## 3 Digital Twin Framework for Geometry Assurance  
The digitization of manufacturing is increasing. In the manufacturing business, 68% of the companies in a recent study stated that digital manufacturing is a top priority [11]. The number was even higher in countries such as India (94%) and China (87%). It is, however, also reported that the expected benefits are perhaps not yet fully reached. In the context of Industry 4.0, digitals twins are seen as one of the top ten technology strategic trends, according to Gartner Research [12], and various potential applications of digital twins along the product life-cycle have been identified [13, 14].  
A digital twin is a digital replica of a physical entity. In manufacturing, the terms digital model, digital shadow, and digital twin are used to indicate different levels of data exchange [15]. A digital model is a digital representation of a physical part or assembly without data exchange, a digital shadow  
Figure 3: Responses filtered based on the affiliations of the respondents. Significant differences, using \(\alpha=0.10\), are encircled.  
enables a one-way data flow between the physical and virtual representations of an object, while a digital twin allows for a bi-directional automatic data exchange between the physical and virtual representation. In this regard, different reference models for digital twins have been proposed, such as in [16], considering important properties, such as model scalability, interoperability, expansibility, and fidelity. Most likely, a family of digital twins is needed to achieve optimized products and production flow, where each twin has its own purpose. The digital twins must represent both the product and the production system. As stated in [17], multi-scale analyses and distributed decisions will be required for optimizing the activities on the shop floor, as well as processes, resources, and machines. In many cases, digital twins will be interlinked. For example, the digital twin for geometry assurance described below must be linked to twins controlling the assembly cell equipment.  
For the geometry assurance application, a digital twin approach was presented by [PERSON] et al. [3]. This approach is also adopted in this paper. It was suggested that the simulation models, used in the design phases, can be reused and fed with inspection data during full production to do real-time individualized optimization of the assembly process to reach high-quality products. In Figure 4, an overview of the idea can be seen.  
The idea is that two parts, A and B, are inspected using, for example, 3D scanning. This data is fed into the simulation model, which constitutes the kernel of the digital twin, to match individual parts over a batch of parts to minimize the geometrical deviation and variation of the assembly of A/B. This is also referred to as selective assembly [18]. Furthermore, the joining process can be optimized with respect to geometrical quality. Locators can be adjusted [19], and spot welding sequences can be optimized [20] for each individual assembly. By those suggested adjustments, the geometrical quality of the assembly can be improved without changing the tolerances of the parts, which is beneficial from a cost perspective.  
With this approach, studies on several industrial cases have shown that the variation of the final subassembly can be reduced up to 50%, compared to when no adjustments are done [18; 19; 20].  
With the labeling digital model, digital shadow, and digital twin mentioned at the beginning of this section, a digital twin for geometry assurance can be interpreted as:  
1. a digital model, containing all nominal information about parts and assembly and joining processes. The model must also provide simulation capabilities.
2. input to the digital model about deviations from nominal values on the part and process levels.
3. output from the digital model to adjust the assembly and joining processes.  
Those three pillars constitute together a digital twin.