Metrology

With a view to improve measurements, this paper presents a statistical approach for characterizing the behaviour of roughness parameters based on measurements performed on ground surface topographies (grit #080/#120). A S neox^TM (Sensofar^®, Terrassa, Spain), equipped with three optical instrument modes (Focus Variation (FV), Coherence Scanning Interferometry (CSI), and Confocal Microscopy (CM)), is used according to a specific measurement plan, called Morphomeca Monitoring, including topography representativeness and several time-based measurements. Previously applied to the Sa parameter, the statistical approach based here solely on the Quality Index (QI) has now been extended to a multi-parameter approach. Firstly, the study focuses on detecting and explaining parameter disturbances in raw data by identifying and quantifying outliers of the parameter’s values, as a new first indicator. This allows us to draw parallels between these outliers and the surface topography, providing reflection tracks. Secondly, the statistical approach is applied to highlight disturbed parameters concerning the instrument mode used and the concerned grit level with two other indicators computed from QI, named homogeneity and number of modes. The applied method shows that a cleaning of the data containing the parameters values is necessary to remove outlier values, and a set of roughness parameters could be determined according to the assessment of the indicators. The final aim is to provide a set of parameters which best describe the measurement conditions based on monitoring data, statistical indexes, and surface topographies. It is shown that the parameters Sal, Sz and Sci are the most reliable roughness parameters, unlike Sdq and S5p, which appear as the most unstable parameters. More globally, the volume roughness parameters appear as the most stable, differing from the form parameters. This investigated point of view offers thus a complementary framework for improving measurement processes. In addition, this method aims to provide a global and more generalizable alternative than traditional methods of uncertainty calculation, based on a thorough analysis of multi-parameter and statistical indexes. Full article

The moiré effect is typically observed in regular periodic structures and sometimes in random (aperiodic) structures. However, currently, only regular graphical objects are used in measurements. We propose using graphical objects that are not regular but not entirely random and that resemble rows, such as grids of dotted lines or matrixes of dots. The moiré effect in such objects may become similar to the moiré effect in regular graphical objects if a relatively simple modification of the image processing algorithm is applied. We demonstrated that the results of measurements with five different graphical objects arranged in rows (including text) are similar. Using such objects can be helpful for practical moiré measurements. Full article

Additive manufacturing (AM), or 3D printing, has revolutionized the fabrication of complex parts, but assessing their quality remains a challenge. Quality assessment, especially for the interior part geometry, relies on post-print inspection techniques unsuitable for real-time in situ analysis. Vision-based approaches could be employed to capture images of any layer during fabrication, and then segmentation methods could be used to identify in-layer features in order to establish dimensional conformity and detect defects for in situ evaluation of the overall part quality. This research evaluated five image segmentation methods (simple thresholding, adaptive thresholding, Sobel edge detector, Canny edge detector, and watershed transform) on the same platform for their effectiveness in isolating and identifying features in 3D-printed layers under different contrast conditions for in situ quality assessment. The performance metrics used are accuracy, precision, recall, and the Jaccard index. The experimental set-up is based on an open-frame fused filament fabrication printer augmented with a vision system. The control system software for printing and imaging (acquisition and processing) was custom developed in Python running on a Raspberry Pi. Most of the segmentation methods reliably segmented the external geometry and high-contrast internal features. The simple thresholding, Canny edge detector, and watershed transform methods did not perform well with low-contrast parts and could not reliably segment internal features when the previous layer was visible. The adaptive thresholding and Sobel edge detector methods segmented high- and low-contrast features. However, the segmentation outputs were heavily affected by textural and image noise. The research identified factors affecting the performance and limitations of these segmentation methods and contributing to the broader effort of improving in situ quality assessment in AM, such as automatic dimensional analysis of internal and external features and the overall geometry. Full article

This paper presents a comprehensive methodology for the precise calibration of high-voltage capacitance and dissipation factor (DF) bridges. The technique involves meticulous adjustments using a digital high-precision phase and ratio-measuring system to determine correction factors for DF and capacitance measurements. Unlike other methods that are limited to a narrow range, this approach allows calibration across the entire operational working spectrum of any bridge. While the method has been developed up to 1 kHz, its adaptability for future requirements is facilitated by the developed software. This method has been carried out by calibrating a highly accurate bridge for a capacitor ratio of up to 100, with DFs ranging from −0.01 to 0.01 and currents ranging from 0.1 mA to 1 A. Linear correction factors are established, with their accuracies being rigorously quantified. This methodology achieves expanded uncertainties as low as 3.5 µF/F (3.5 ppm) for capacitance and 2.2 × 10⁻⁶ for DFs, significantly enhancing measurement reliability across diverse high-voltage capacitor applications. Full article

