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.

翻译：向工业4.0的转型也改变了我们开发智能制造生产系统的流程。为推进这些新型（嵌入式）软件系统的软件开发，数字孪生技术可被采用。然而，目前对数字孪生的定义尚未达成共识。本文概述了数字孪生概念的当前发展状况，并采用Object-Z符号对数字孪生概念进行了形式化定义。该形式化体系包含物理孪生、数字模型、数字模板、数字线程、数字阴影、数字孪生及数字孪生原型等概念。所有概念间的关系均以UML类图形式可视化呈现。我们的数字孪生原型（DTP）方法可在复杂嵌入式软件系统的开发与自动化测试过程中为工程师提供支持。该方法使工程师能够在虚拟环境中测试嵌入式软件系统，无需连接物理对象。在持续集成/持续部署流水线中，此类数字孪生原型可用于自动化集成测试，从而支持敏捷验证与确认流程。本文通过两个真实场景的现场研究（海洋观测系统与智慧农业）案例，展示并报告了如何应用与实现数字孪生。为便于其他研究者独立复现和扩展我们的方法，我们还提供了在GitHub上开源发布的实验室研究。