Towards the Development of an Operational Digital Twin
Abstract
:1. Introduction
 Models: computational models based on physical reasoning;
 Data: both quantitive and qualitative sets of information from the physical twin;
 Knowledge: both indepth expert understanding and context specific detail;
 Connectivity: time evolving digital and organisational interactions that are free from significant interruptions or other barriers.
2. Overview of the Digital Twin
2.1. Experimental Data
2.2. Initial Validated Model
 1.
 What does a digital twin do when predictive performance is poor?
 2.
 How does a digital twin account for missing physics?
 3.
 How does a digital twin learn new physics?
 4.
 What is the impact on the control of the structure?
2.3. Proposed Digital Twin Model Structure
 Recalibrate the physicsbased model: improve estimates of the model parameters.
 Update the databased component: improve modelling of unknown physics.
 Addition of more physics: add new identified physics into the physicsbased model.
 Do nothing.
3. The Problem of Model Updating
4. DataAugmented Modelling
4.1. Gaussian Process Regression
4.2. DataBased Model Component
4.3. Active Learning Approach
Algorithm 1 Active learning for databased component of a digital twin 

4.4. Autonomous Decision Making: Challenges and Limitations
5. Identifying Physics through Hybrid Testing
6. Impact of a Digital Twin on Active Control
7. Discussion
8. Conclusions
Author Contributions
Funding
Conflicts of Interest
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Masses, m  Damping Coefficients, c  Stiffness Coefficients, k  Signal Noises, ${\mathit{\sigma}}_{\mathit{n}}^{2}$  

kg  Ns/m  N/m  (g/N) ^{2}  
$\mu $  $\{5.200,5.200,5.200\}$  $\{4.605,4.605,4.605\}$  $\{4021,4021,4021\}$  $\{1.022,0.359,1.004\}$ 
${\sigma}^{2}$  $\{0.5,0.5,0.5\}$  $\{1,1,1\}$  $\{10,000,10,000,10,000\}$  $\{0.1,0.1,0.1\}$ 
${\mathit{\theta}}_{\mathcal{D}1}^{MAP}$  $\{4.908,5.577,5.187\}$  $\{3.307,0.002,{0.000}^{\ast}\}$  $\{4051,4320,4964\}$  $\{0.006,0.106,0.031\}$ 
${\mathit{\theta}}_{\mathcal{D}3}^{MAP}$  $\{5.187,5.281,5.292\}$  $\{0.198,{0.000}^{\u2020},{0.000}^{\u2020}\}$  $\{4263,4332,5263\}$  $\{0.223,0.281,0.165\}$ 
Dataset  Uniform  Fixed  ${\mathbf{f}}_{\mathbf{f}}=1$  ${\mathbf{f}}_{\mathbf{f}}=0.999$  ${\mathbf{f}}_{\mathbf{f}}=0.99$  ${\mathbf{f}}_{\mathbf{f}}=0.9$ 

One  18  69  11  14  17  40 
Two  21  16  21  18  37  71 
Three  21  280  98  115  106  135 
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Gardner, P.; Dal Borgo, M.; Ruffini, V.; Hughes, A.J.; Zhu, Y.; Wagg, D.J. Towards the Development of an Operational Digital Twin. Vibration 2020, 3, 235265. https://doi.org/10.3390/vibration3030018
Gardner P, Dal Borgo M, Ruffini V, Hughes AJ, Zhu Y, Wagg DJ. Towards the Development of an Operational Digital Twin. Vibration. 2020; 3(3):235265. https://doi.org/10.3390/vibration3030018
Chicago/Turabian StyleGardner, Paul, Mattia Dal Borgo, Valentina Ruffini, Aidan J. Hughes, Yichen Zhu, and David J. Wagg. 2020. "Towards the Development of an Operational Digital Twin" Vibration 3, no. 3: 235265. https://doi.org/10.3390/vibration3030018