The foot is considered a wonder of biological engineering due to its structure, formed by bones, ligaments, and tendons that collaborate to ensure stability and mobility. A key area often examined by medical professionals in patients with diabetic feet is the plantar surface, due to the risk of ulcer development. If left untreated, these ulcers can lead to severe complications, including amputation of the toe, foot, or even the limb. Interpolation methods are used to find areas with overloads in a system of sensor maps that are based on capacitive, load cells, or force-sensitive resistors (FSRs). This manuscript presents the assessment of linear, nearest neighbors, and bicubic methods in comparison with ground truth to calculate the root mean square error (RMSE) in two assessments using a dataset of eight healthy subjects, four men and four women, with an average age of 25 years, height of 1.63 m, and weight of 72 kg with shoe sizes from 7.3 USA using FSR map with 48 sensors. Additionally, this paper describes the conditioning circuit development to implement a plantar surface system that enables interpolating loads on the plantar surface. The proposed system’s results show that the first assessment indicates an RMSE of 0.089, 0.126, and 0.089 for linear, nearest neighbor, and bicubic methods, while the second assessment shows a mean RMSE for linear, nearest neighbor, and bicubic methods of 0.114, 0.159, and 0.112. Full article

Semiconductor layers employed in fabricating advanced node devices are becoming thinner and their electrical properties are diverging from those established for highly crystalline standards. Since these properties also change as a function of depth within the film, accurate carrier profiling solutions are required. The Differential Hall Effect (DHE) technique has the unique capability of measuring mobility and carrier concentration (active carriers) through the depth of a semiconductor film. It comprises making successive sheet resistance and sheet Hall coefficient measurements as the thickness of the electrically active layer at a test region is reduced through successive material removal steps. Difference equations are then used to process the data and plot the desired depth profiles. The fundamentals of DHE were established in 1960s. Recently, the adaption of electrochemical processing for the material removal steps, and the integration of all other functionalities in a Differential Hall Effect Metrology (DHEM) tool, has made this technique more practical and accurate and improved its depth resolution to a sub-nm range. In this contribution, we review the development history of this important technique and present data from recent characterization work carried out on Si, Ge and SiGe layers. Full article

Virtual experiments are a digital representation of a real measurement and play a crucial role in modern measurement sciences and metrology. Beyond their common usage as a modeling and validation tool, a virtual experiment may also be employed to perform a parameter sensitivity analysis or to carry out a measurement uncertainty evaluation. For the latter to be compliant with statistical principles and metrological guidelines, the procedure to obtain an estimate and a corresponding measurement uncertainty requires careful consideration. We employ a Monte Carlo sampling procedure using a virtual experiment that allows one to perform a measurement uncertainty evaluation according to the Monte Carlo approach of JCGM-101 and JCGM-102, two widely applied guidelines for uncertainty evaluation in metrology. We extend and formalize a previously published approach for simple additive models to account for a large class of non-linear virtual experiments and measurement models for multidimensionality of the data and output quantities, and for the case of unknown variance of repeated measurements. With the algorithm developed here, a simple procedure for the evaluation of measurement uncertainty is provided that may be applied in various applications that admit a certain structure for their virtual experiment. Moreover, the measurement model commonly employed for uncertainty evaluation according to JCGM-101 and JCGM-102 is not required for this algorithm, and only evaluations of the virtual experiment are performed to obtain an estimate and an associated uncertainty of the measurand. We demonstrate the efficacy of the developed approach and the effect of the underlying assumptions for a generic polynomial regression example and an example of a simplified coordinate measuring machine and its virtual representation. The results of this work highlight that considerable effort, diligence, and statistical considerations need to be invested to make use of a virtual experiment for uncertainty evaluation in a way that ensures equivalence with the accepted guidelines. Full article

Car accidents, a major US public safety issue, demand precise analysis and predictive models for mitigation. This study asks the following question: Can the safest car routes across the US be determined? The paper analyzes historical data to forecast future accidents and calculates the safest route between two locations. The study builds a predictive model utilizing statistical analyses, data mining, and machine learning. A joint probability density function (PDF) is devised to calculate the safest route for risk modeling, factoring in latitude and longitude. The model quantifies accident probabilities in areas and travel routes. Additionally, the safest direction can be determined using the gradient of the joint PDF curve. The predictive model enables policymakers to allocate resources proactively. The safest route selection enables drivers to navigate safer areas and routes, which can reduce the number of accidents. Through its analysis and joint PDF model, this research enriches accident analysis and prevention engineering, potentially fostering safer US roads. Full article

Irreversible demagnetization processes in high-performance Fe-Nd-B magnets were investigated using a novel test rig. Designed to capture local magnetic field distributions and integral average magnetization in situ, the rig operates under field and temperature conditions similar to those found in electric motors. Validation against established techniques such as the hysteresisgraph and Hall mapper confirmed its accuracy. Furthermore, we observed the ability to detect even small variations of less than 2.5% in coercive field strength across the sample volume using field scans. The system significantly reduces measurement times from days to hours, enabling efficient in situ detection of magnetic field distributions during the whole demagnetization process. Full article

