On Digital Twins, Mirrors, and Virtualizations: Frameworks for Model Verification and Validation

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.

On generative models as the basis for digital twins

“…Although the term digital twin has been widely used in many disciplines and in industry sectors, an alternative terminology is used here to make the subsequent analysis more precisely defined. The physical twin (also called the structure and denoted S) has N S different states s ¼ s 1 ,s 2 , …s N S f g(in contrast to Worden et al [2020] where each state refers to a time instant t, the notation here is simplified for convenience and since the problems to be presented here are not dynamic but static). Together with the structural states, the environment E of the structure has N E corresponding states, e ¼ e 1 ,e 2 ,…e N E f g .…”

“…Following Worden et al (2020), definitions are constructed according to the mirror's ability to predict the states s C j . This ability is measured using metrics defined below, and based on this the mirror models can be considered to be either ε-mirrors or α-mirrors.…”

“…where P p C is the probability density function of the quantity of interest. Furthermore, following Worden et al (2020), the definition of a virtualization is provided. Given some context C, a virtualization is defined as the pair,…”

“…The layout of the paper is as follows. In Section 2, mirrors are defined based on the work in Worden et al (2020). In Section 3, details of the GANs and cGANs are given.…”

Towards the Development of an Operational Digital Twin

“…Since its inception, the meaning of the term digital twin has been widely interpreted, and as a result the details of the precise meaning depend on the specific context involved. In terms of asset management (the context of this paper) digital twins have been considered for tasks such as damage detection and structural-health/condition monitoring [4][5][6][7], predictive maintenance [8][9][10][11], and uncertainty quantification [12][13][14]. In this context the key application areas are offshore oil & gas [15,16], offshore wind turbines [17][18][19][20], aerospace [21][22][23] and nuclear fusion [24][25][26].…”