Lasers stabilized to optical fiber delay lines have been shown to deliver a comparable short-term (<1 s) frequency noise performance to that achieved by lasers stabilized to ultra-low expansion (ULE) cavities, once the linear frequency drift has been removed. However, for continuous stable laser operations, the drift can be removed only when it can be predicted, e.g., when it is linear over very long timescales. To date, such long-term behaviour of the frequency drift in fiber delay lines has not been, to the best of our knowledge, characterised. In this work we experimentally characterise the frequency drift of a laser stabilised to a 500 m-long optical fiber delay line over the course of several days. We show that the drift still follows the temperature variations even when the spool temperature is maintained constant with fluctuations below tens of mK. Consequently, the drift is not linear over long timescales, preventing a simple feed-forward compensation. However, here we show that the drift can be reduced by exploiting the high level of correlation between laser frequency and the fiber temperature. In our demonstration, by applying a frequency correction proportional to temperature readings, a calculated frequency drift of less than 16 Hz/s over the several days of our test was obtained, corresponding to a 23-fold improvement from uncorrected values.

Digital twinning is a rapidly growing area of research. Digital twins combine models and data to provide up-to-date information about the state of a system. They support reliable decision-making in fields such as structural monitoring and advanced manufacturing. The use of metrology data to update models in this way offers benefits in many areas, including metrology itself. The recent activities in digitalisation of metrology offer a great opportunity to make metrology data ‘twin-friendly’ and to incorporate digital twins into metrological processes. This paper discusses key features of digital twins that will inform their use in metrology and measurement, highlights the links between digital twins and virtual metrology, outlines what use metrology can make of digital twins and how metrology and measured data can support the use of digital twins, and suggests potential future developments that will maximise the benefits achieved.

Delamination in the interlayers of multi-layer systems can cause a degradation in functionality, stability and life span of such systems. This is even more pertinent for systems at high temperatures. Laser flash analysis (LFA) has long been used for thermophysical properties measurements at high temperatures. In the European Metrology Programme for Innovation and Research (EMPIR) funded JRP 17IND11 Hi-TRACE project, the National Physical Laboratory (NPL) is developing multi-layer reference artefacts, including both fully bonded and partially de-bonded systems for validating thermal characterisation of multi-layer systems at temperatures from room temperature to above 1000 °C using LFA. The sensitivity studies carried out before creating the partially debonded artefacts have shown that the measurement area of the detector is one the important parameters that affect the accuracy of the thermal characterisation using LFA. However, this parameter is unknown to users of the early version of the Netzsch LFA 427, as it has negligible effect on radially homogenous samples which LFA is typically used for. This paper details the effect of measurement area on thermal characterisation of artefacts with partial debonding in the interface using LFA. For a bi-layer IG-210 grade graphite-hafnium foil system with a 6 mm diameter defect at the centre of the foil interface, variation in the measurement area can change the heat pulse transmission half-rise time by up to ~ 40%. Three methods to determine the system measurement area are discussed. The physical measurement diameter for the LFA 427 at NPL was estimated to be 7.7 mm ± 0.3 mm, independent of temperature. Within the uncertainty range of the measurement diameter, the thermal conductance of the defect region and the average heat transfer coefficient (HTC) can vary by ± 36% and ± 3.5% respectively. It is important to remember that this change is for a defect of 6 mm diameter which is a significant portion of the measurement area. For much smaller defects a much smaller change can be expected.

Laser flash analysis (LFA) has long been used for thermophysical properties measurements at high temperatures for both monolayer and multi-layer materials. Although some high-temperature bulk candidate reference materials were developed and studied, e.g., in the European Metrology Research Programme (EMRP) funded Joint Research Project (JRP) ENG08 Metrofission, they were not able to meet the requirements for validating thermal measurements of multi-layer systems using LFA. In the European Metrology Programme for Innovation and Research (EMPIR) funded JRP 17IND11 Hi-TRACE project, the National Physical Laboratory (NPL) is developing multi-layer reference artifacts, including both fully bonded and partially debonded systems for validating thermal characterization of multi-layer systems at temperatures from room temperature to above 1000 °C using LFA. This paper details the methodology of production, measurement and validation of silicon carbide and molybdenum foil-based multi-layer systems with, and without, partial debonding. Reproducibility and thermal stability of the artifacts will be discussed, with recommendation on the usage criteria as LFA multi-layer reference artifacts. The multi-layer system was found to be thermally stable for at least ten thermal cycles between room temperature and 1200 °C. The interface thermal conductance of both the bonded and debonded region of the artifacts was calculated using an inverse model and was shown to remain stable with varying temperatures and over five thermal cycles.

