Uncertainty Budget Research Articles

Preliminary dosimetric characterization of EDBreast gel

Purpose. EDBreast gel is an alternative Fricke gel dosimeter, read by Magnetic Resonance Imaging, in which sucrose is added to lower diffusion effects. This paper aims at determining the dosimetric characteristics of this dosimeter. Methods. The characterization has been performed in high energy photon beams. The dose-response of the gel has been evaluated as well as its detection limit, its fading effects, the reproducibility of its response and its stability over time. Its energy and dose-rate dependence has been investigated, and the overall dose uncertainty budget established. Once characterized, the dosimetry method has been applied to a simple reference irradiation case in a 6 MV photon beam, with the measurement of the lateral dose profile of a 2 × 2 cm2 field. The results have been compared with microDiamond measurements. Results. In addition to its low diffusivity, the gel presents a high sensitivity, no dose-rate dependence considering values ranging from 0.66 to 0.79 and an energy response comparable to ionization chambers. However, its non-linear dose-response induces a high uncertainty on the measured dose (8 % () at 20 Gy) and reproducibility issues. The profile measurements displayed discrepancies compared to the microDiamond due to diffusion effects. The appropriate spatial resolution was estimated using the diffusion coefficient. Conclusion. EDBreast gel dosimeter presents interesting characteristics for applications in clinics, but the linearity of its dose-response should be improved to lower the uncertainties and to enhance the reproducibility.

Uranyl - PyridylAzo Resorcinol System: Uncertainty Budget Evaluation and Interference Elimination

The spectrophotometric determination of uranyl ion with 4-(2-Pyridylazo)resorcinol (PAR) is a well known and old method. However this technique gives scope for further research in order to make it more selective as well as sensitive for uranyl ion determination. In this study, the experimental protocol has simplified as compared to previous report. An attempt to evaluate the uncertainty budget associated with the determination has been carried out. The effect of different cationic interferences has been studied and a simple method was developed to reduce the interferences.

Error analysis of laser interferometric system for measuring radius of curvature

Spherical surfaces are essential components of optical systems and imaging devices. Moreover, precision spheres are calibration standards for many accurate instruments in dimensional and mass metrology. A spherical surface's main property is its radius of curvature, which can be measured using contact or non-contact methods. Interferometry is an accurate non-contact technique, but some error sources impact it. This study investigates seventeen error sources that affect a laser interferometric system for measuring the radius of curvature of a precision sphere. The measurements are obtained using a Fizeau laser interferometer (GPI-XP, Zygo) with phase-shifting capability and a displacement measuring interferometer (ZMI-1000, Zygo). A silicon–nitride precision sphere with a nominal radius of 12.49965 mm is dealt with in this study. One of the main contributions of this study is proposing three additional error sources: focal shift, optical distortion, and y-axis vibration. Besides, deadpath, nulling, and focal shift error sources contributed 70% of the total uncertainty budget. Also, to correlate measurement accuracy with the reference surface, three transmission spheres (f/3.3, f/1.5, and f/0.65) are employed; f/0.65 reported the most accurate radius measurement of 12.49922 ± 0.00089 mm. This study also investigates the dependence of the nulling error on the coverage factor that defines the tested surface area. The analysis of the measurement uncertainty and the optimum conditions that minimize the system's potential error sources are described in this work.

Optimum exploitation of an integrated energy system considering renewable sources and power-heat system and energy storage

The increasing population and energy consumption have led to a greater emphasis on managing and storing different energy sources. Researchers are now focusing on integrating renewable energy into energy systems and improving efficiency through accurate modeling and calculations. This article presents the optimal operation of an integrated energy system that incorporates wind energy as a renewable source. The study focuses on enhancing the modeling accuracy of equipment such as combined heat and power units and storage devices to align the obtained results with real-world scenarios. To effectively manage electrical and thermal loads, a load management program is implemented. Furthermore, the uncertainty of wind speed is addressed using the interval-valued grey decision Theory method. Two sensitivity analyses are conducted to further investigate the system's performance. Firstly, the impact of incorporating storage resources and load management programs on the overall operating cost is examined. The results demonstrate a significant 22.87% improvement in the objective function when both storage devices and load management programs are employed simultaneously. Secondly, a sensitivity analysis is performed to evaluate the objective function's response to changes in the uncertainty budget parameters and wind speed deviation. The findings highlight the greater impact of wind speed deviation on the objective function compared to changes in the uncertainty budget. The problem is formulated as a mixed integer linear programming problem, and the GAMS software and CPLEX solver are utilized to obtain the relevant results. The findings emphasize the potential of integrating wind energy into an integrated energy system and underscore the importance of accurate modeling, load management, and the consideration of storage resources. These insights contribute to the optimization of energy system operations and the advancement of sustainable energy practices.