As modern systems become more complex, their control strategy no longer relies only on measurement data from probes; it also requires information from mathematical models for non-measurable places. On the other hand, those mathematical models can lead to unbearable computation times due to their own complexity, making the control process non-viable. To overcome this problem, it is possible to implement any kind of surrogate model that enables the computation of such estimates within an acceptable time frame, which allows for making decisions. Using a Physics-Informed Neural Network as a surrogate model, it is possible to compute the temperature distribution at each time step, replacing the need for running direct numerical simulations. This approach enables the use of a Deep Reinforcement Learning algorithm to train a control strategy. On this work, we considered a one-dimensional heat conduction problem, in which temperature distribution feeds a control system. Such control system has the objective of reacing and maintaining constant temperature value at a specific location of the 1D problem by activating a heat source; the desired location somehow cannot be directly measured so, the PINN approach allows to estimate its temperature with a minimum computational workload. With this approach, the control training becomes much faster without the need of performing numerical simulations or laboratory measurements. Full article

This article presents the results of comparative tests of gear wheels based on the contactless and contact measurement methods. Measurements of gear wheels in accuracy classes containing deviations within the range of measurement capabilities of the GOM ATOS II optical scanner are proposed. Elementary deviations of teeth related to the involute profile were analyzed. In undertaking a non-contact gear measurement using the GOM ATOS II scanner, a new method was developed to extract parameters from the point cloud, which were then used to determine the total deviation of the profile. The results of the measurements obtained using the non-contact method were compared with the results obtained with the contact method using the Wenzel WGT 600 four-axis machine specialized for measuring gear wheels. Measurement uncertainty was also compared. The result of the conducted tests is the comparability of results for gear wheels made in accuracy class 10 according to DIN 3961/62. The proposed non-contact method shows the possibility of using it to measure gear wheels commonly used in agricultural and construction machines. The information obtained from comparing the measurement model and the nominal wheel model provides additional information about surface defects of the part which result from the production and operation process. Full article

The structural resolution describes the ability of a measuring device to detect small structures on the surface of a component or test specimen by means of a quantitative value. However, the structural resolution in the computer tomograph depends on the object and must therefore be determined separately for each measurement task. The previous approaches to structural resolution determination are only related to test specimens. In this paper, less discrete approaches based on a circular pattern are presented, which can be integrated into the measured component. A voxel-based methodology as well as two surface-based methodologies are described. The investigation results regarding the effect of the component position on the structural resolution are obtained on the basis of real CT measurements. A comparison is also completed with the well-known hourglass method. The results show that the resolution depends on the object being measured, with similar values being obtained for the same object using different methods. Full article

The topography measurement accuracy of coherence scanning interferometry (CSI) suffers from the local characteristic of micro-structured surfaces, such as local surface slopes. A cylindrical reference artefact made of single-mode fiber with high roundness and low roughness has been proposed in this manuscript to traceably investigate the surface tilting induced measurement deviations using coherence scanning interferometry with high NA objectives. A feed-forward neural network (FF-NN) is designed and trained to model and thereafter compensate the systematic measurement deviations due to local surface tilting. Experimental results have verified that the FF-NN approach can well enhance the accuracy of the CSI for radius measurement of cylindrical samples up to 0.3%. Further development of the FF-NN for modelling of the measurement errors in CSI due to the optical properties of surfaces including areal roughness is outlined. Full article

African scientific research faces formidable challenges, particularly with limited access to state-of-the-art measurement instruments. The high cost associated with these devices presents a significant barrier for regional research laboratories, impeding their ability to conduct sophisticated experiments and gather precise data. This predicament not only hampers the individual laboratories but also has broader implications for the African scientific community and the advancement of knowledge in developing nations—the financial cost barrier considerably impacts the research quality of these laboratories. Reflection on technical and economical solutions needs to be quickly found to help these countries advance their research. In civil engineering, the thermal conductivity property is the most important measurement for characterizing heat transfer in construction materials. Existing devices (i.e., conductometers) in a laboratory are expensive (approximately EUR 30,000) and unavailable for some African laboratories. This study proposes a new and affordable device to evaluate thermal conductivity in construction materials. The method involves establishing a thermal flux between a heat source (from the Joule effect provided by steel wool where a current is circulating) and a cold source (generated by ice cubes) under steady-state conditions. The development of the cylindrical prototype is based on the comparative flux-meter method outlined in the measuring protocol of the ASTM E1225 standard document. Experiments were conducted on four distinct materials (polystyrene, wood, agglomerated wood, and rigid foam). The results indicate a correct correlation between the experimental values obtained from the newly developed prototype and the reference values found in the literature. For example, concerning the experimental polystyrene study, the detailed case analysis reveals a good correlation, with a deviation of only 4.88%. The percent error found falls within the acceptable range indicated by the standard recommendations of the ASTM E1225 standard, i.e., within 5% acceptable error. Full article