Cardiac models of electrophysiology capable of generating simulated electrocardiogram (ECG) signals are an increasingly valuable tool for both personalised medicine and understanding cardiac pathologies.Sensitivity analysis (SA) can provide crucial insight into how simulation parameters affect ECG morphology.We use two SA methods, direct numerical evaluation of integrals and polynomial chaos expansion, to calculate main and total effects for ECG features extracted from QRS complexes generated by a cardiac ventricular model.The importance of stimulation site parameters on output ECG features is evaluated.SA methods can highlight and quantify important input parameters for different ECG morphology features, which in some cases can be linked to physiological explanations.For example R peak amplitude in lead II depends on apicobasal location of stimulation sites in the left ventricle.Furthermore, different SA methods have different strengths and weaknesses.Insight into parameter importance supports model development and allows for more nuanced and patient-specific simulation changes.

There has been a significant quantity of debate recently about how metrology and the SI should embrace the emerging societal and scientific trends of digitalisation and the open data movement. Much of this discussion has focussed on ‘how’ this transition will be implemented, and recent conferences and significantly advanced this understanding (International Bureau of Weights and Measures, 2021 [1]). However, there has been little if any reflection on ‘why’ this transition is required. This deficiency is worth addressing to provide the evidence base for the ‘why’ and so drive forward faster progress with the ‘how’. Analogy is drawn between the recent revision of the SI and the need to provide a similar step change in end users’ experience of the benefits that digitalisation should bring.

Delamination in the interlayers of multi-layer systems can cause a degradation in functionality, stability and life span of that system. This is even more pertinent for systems at high temperature. Laser flash analysis (LFA) has long been used for thermophysical properties measurements at high temperatures. Multi-layer reference artefacts, with and without, debonded regions are required for validating the thermal characterization of such systems using LFA. To aid in the design of these reference artifacts a numerical model was developed to simulate LFA of multi-layer systems, with and without, defects. This paper discusses a sensitivity study that was conducted to determine if a defect in the interlayer can be detected and if so what are the most sensitive parameters. It was found that the area and thermal conductance of the defect had the greatest effect on the simulated half-rise time of the system, with shape and radial location having a significant but lesser effect in comparison. To be able to observe a change of 10% in the half-rise time, a circular defect equivalent to 5 μm air gap with an area of 25% of the measurement area in the radial centre of the sample would have to be present.

Delamination of the interlayers of multi-layer systems can cause a degradation in functionality, stability and life span of that system. This is even more pertinent for systems at high temperature. Laser flash analysis (LFA) has long been used for thermophysical properties measurements at high temperatures. Multi-layer reference artefacts, with and without, debonded regions are required for validating the thermal characterisation of such systems using LFA. Although some high-temperature bulk candidate reference materials were developed and studied, e.g. in the European Metrology Research Programme (EMRP) funded Joint Research Project (JRP) ENG08 Metrofission, they were not able to meet the requirements for validating thermal measurements of multi-layer systems using LFA. In the European Metrology Programme for Innovation and Research (EMPIR) funded JRP 17IND11 Hi-TRACE project, the National Physical Laboratory is developing multi-layer reference artefacts, including both fully bonded and partially de-bonded systems for validating thermal characterisation of multi-layer systems at temperatures from room temperature to above 1000 °C using LFA. This paper details the methodology of production, measurement and validation of isotropic graphite and hafnium based multi-layer systems with, and without, partial debonding. Reproducibility, thermal stability and sensitive parameters concerning the thermal response of the artefacts will be discussed, with recommendation on the usage criteria as LFA multi-layer reference artefacts.

Metal powder bed fusion (MPBF) is not a standalone process, and other manufacturing technologies, such as heat treatment and surface finishing operations, are often required to achieve a high-quality component. To optimise each individual process for a given component, its progression through the full process chain must be considered and understood, which can be achieved through the use of validated models. This article aims to provide an overview of the various modelling techniques that can be utilised in the development of a digital twin for MPBF process chains, including methods for data transfer between physical and digital entities and uncertainty evaluation. An assessment of the current maturity of modelling techniques through the use of technology readiness levels is conducted to understand their maturity. Summary remarks highlighting the advantages and disadvantages in physics-based modelling techniques used in MPBF research domains (i.e. prediction of: powder distortion; temperature; material properties; distortion; residual stresses; as well as topology optimisation), post-processing (i.e. modelling of: machining; heat treatment; and surface engineering), and digital twins (i.e. simulation of manufacturing process chains; interoperability; and computational performance) are provided. Future perspectives for the challenges in these MPBF research domains are also discussed and summarised.

