From Digital Twins to Digital Twin Prototypes: Concepts, Formalization, and Applications
Alexander Barbie, Wilhelm Hasselbring
TL;DR
This work tackles the lack of a consensual Digital Twin definition by providing a formal Object-Z specification framework that unifies Physical Twin, Digital Model, Digital Template, Digital Thread, Digital Shadow, Digital Twin, and Digital Twin Prototype. It introduces a three-layer formalization approach (informal, UML-like semi-formal, Object-Z) and demonstrates how continuous twinning supports agile, CI/CD-enabled verification of embedded CPS, including emulated hardware in a Digital Twin Prototype. The authors provide detailed Object-Z schemas for each component, outline how MAPE-K maps to digital thread and twin architectures, and illustrate practical applications through ocean-observation and smart-farming field studies with open-source replication. The results show that digital twins, especially via DTP and emulation, can reduce hardware costs, accelerate development, and enable automated integration testing while preserving fidelity across life-cycle stages. Overall, the paper advances a rigorous, reproducible foundation for Digital Twins in Industry 4.0 and highlights avenues for broader adoption and extension in embedded systems engineering.
Abstract
The transformation to Industry 4.0 also transforms the processes of how we develop intelligent manufacturing production systems. To advance the software development of these new (embedded) software systems, digital twins may be employed. However, there is no consensual definition of what a digital twin is. In this paper, we give an overview of the current state of the digital twin concept and formalize the digital twin concept using the Object-Z notation. This formalization includes the concepts of physical twins, digital models, digital templates, digital threads, digital shadows, digital twins, and digital twin prototypes. The relationships between all these concepts are visualized as UML class diagrams. Our digital twin prototype (DTP) approach supports engineers during the development and automated testing of complex embedded software systems. This approach enable engineers to test embedded software systems in a virtual context, without the need of a connection to a physical object. In continuous integration / continuous deployment pipelines such digital twin prototypes can be used for automated integration testing and, thus, allow for an agile verification and validation process. In this paper, we demonstrate and report on how to apply and implement a digital twin by the example of two real-world field studies (ocean observation systems and smart farming). For independent replication and extension of our approach by other researchers, we provide a lab study published open source on GitHub.