This research investigates the influence of printing parameters and different materials on the geometrical and dimensional deviations of Fused Deposition Modelling (FDM) additive manufacturing. Using the Taguchi method, experiments with four factors are designed: print layer height, printing material, printing speed, and nozzle size, employing an L9 orthogonal array. Deviations in flatness, perpendicularity, parallelism, cylindricity, spherical form, and surface roughness of 3D-printed parts are evaluated. The results reveal that print speed and nozzle size significantly affect flatness and surface roughness, while layer height and material influence perpendicularity and parallelism deviations. Notably, nozzle size critically impacts cylindricity and spherical form deviations. Our study demonstrates that lower printing speed, smaller nozzle diameter, and reduced layer height are not universally optimal; instead, parameter adjustments based on specific geometrical requirements and part orientation are necessary. These findings are essential for improving the accuracy and quality of FDM-printed parts, supporting their broader application in precision manufacturing industries. Full article

This study presents an automated methodology for evaluating micro-channels fabricated using a femtosecond laser on stainless steel substrates. We utilize 3D surface topography and metrological analyses to extract geometric features and detect fabrication defects. Standardized samples were analyzed using a light interferometer, and the resulting data were processed with Principal Component Analysis (PCA) and RANSAC algorithms to derive channel characteristics, such as depth, wall taper, and surface roughness. The proposed method identifies common defects, including bumps and V-defects, which can compromise the functionality of micro-channels. The effectiveness of the approach is validated by comparisons with commercial solutions. This automated procedure aims to enhance the reliability and precision of femtosecond laser micro-milling for industrial applications. The detected defects, combined with fabrication parameters, could be ingested in an AI-based process to optimize fabrication processes. Full article

Distributed energy resources and the number of relays are expected to rise in modern electrical grids; consequently, relay misoperations are also expected to grow. Relays can detect electrical fault types using an internal algorithm and can display the result using light indicators on the front of the relay. However, some relays’ internal algorithms for predicting types of electrical faults could be improved. This study assesses a relay’s external and internal algorithms with an Advanced Synchronized Time Digital Grid Twin (ASTDGT) testbed with paired relays. A misoperation relay analysis focused on measuring the accuracy of using the boundary admittance (the external algorithm) versus the set-default (the internal algorithm) relay method to determine the electrical fault types was performed. In this study, the internal and external relay algorithms were assessed with a synchronized time digital grid twin testbed using a real-time simulator. This testbed evaluated two sets of logic at the same time with the digital grid twin and paired relays in the loop. Different types of electrical faults were simulated, and the relays’ recorded events and electrical fault light indicator states were collected from the human–machine interfaces. This ASTDGT testbed with paired relays successfully evaluated the relay algorithm misoperations. The boundary admittance method had an accuracy of 100% for line-to-line, line-to-ground, and line-to-line ground faults. Full article

Wigner’s friend scenarios—in which external agents describe a closed laboratory containing a friend making a measurement—highlight the difficulties of quantum theory when accounting for measurements. The problem is to accommodate for unitary evolution from the point of view of the external agent with the measurements or other operations carried out by the friend. Here, we show in the context of a relativistic thought experiment that an operation that may be accounted for unitarily in a given reference frame cannot be described unitarily in a different reference frame. This result, based on the frame dependence of the state update in relativistic contexts, could point to some fundamental inadequacy when attempting to model actions taken by a complex agent as unitary operations. Full article

Virtual experiments (VEs) and digital twins (DTs), pivotal for realizing European strategic policies on sustainability and digitalization within Industry 4.0 and the European Green Deal, simulate physical systems and characteristics in a virtual environment, with DTs incorporating dynamic inputs from and outputs to the real-world counterpart. To ensure confidence in their use and outcomes, traceability and methods to evaluate measurement uncertainty are needed, topics that are hardly covered by the literature so far. This paper provides a harmonized definition of VEs and DTs and introduces a framework for evaluating measurement uncertainty. Furthermore, it discusses how to propagate the uncertainty of the contributions coming from the different parts of the DT. For the core part of the DT, the framework derived for VEs can be used. For the physical-to-virtual (P2V) connection and the virtual-to-physical (V2P) connection, additional sources of uncertainty need to be considered. This paper provides a metrological framework for taking all these uncertainty contributions into account while describing a framework to establish traceability for DTs. Two case studies are presented to demonstrate the proposed methodology considering industrially relevant measuring instruments and devices, namely, a coordinate measuring machine (CMM) and a collaborative robot arm (cobot). Full article