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Metrology
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Virtual Measuring Systems and Digital Twins
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Virtual Measuring Systems and Digital Twins

A special issue of Metrology (ISSN 2673-8244).

Deadline for manuscript submissions: closed (30 April 2022) | Viewed by 18396

Special Issue Editors

Dr. Sascha Eichstädt

E-Mail Website
Guest Editor
Physikalisch-Technische Bundesanstalt, Abbestr, 2-12, 10587 Berlin, Germany
Interests: metrology for heterogeneous sensor networks; uncertainty in sensor fusion; uncertainty sensor models; digitalisation in metrology; Internet of Things
Prof. Dr. Markus Bär

E-Mail Website
Guest Editor
Department of Mathematical Modelling and Data Analysis, Physikalisch-Technische Bundesanstalt, Abbestr. 2 - 12, 10587 Berlin, Germany
Interests: modelling, simulation and data analysis in metrology; uncertainty quantification; inverse problems; virtual experiments/digital twins; machine learning; complex systems; fluid dynamics; computational optics; biological physics; active matter
Dr. Karin Kniel

E-Mail Website
Guest Editor
Department of Coordinate Metrology, Physikalisch-Technische Bundesanstalt (PTB), 38116 Braunschweig, Germany
Interests: advanced manufacturing; digitalization in coordinate metrology; simulation-based uncertainty determination; digital twin applications; numerical standards; software verification

Special Issue Information

Dear Colleagues,

In the course of the digital transformation, the importance of mathematical–physical simulations and in silico experiments is increasing rapidly. If real measuring equipment and measurements are simulated with such simulations, this can be called a “virtual measuring device” or “virtual measurement”. In many areas, these are now in everyday use. For example, simulations serve to gain a better understanding of the real experiment, to plan new experiments or to evaluate existing ones. In the meantime, simulations are increasingly being used as an essential component of a real measurement, usually as part of an inverse problem.

In this development, the task of metrology is to secure confidence in simulation results when they are used in the same way as or combined with real measurements. From the point of view of metrology, this results in several overriding questions:

  1. How to ensure confidence in simulation results
  2. How to establish comparability of virtual and real measurements
  3. Which standards for interfaces, metadata and data formats are necessary

Treatment of these issues requires continuous and intensive interdisciplinary cooperation in addressing simulations, virtual experiments, digital twins, software architectures, validation, calibration, machine learning, and artificial intelligence methods.

This Special Issue is related to the VirtMet Workshop 2021. In addition to VirtMet Workshop 2021 papers, other independent submissions are also welcome.

Dr. Sascha Eichstädt
Prof. Dr. Markus Bär
Dr. Karin Kniel
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Metrology is an international peer-reviewed open access quarterly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • simulation
  • digital twin
  • virtual measurement
  • uncertainty
  • machine learning
  • software
  • calibration
  • validation

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Published Papers (5 papers)

