated eigenfrequencies depending on its exact component structure. With the defined geometric model, we generated numerous specific parts, namely thousands of virtual parts as well as real machine-made parts. The virtual parts exist as computer models. Within the investigations, they were used as separate, independent objects of investigation or served as digital twins of the real parts. An important factor for the demonstration within this work are purposefully given part-to-part variations regarding the exact geometric dimensions. An identical but component-specific value \(h_{\text{R}}\) for the two cylinder ring heights \(h_{\text{R1}}\) and \(h_{\text{R2}}\), as well as a constant value of 3 mm for the edge radii were specified. Thus, only 8 individual geometric dimensions were used for initial geometric generation of the virtual parts. In the same way, each real part was produced according to an individual set of 8 specified parameters. By default, unless otherwise specified,a consistent geometric model using also 8 individually updated geometric dimensions according to measurement data was selected as a virtual representation of each real part. Stochastically independent, either normally or uniformly distributed, random variables or random numbers were used for describing small geometric variations from part to part. To create suitable random numbers corresponding to the 8 geometric parameters, Table 1 was taken into account. In case of normal distribution, the mean value corresponds to the expected value and the scatter value corresponds to the standard deviation of the random variable, respectively. For a normal distribution, approximately 99.73% and thus almost all values deviate by a maximum of three standard deviations from the expected value. Therefore, the interval borders of the corresponding uniform distribution were set to the mean value plus or minus three times the scatter value. This rule, together with the chosen scatter values as given in Table 1, describes linear geometrical dimensions or essential value ranges that are usually covered by the accuracy class _c (coarse)_ or _v (very coarse)_ of the general tolerances according to DIN ISO 2768, compare Reference [33]. Such variations in geometry are considered still realistic, especially in the case of unfinished blanks from a forging or casting process. The eigenfrequencies and eigenmodes of the virtual parts were assessed numerically with the FEM software _COMSOL Multiphysics_ (basic software functionality and Structural Mechanics Module, software version 5.2a) supposing perfect linearity. Thereby, quadratic 3D tetrahedral elements with a maximum size of 1.1 mm were used, damping effects were ignored, and each part was chosen to be completely free.