# Digital Twin-Enabled Decision Support Services in Industrial Ecosystems
## 4 Results
### A Semantic Modeling Approach for Integrating Digital Twins  
As shown in Figure 6, a real semantic modeling tool chain is proposed to support digital twin integration across the product lifecycle. An architecture modeling tool MetaGraph 2.0 is used to develop architecture models for managing the complexity of the digital twins using a model-based systems engineering approach [43]. Through different models, architectural views of different digital twins are described using KARMA language. Then through the GOPPRRE (Graph-object-relationship-role-point-property) ontology transformer, a GOPPRRE ontology model is generated. Then a model in the software suite AnyLogic is generated from the ontology model using a model transformer. Through this approach, the complexity of digital twins is formalized through a unified formalism and simulation models can be implemented automatically through ontology models. Figure 5: Semantic modeling for digital twins. The GOPPRRE ontology refers to a unified MBSE (model-based systems engineering) ontology based on a basic MBSE formalism developed in [43]. The ontology entities and their topology were developed based on a M0-M3 modeling framework whose class and object properties are shown in Table 1. The ontology entity enables the representation of a model structure as shown in Figure 7. From the model topology, the graph individual is defined as a model to represent model compositions and the connections between them. Within one graph individual (model structure), object individuals are defined to represent model compositions. Relationship individuals are defined to represent connections between object individuals. Each relationship individual has two role individuals representing the two ends of the relationship individual. The point individuals are defined as the port for each object individual. In order to formalize the connection between object individual1 and object individual2 through relationship individu1, two connector individuals are defined to bind role individual, relationship relationship individual, and point individual. All the non-property individuals have their own property individuals to define their attributes. \begin{table}
\begin{tabular}{p{142.3 pt} p{142.3 pt}} \hline \hline
**Class** & \\ \hline connector & its subclass defines the connection rule between one role, relationship, and object in one end of each connection. \\ graph & its subclass refers to a metamodel representing model topology. \\ object & its subclass refers to a metamodel representing model composition. \\ relationship & its subclass refers to a metamodel representing a connection between model compositions. \\ role & its subclass refers to a metamodel representing one end of a connection between model compositions \\ point & its subclass refers to a metamodel representing a point in each model composition. \\ property & its subclass refers to an attribute for developing other metamodels. \\ language & its subclass refers to a language constructed by other metamodels. \\ \hline Object property & \\ \hline binding & \begin{tabular}{l} Defines the connector individuals between point individual or object individual and role individual in connector individuals. \\ \end{tabular} \\ has Property & \begin{tabular}{l} Represents the non-property metamodel individuals having a property individual referring to an attribute. \\ \end{tabular} \\ including & \begin{tabular}{l} Defines the containment from a graph individual (model) to its compositions (object individuals) and relationship individuals. \\ \end{tabular} \\ link & \
\begin{tabular}{l} Defines the relationship individual and its two role individuals. \\ \end{tabular} \\ mapping &
\begin{tabular}{l} Defines the decomposition and exploration between object individual and graph individual. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ontology class and object property. Figure 6: Ontology models for digital twins integration.