Abstract
Abstract 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.
Highlights
The digital twin has emerged in the last two decades as a highly sought-after generalisation of the computation 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 [1,2,3]
Such a theory would be invaluable in the design and construction of digital twins, because one of the main uses of digital twins will be to make predictions in circumstances where their core models have not been explicitly validated, and it will be critical to obtain estimates of how much models can be trusted when they are used to extrapolate or generalise i.e. when they are used to make inferences about different structures or in different contexts
As discussed in the introduction, there are already attempts to define a unifying framework for model calibration and validation
Summary
The digital twin has emerged in the last two decades as a highly sought-after generalisation of the computation 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 [1,2,3]. The interrogator is allowed to present the oracle with a set of schedules eCW from some given context, and the oracle is required to return either the test responses of the structure rCW , or simulations from the model mCW 7. A computer model M may be established as an ε-mirror for some context C1, given some measured response rC1 (t) from the physical structure S. This in turn could be inferred from multiple perfect joint models that may have been validated for different geometry and boundary condition scenarios, the idea being that the mapping for a perfect joint can be learnt from this set If this is the case the three models could be used as source data in order to obtain the target deflections for the encastrebeam. A mapping would be inferred for the updated model design, again providing an estimated bound on ε′
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