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Research

28 pages, 1668 KiB  
Article
Global Sensitivity Analysis and Uncertainty Quantification for Simulated Atrial Electrocardiograms
by Benjamin Winkler, Claudia Nagel, Nando Farchmin, Sebastian Heidenreich, Axel Loewe, Olaf Dössel and Markus Bär
Metrology 2023, 3(1), 1-28; https://doi.org/10.3390/metrology3010001 - 26 Dec 2022
Cited by 5 | Viewed by 2771
Abstract
The numerical modeling of cardiac electrophysiology has reached a mature and advanced state that allows for quantitative modeling of many clinically relevant processes. As a result, complex computational tasks such as the creation of a variety of electrocardiograms (ECGs) from virtual cohorts of [...] Read more.
The numerical modeling of cardiac electrophysiology has reached a mature and advanced state that allows for quantitative modeling of many clinically relevant processes. As a result, complex computational tasks such as the creation of a variety of electrocardiograms (ECGs) from virtual cohorts of models representing biological variation are within reach. This requires a correct representation of the variability of a population by suitable distributions of a number of input parameters. Hence, the assessment of the dependence and variation of model outputs by sensitivity analysis and uncertainty quantification become crucial. Since the standard metrological approach of using Monte–Carlo simulations is computationally prohibitive, we use a nonintrusive polynomial chaos-based approximation of the forward model used for obtaining the atrial contribution to a realistic electrocardiogram. The surrogate increases the speed of computations for varying parameters by orders of magnitude and thereby greatly enhances the versatility of uncertainty quantification. It further allows for the quantification of parameter influences via Sobol indices for the time series of 12 lead ECGs and provides bounds for the accuracy of the obtained sensitivities derived from an estimation of the surrogate approximation error. Thus, it is capable of supporting and improving the creation of synthetic databases of ECGs from a virtual cohort mapping a representative sample of the human population based on physiologically and anatomically realistic three-dimensional models. Full article
(This article belongs to the Special Issue Virtual Measuring Systems and Digital Twins)
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25 pages, 1972 KiB  
Article
Simulation Uncertainty for a Virtual Ultrasonic Flow Meter
by Martin Straka, Andreas Weissenbrunner, Christian Koglin, Christian Höhne and Sonja Schmelter
Metrology 2022, 2(3), 335-359; https://doi.org/10.3390/metrology2030021 - 18 Jul 2022
Cited by 6 | Viewed by 4294
Abstract
Ultrasonic clamp-on meters have become an established technology for non-invasive flow measurements. Under disturbed flow conditions, their measurement values must be adjusted with corresponding fluid mechanical calibration factors. Due to the variety of flow disturbances and installation positions, the experimental determination of these [...] Read more.
Ultrasonic clamp-on meters have become an established technology for non-invasive flow measurements. Under disturbed flow conditions, their measurement values must be adjusted with corresponding fluid mechanical calibration factors. Due to the variety of flow disturbances and installation positions, the experimental determination of these factors often needs to be complemented by computational fluid dynamics (CFD) simulations. From a metrological perspective, substituting experiments with simulation results raises the question of how confidence in a so-called virtual measurement can be ensured. While there are well-established methods to estimate errors in CFD predictions in general, strategies to meet metrological requirements for CFD-based virtual meters have yet to be developed. In this paper, a framework for assessing the overall uncertainty of a virtual flow meter is proposed. In analogy to the evaluation of measurement uncertainty, the approach is based on the utilization of an expanded simulation uncertainty representing the entirety of the computational domain. The study was conducted using the example of an ultrasonic clamp-on meter downstream of a double bend out-of-plane. Nevertheless, the proposed method applies to other flow disturbances and different types of virtual meters. The comparison between laboratory experiments and simulation results with different turbulence modeling approaches demonstrates a clear superiority of hybrid RANS-LES models over the industry standard RANS. With an expanded simulation uncertainty of 1.44 × 10−2, the virtual measurement obtained with a hybrid model allows for a continuous determination of calibration factors applicable to the relevant mounting positions of a real meter at a satisfactory level of confidence. Full article
(This article belongs to the Special Issue Virtual Measuring Systems and Digital Twins)
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9 pages, 1363 KiB  
Article
Impact of Imperfect Artefacts and the Modus Operandi on Uncertainty Quantification Using Virtual Instruments
by Gertjan Kok, Gerd Wübbeler and Clemens Elster
Metrology 2022, 2(2), 311-319; https://doi.org/10.3390/metrology2020019 - 12 Jun 2022
Cited by 3 | Viewed by 2046
Abstract
