The combination of virtual data, produced by VEs, and real measurements is crucial for the digitalisation of industry and metrology. The aim of WP1 is to specify what is needed in order to evaluate the uncertainty associated with real measurements when using VEs, to assess state‑of‑the‑art uncertainty quantification methods for this purpose, and to carry out their further development. JCGM:GUM‑compliant methods as well as methods based on Bayesian inference will be used. The work will be performed in conjunction with three real‑world applications (tilted‑wave interferometer (TWI), coordinate measuring machine (CMM) and flow measurement (FLOW)).

This work package is structured into four tasks. Task 1.1 will assess state‑of‑the‑art uncertainty quantification methods with respect to the goals of this WP. For this task, a set of 3 benchmark scenarios (TWI, CMM and FLOW) will be developed. In Task 1.2, JCGM:GUM‑compliant uncertainty evaluation methods will be developed, and their performance will be verified using the 3 benchmark scenarios. Task 1.3 will go beyond the techniques pursued in the JCGM:GUM, by applying a Bayesian inference to the combined analysis of the VEs and the measurement data. The statistical models and numerical techniques developed for uncertainty evaluation will again be verified using the 3 benchmark scenarios. Finally, Task 1.4 will apply the resulting methods from Task 1.2 and Task 1.3 to the three real‑world applications TWI, CMM and FLOW. In addition, Task 1.4 will deliver a GPG for the developed methods.

The aim of this work package is to develop a task-specific method to evaluate the measurement uncertainty of DTs. Four DTs of state-of-the-art and industrially relevant measurement systems will be developed along with holistic strategies to evaluate the measurement uncertainty and metrological characteristics of the DTs. The measurement uncertainty will be complemented with a methodological and definition framework to allow it to be scalable, portable and applicable in other case studies.

DTs are a strategic key enabling technology to enable zero defect manufacturing and zero waste within the current interconnected Industry 4.0 framework. The creation of a DT requires complex modelling knowledge and a deep understanding of the system. The quality control system of the DT, which includes the measurement system, is critical to ensuring real-time quality control, in cyber physical systems, for zero defect manufacturing and zero waste. However, the creation of the measurement system’s DT is beyond the state‑of‑the‑art and it is not reported in the literature. The development of a DT of the measurement system (Task 2.1) requires metrological traceability to be established in order to provide end users with trustworthy results. To establish traceability, it is necessary to develop a methodology to estimate the metrological characteristics, e.g. the accuracy, precision and sensitivity of the DT, and the related measurement uncertainty (Task 2.2). The different components of the DT, i.e. the P2V and the V2P connection, the fidelity and the DT parameters must all be included. Moreover, some computation and modelling approaches, i.e. hybrid and data‑driven modelling, may not be suitable for JCGM:GUM‑compliant uncertainty evaluation and may instead require simulation or Bayesian methods to be used. WP2 specifies the requirements and the methodologies needed for the uncertainty evaluation of DTs. A specific objective will be to assess state‑of‑the‑art uncertainty quantification methods. In Task 2.4, further uncertainty quantification approaches will be developed including JCGM:GUM‑compliant, simulation and numeric, and Bayesian inference-based methods. The work will be carried out in conjunction with 4 real‑world applications related to complex measurement systems. The selected applications are: (1) mechanical characterisation using a nano‑instrumented indentation test (nanoindentation), (2) contactless form measurement (cylindricity measurement machine NanoCyl), (3) an optical measurement system integrated on an articulated‑arm robot for dimensional measurements, (4) electrical measurements (high voltage (> 50 kV) for studying the induced currents in electrical power systems, for short circuit withstand tests of a medium voltage electrical cell and the quantum voltage standard). WP2 will create and implement 7 DTs for the 4 applications (Task 2.1) and will report definitions and methods to evaluate the measurement uncertainty and metrological characteristics of the DTs (Task 2.2). The factors that influence the evaluation of the measurement uncertainty will be statistically modelled for the 7 DTs (Task 2.3). These 7 DTs will be used to apply uncertainty evaluation methods to the 7 DT applications and to compare their performance in order to determine the best uncertainty method (if > 1) for each application (Task 2.4).

The aim of this work package is to develop approaches to validate the VEs and DTs of the applications presented in WP1 and WP2, and to develop and validate surrogate models, either to account for errors in the models, or to replace the computationally expensive VE/DT in setups where fast simulation results are required (e.g. CFD). The validation of VEs and DTs is fundamental for their deployment in industry and metrology because it ensures trust in the results that are obtained. Differences between calibrated standards, or measurement data obtained with calibrated instruments, and the corresponding data from the virtual counterpart will be analysed by statistical procedures for the applications presented in WP1 and WP2. A GPG on the validation of VEs and DTs will be developed based on the knowledge acquired in the different applications.

In Task 3.1, the VEs, of the applications presented in WP1, will be validated against measurements obtained with calibrated instruments or against reference materials. In Task 3.2, the DTs, of the applications presented in WP2, will be validated against measurements obtained with calibrated instruments or against reference materials. The validation procedures presented in this task will account for the dynamic behaviour of the DTs. VEs and DTs can be computationally expensive. In situations where fast results are necessary, computationally cheaper models, also known as surrogate models, are used. These surrogate models can be potentially less accurate; hence, the validation and optimisation of such surrogate models is of utmost importance for their use in industry and metrology. Complementary to the validation of the VEs and DTs, this work package aims to develop and validate surrogate models for one VE application from WP1 (FLOW) and for one DT application from WP2 (3D robotic measurement). The surrogate models will then be validated against traceable measurement data, and improved as necessary (Task 3.3).

VEs and DTs have garnered significant interest in all industrial sectors over the last few years as the Internet of Things has become more and more pervasive. It corresponds with the first policy recommendation of the EC which is promoting digital and green transformations. Therefore, the aim of this work package is to apply both the VEs and DTs, which are associated to certified methods for uncertainty estimation, to twelve industrial case studies (five case studies on VEs and seven case studies on DTs). These were selected in close consultation between the participants and potential industrial stakeholders in order to demonstrate the practical application of the developed methods.

The selected industrial case studies cover a large panel of metrological applications, which have been categorised as follows: coordinate measurement (Task 4.1), optical/contactless form measurement (Task 4.2), flow measurement (Task 4.3), robotic 3D scanning system (Task 4.4), nanoindentation measurement (Task 4.5) and electrical measurement (Task 4.6). At present, only one traceable VE solution “Virtual Coordinate Measuring Machine (VCMM)”, which was developed and certified at PTB for tactile CMMs, has been commercialised by Zeiss and Hexagon. The VCMM takes into account three main error sources (geometrical errors, thermal drift errors and mechanical errors), and the estimated uncertainty is based on a classical Monte Carlo simulation. Task 4.7 will summarise the outcomes from applying the VE and DT tools, which were developed in the previous WPs, to the twelve selected case studies. The findings will be documented in a report stating the practical applicability of the implemented solutions for VEs, DTs and uncertainty evaluation methods. This report will be drafted in close collaboration with the industrial participants and stakeholders. Furthermore, online training material will be drafted, which will support the dissemination of the results within the EU’s industrial and metrological communities.