“When I use a word, it means whatever I want it to mean”: Humpty Dumpty in Alice’s Adventures Through The Looking Glass, Lewis Carroll. “Digital twin” is currently a term applied in a wide variety of ways. Some differences are variations from sector to sector, but definitions within a sector can also vary significantly. Within engineering, claims are made regarding the benefits of using digital twinning for design, optimisation, process control, virtual testing, predictive maintenance, and lifetime estimation. In many of its usages, the distinction between a model and a digital twin is not made clear. The danger of this variety and vagueness is that a poor or inconsistent definition and explanation of a digital twin may lead people to reject it as just hype, so that once the hype and the inevitable backlash are over the final level of interest and use (the “plateau of productivity”) may fall well below the maximum potential of the technology. The basic components of a digital twin (essentially a model and some data) are generally comparatively mature and well-understood. Many of the aspects of using data in models are similarly well-understood, from long experience in model validation and verification and from development of boundary, initial and loading conditions from measured values. However, many interesting open questions exist, some connected with the volume and speed of data, some connected with reliability and uncertainty, and some to do with dynamic model updating. In this paper we highlight the essential differences between a model and a digital twin, outline some of the key benefits of using digital twins, and suggest directions for further research to fully exploit the potential of the approach.

We present a generalised framework for resolving the electrochemistry-diffusion interface and modelling hydrogen transport near a crack tip. The adsorption and absorption kinetics are captured by means of Neumanntype generalised boundary conditions. The diffusion model includes the role of trapping, with a constant or evolving trap density, and the influence of the hydrostatic stress. Both conventional plasticity and strain gradient plasticity are used to model the mechanical behaviour of the solid. Notable differences are found in the estimated crack tip hydrogen concentrations when comparing with the common procedure of prescribing a constant hydrogen concentration at the crack surfaces.

Determination of the thermal properties of a material is an important task in many scientific and engineering applications. How a material behaves when subjected to high or fluctuating temperatures can be critical to the safety and longevity of a system's essential components. The laser flash experiment is a well-established technique for indirectly measuring the thermal diffusivity, and hence the thermal conductivity, of a material. In previous works, optimization schemes have been used to find estimates of the thermal conductivity and other quantities of interest which best fit a given model to experimental data. Adopting a Bayesian approach allows for prior beliefs about uncertain model inputs to be conditioned on experimental data to determine a posterior distribution, but probing this distribution using sampling techniques such as Markov chain Monte Carlo methods can be incredibly computationally intensive. This difficulty is especially true for forward models consisting of time-dependent partial differential equations. We pose the problem of determining the thermal conductivity of a material via the laser flash experiment as a Bayesian inverse problem in which the laser intensity is also treated as uncertain. We introduce a parametric surrogate model that takes the form of a stochastic Galerkin finite element approximation, also known as a generalized polynomial chaos expansion, and show how it can be used to sample efficiently from the approximate posterior distribution. This approach gives access not only to the sought-after estimate of the thermal conductivity but also important information about its relationship to the laser intensity, and information for uncertainty quantification. Moreover, this approach leads to significant speed up over traditional methods by orders of magnitude. We also investigate the effects of the spatial profile of the laser on the estimated posterior distribution for the thermal conductivity.

The existing optical fiber network for telecommunication, together with coherent laser interferometry techniques such as narrow-linewidth lasers and heterodyne detection, is proposed as a tool for the detection of earthquakes. Using this infrastructure, we were able to detect several earthquakes, with moment magnitude as small as 3.4 and distances to the epicenter ranging between 25 and 18500 km. Such capability is extremely relevant for the detection of earthquakes in the seas and oceans, which are today poorly covered by bulk seismometers. We propose this technique as complementary to traditional detection and show how it can be established on the existing fiber network.

