This paper presents a review of the state of the art for digital twins in the application domain of engineering dynamics. The focus on applications in dynamics is because: (i) they offer some of the most challenging aspects of creating an effective digital twin, and (ii) they are relevant to important industrial applications such as energy generation and transport systems. The history of the digital twin is discussed first, along with a review of the associated literature; the process of synthesizing a digital twin is then considered, including definition of the aims and objectives of the digital twin. An example of the asset management phase for a wind turbine is included in order to demonstrate how the synthesis process might be applied in practice. In order to illustrate modeling issues arising in the construction of a digital twin, a detailed case study is presented, based on a physical twin, which is a small-scale three-story structure. This case study shows the progression toward a digital twin highlighting key processes including system identification, data-augmented modeling, and verification and validation. Finally, a discussion of some open research problems and technological challenges is given, including workflow, joints, uncertainty management, and the quantification of trust. In a companion paper, as part of this special issue, a mathematical framework for digital twin applications is developed, and together the authors believe this represents a firm framework for developing digital twin applications in the area of engineering dynamics.

A powerful new idea in the computational representation of structures is that of the digital twin. The concept of the digital twin emerged and developed over the last decade, and has been identified by many industries as a highly desired technology. The current situation is that individual companies often have their own definitions of a digital twin, and no clear consensus has emerged. In particular, there is no current mathematical formulation of a digital twin. A companion paper to the current one will attempt to present the essential components of the desired formulation. One of those components is identified as a rigorous representation theory of models; most importantly, governing how they are verified and validated, and how validation information can be transferred between models. Unlike its companion, which does not attempt detailed specification of any twin components, this paper will attempt to outline a rigorous representation theory of models, based on the introduction of two new concepts: mirrors and virtualizations. The paper is not intended as a passive wish list; it is intended as a rallying call. The new theory will require the active participation of researchers across a number of domains including: pure and applied mathematics, physics, computer science, and engineering. The paper outlines the main objects of the theory and gives examples of the sort of theorems and hypotheses that might be proved in the new framework.