Chapter 34 On Digital Twins, Mirrors and Virtualisations K. Worden, E. J. Cross, P. Gardner, R. J. Barthorpe, and D. J. Wagg Abstract A powerful new idea in the computational representation of structures is that of thedigital twin. The concept of the digital twin emerged and developed over the last two decades, 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, how they are validated, and how validation information can be transferred between models. The current paper will outline the basic ingredients of such a theory, based on the introduction of two new concepts: mirrors andvirtualisations. 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. Keywords Digital twins · Mirrors · Virtualisations · Verification and validation (V&V) 34.1 Introduction The digital twin has emerged in the last two decades as a highly sought-after generalisation of the computational models routinely used by industry and academia in attempts to understand the behaviour of real structures, systems and processes and to make predictions in previously unseen circumstances [1–3]. There is currently no real concensus on what the necessary and sufficient ingredients of a digital twin are, although a sister paper to this one [4] will attempt to bring some order to the subject. What is inarguable, is that because the digital twin extends the concept of a computational model, such a model must be a core ingredient. Furthermore the model must be validated; it must be demonstrated to be in correspondence with reality, at least in the context of immediate engineering importance. Because of the problems which a digital twin will be required to address, it will also potentially need to extrapolate or generalise to predictions on different structures or the same structure in different contexts. This paper will argue that, in order to ensure the correct operation of digital twins, a mathematical framework is needed in order to quantify the likely fidelity of validated models when used to generalise or extrapolate. This paper will propose that what is needed is a type of algebraof models, which can be used in order to extend current concepts of verification and validation (V&V). For the purposes of this paper, the fundamental problem of V&V will be regarded as the need to answer two questions: 1. What is the lowest-cost model that will allow predictions of the required accuracy for the structure of interest in the context of interest? 2. What is the lowest-cost programme of experimental testing that will validate the model with prescribed confidence? Note that in answering these questions, one does not need a model that represents the whole structure across its entire range of possible behaviours; one only needs a model that matches in the context of interest.1 In a machine learning context, 1Some would argue that a true ‘digital twin’ has to match the structure of interest in all contexts. This viewpoint does not make complete sense, as the physics of a given structure is unlikely to be known at all scales and in all contexts; this means that modelling would not be possible. K.Worden ( ) · E. J. Cross · P. Gardner · R. J. Barthorpe · D. J. Wagg Dynamics Research Group, Department of Mechanical Engineering, University of Sheffield, Sheffield, UK e-mail: k.worden@sheffield.ac.uk © Society for Experimental Mechanics, Inc. 2020 R. Barthorpe (ed.), Model Validation and Uncertainty Quantification, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series, https://doi.org/10.1007/978-3-030-12075-7_34 285
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