Earthquake monitoring across the globe is currently achieved with networks of seismic stations. The data from these networks have been instrumental in advancing our understanding of the Earth's interior structure and dynamic behaviour. However, almost all seismic stations are located on land and earthquakes of magnitude smaller than 4 at the bottom of the oceans remain largely undetected. Here we show that ordinary telecommunication optical fibre links can detect seismic events when combined with state-of-the-art frequency metrology techniques. We have detected earthquakes over terrestrial and submarine optical fibre links with length ranging from 75 to 535 km and a geographical distance from the earthquake's epicentre ranging from 25 to 18,500 km. In contrast to existing commercial reflectometry-based acoustic sensing methods used widely in the oil and gas industry, which are limited to only a few tens of kilometres, the technique presented here can be extended over thousands of kilometres, paving the way for detection of remote underwater earthquakes. By using the proposed technique on the existing extensive submarine optical fibre infrastructure, which already criss-crosses the seas and oceans, a global seismic network for real-time detection of underwater earthquakes could be implemented. The ability to detect off-shore earthquakes closer to the source could also enable a cost-effective solution for early detection of tsunamis.

Detecting ocean-floor seismic activity is crucial for our understanding of the interior structure and dynamic behavior of Earth. However, 70% of the planet's surface is covered by water, and seismometer coverage is limited to a handful of permanent ocean bottom stations. We show that existing telecommunication optical fiber cables can detect seismic events when combined with state-of-the-art frequency metrology techniques by using the fiber itself as the sensing element. We detected earthquakes over terrestrial and submarine links with lengths ranging from 75 to 535 kilometers and a geographical distance from the earthquake's epicenter ranging from 25 to 18,500 kilometers. Implementing a global seismic network for real-time detection of underwater earthquakes requires applying the proposed technique to the existing extensive submarine optical fiber network.

This paper provides a demonstration of data fusion applied to the measurement of charge mobility, an important organic electronic material parameter. It is shown that the fusion of independent data sets reduces the uncertainty associated with the charge mobility. The models used in the demonstrator are extremely simple, but the overall approach is flexible and will be applied to more complex models of organic electronic material characterization measurements in the future. The method will be used within an Open Innovation Environment for organic electronics currently under development by an EU funded project, CORNET.

Partial differential equations with uncertain input parameters are used in many applications in metrology, physics and engineering. The effect of input uncertainties on the solutions can be determined by the law of propagation of uncertainties. According to the guide to the expression of uncertainties in measurements (GUM) and its supplements, Monte Carlo sampling is recommended for nonlinear problems. In practice, large sampling sizes have to be chosen to ensure accuracy and precision. For computationally expensive problems only small sampling sizes are accessible. In this article we study and compare the propagation of uncertainties using three different sampling methods. The sampling methods chosen are Monte Carlo sampling, Latin hypercube sampling and a Sobol sequence based quasi Monte Carlo sampling. The methods are applied to the inverse problem of scatterometry with several simplifying assumptions in the measurement model. The solution of the inverse problem of scatterometry involves finite element solutions of a two dimensional Helmholtz equation. We found that among methods chosen Latin hypercube provides the most accurate and reliable results with respect to estimates of the geometry parameters, uncertainties and to repeatability.

The influence of Ti on hydrogen diffusion and trapping in various advanced high strength steels was investigated. Electrochemical hydrogen permeation tests were performed on various model steels, with and without Ti, with benchmark tests performed using a commercial steel variant. The hydrogen trapping parameters for each steel were determined by fitting the permeation curves with a finite element model based on the McNabb and Foster equations using least squares minimisation. The influence of Ti on the hydrogen trapping parameters was greatly dependent on microstructure, with ferrite-containing grades being most affected. The results are inconsistent with hydrogen trapping by TiC particles, but consistent with trapping by boundaries between neighbouring ferrite and martensite grains.

The determination of thermal diffusivity is at the heart of modern materials characterisation. The evaluation of the associated uncertainty is difficult because the determination is performed in an indirect way, in the sense that the thermal diffusivity cannot be measured directly. The well-known GUM uncertainty framework does not provide a reliable evaluation of measurement uncertainty for such inverse problems, because in that framework the underlying measurement model is supposed to be a direct relationship between the measurand (the quantity intended to be measured) and the input quantities on which the measurand depends. This paper is concerned with the development of a Bayesian approach to evaluate the measurement uncertainty associated with thermal diffusivity. A Bayesian model is first developed for a single thermogram and is then extended to the case of several thermograms obtained under repeatability and reproducibility conditions. This multi-thermogram based model is able to take into consideration a large set of influencing quantities that occur during the measurements and yields a more reliable uncertainty evaluation than the one obtained from a single thermogram. Different aspects of the Bayesian model are discussed, including the sensitivity to the choice of the prior distribution, the Metropolis-Hastings algorithm used for the inference and the convergence of the Markov chains.