The usage of virtual instruments (VIs) to analyze measurements and calculate uncertainties is increasing. Well-known examples are virtual coordinate measurement machines (VCMMs) which are often used and even commercially offered to assess measurement uncertainties of CMMs. A more recent usage of the VI [...] Read more.
The usage of virtual instruments (VIs) to analyze measurements and calculate uncertainties is increasing. Well-known examples are virtual coordinate measurement machines (VCMMs) which are often used and even commercially offered to assess measurement uncertainties of CMMs. A more recent usage of the VI concept is posed by the modeling of scatterometers. These VIs can be used to assess the measurement uncertainty after the measurement has been performed based on the real measurement data or prior to the measurement to predict the measurement uncertainty using a type of simulated measurement data. The research question addressed in this paper is to assess if this predicted uncertainty will be similar in magnitude to the calculated uncertainty based on the measurement data. It turns out that this is not necessarily the case. The main observation of this paper was that the uncertainty predicted by a VI can be highly sensitive to the chosen way of operating the VI. To amend this situation, a simple procedure was proposed that can be used prior to performing the real measurement and that is believed to produce a conservative prediction of the measurement uncertainty in most cases. This was verified in a case study involving the measurement of the asphericity of an imperfect sphere using a CMM, with the uncertainty calculated by means of a VCMM. Full article
(This article belongs to the Special Issue Virtual Measuring Systems and Digital Twins)
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14 pages, 4177 KiB  
Article
GUM-Compliant Uncertainty Evaluation Using Virtual Experiments
by Gerd Wübbeler, Manuel Marschall, Karin Kniel, Daniel Heißelmann, Frank Härtig and Clemens Elster
Metrology 2022, 2(1), 114-127; https://doi.org/10.3390/metrology2010008 - 1 Mar 2022
Cited by 8 | Viewed by 3946
Abstract
A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual [...] Read more.
A virtual experiment simulates a real measurement process by means of a numerical model. The numerical model produces virtual data whose properties reflect those of the data observed in the real experiment. In this work, we explore how the results of a virtual experiment can be employed in the context of uncertainty evaluation for a corresponding real experiment. The uncertainty evaluation was based on the Guide to the Expression of Uncertainty in Measurement (GUM), which defines the de facto standard for uncertainty evaluation in metrology. We show that, under specific assumptions about model structure and variance of the data, virtual experiments in combination with a Monte Carlo method lead to an uncertainty evaluation for the real experiment that is in line with Supplement 1 to the GUM. In the general case, a GUM-compliant uncertainty evaluation in the context of a real experiment can no longer be based on a corresponding virtual experiment in a simple way. Nevertheless, virtual experiments are still useful in order to increase the reliability of an uncertainty analysis. Simple generic examples as well the case study of a virtual coordinate measuring machine are presented to illustrate the treatment. Full article
(This article belongs to the Special Issue Virtual Measuring Systems and Digital Twins)
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14 pages, 1082 KiB  
Article
Experimental Design for Virtual Experiments in Tilted-Wave Interferometry
by Gregor Scholz, Ines Fortmeier, Manuel Marschall, Manuel Stavridis, Michael Schulz and Clemens Elster
Metrology 2022, 2(1), 84-97; https://doi.org/10.3390/metrology2010006 - 17 Feb 2022
Cited by 8 | Viewed by 2639
Abstract
The tilted-wave interferometer (TWI) is a recent and promising technique for optically measuring aspheres and freeform surfaces and combines an elaborate experimental setup with sophisticated data analysis algorithms. There are, however, many parameters that influence its performance, and greater knowledge about the behavior [...] Read more.
The tilted-wave interferometer (TWI) is a recent and promising technique for optically measuring aspheres and freeform surfaces and combines an elaborate experimental setup with sophisticated data analysis algorithms. There are, however, many parameters that influence its performance, and greater knowledge about the behavior of the TWI is needed before it can be established as a measurement standard. Virtual experiments are an appropriate tool for this purpose, and in this paper we present a digital twin of the TWI that was carefully designed for such experiments. The expensive numerical calculations involved combined with the existence of multiple influencing parameters limit the number of virtual experiments that are feasible, which poses a challenge to researchers. Experimental design is a statistical technique that allows virtual experiments to be planned such as to maximize information gain. We applied experimental design to virtual TWI experiments with the goal of identifying the main sources of uncertainty. The results from this work are presented here. Full article
(This article belongs to the Special Issue Virtual Measuring Systems and Digital Twins)
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