Calibration of high accuracy accelerometers for ESA missions BepiColombo and JUICE at INRIM

High sensitive triaxial accelerometers are used in several space missions to measure the non-gravitational accelerations acting on the spacecraft. Among these, the capacitive accelerometers developed for ESA missions Jupiter Icy moons Explorer (JUICE) and BepiColombo were designed to measure accelerations of the order of 3 · 10−6 m s−2 with an accuracy level of 300 ppm in the frequency range (3 · 10−5–0.1) Hz. Despite the signal to be measured is of the same order of magnitude of the seismic noise on the earth, an accurate on-ground calibration is needed. The facility set-up at INRIM to this purpose is based on a simple principle: the base of the accelerometer is dynamically tilted by an angle α so that the sensor undergoes a component of the gravitational acceleration g proportional to angle α. In practice, several issues have to be addressed by the calibration facility, such as the seismic noise limiting the signal-to-noise ratio, the generation and the accurate measurement of the tilt angle. Furthermore, the calibration was performed taking into account different on-flight conditions such as different operating temperatures and possible deformation of the accelerometers during the launch. The experimental set-up and the calibration procedure are described in the paper. The measurement results and the uncertainty budget show that a relative accuracy of 240 ppm has been achieved.

Features of measurement uncertainty evaluation during calibration of digital ohmmeters

The scheme for transferring the size of the unit of resistance during the calibration of digital ohmmeters at direct current is considered. The procedure for the measurement uncertainty evaluation is described: recording the measurement model and its refinement, evaluation of input and measured values, evaluation of standard uncertainties of the input and measured values, evaluation of the expanded uncertainty. The refined model includes the dependence of the resistance of the reference resistor on temperature and a correction to the drift of the resistance value of the reference resistor since its last calibration. To evaluate the expanded uncertainty, the kurtosis method was used. An uncertainty budget has been made, including the kurtosis of input and measured values. The use of the Excel package makes it possible to implement, based on this budget, a program for automation of measurement uncertainty calculations. An example of the measurement uncertainty evaluation during the calibration of a digital ohmmeter of type 2318 at a point of 1 mOhm using an electrical resistance coil R310 with an accuracy class of 0.01 is considered. The influence of nonlinearity of the measurement model on the estimates of the numerical value of the measurand and its combined standard uncertainty is studied. To verify the results, the distribution law of the measurand was modelled by the Monte Carlo method. An algorithm for determining the expanded uncertainty using the NIST Uncertainty Machine web application for the missing confidence level of 0.9545 is proposed. The comparison of the results of the measurement uncertainty evaluation by the kurtosis and Monte Carlo methods has shown their good agreement.

GRAVEL unfolding of gamma-ray spectra of CeBr3 detectors and related uncertainties

Unfolded spectra are needed for the application of some spectrum analysis methods. Frequently, iterative deconvolution methods are used, especially if the spectra have a high resolution. However, the uncertainties on the obtained results are difficult to judge. In general, the user of an unfolding code gets no information on the influence of chosen parameters, especially the choice of the first estimate of the unfolded spectrum. General studies regarding the uncertainties of unfolding algorithms are difficult to perform, if not impossible, and therefore not available. In this work, uncertainties of the results on the iterative GRAVEL algorithm, which is based on SAND II, are closely investigated by using medium resolution spectra recorded by using a CeBr3 detector. Relevant parameters are varied systematically to gain some information on the associated uncertainties on the basis of examples. The uncertainty budget of the calculation of total fluences and doses of unfolded spectra is compared with the uncertainty budget of the results obtained by applying the conversion method. The results allow, at least, the estimation of the magnitude of typical uncertainties.

A novel and holistic approach for experimental x-ray fundamental parameter determination—the Ru L-shell

The present work aims to improve both the experimental and the data evaluation procedures necessary for a determination of L-subshell atomic fundamental parameters (FPs). The main motivation lies in the fact that the established approach, consisting of a sequential evaluation of recorded transmission and fluorescence spectra in the vicinity of the three L-absorption edges, provides relatively large uncertainties for the Coster–Kronig (CK) factors. Up to now, reliable uncertainty budgets were in the order of 15%–100% and more. The novel holistic evaluation procedure addresses these large uncertainties, by employing a much larger experimental dataset extending far above the L1 absorption edge and a combined evaluation approach for a more reliable determination of the CK factors. Here, using the Ru-L shells as an example, their uncertainties are reduced to under 15%. In addition, this enables also the determination of other relevant FP data, such as the L-subshell Auger yields, the L-subshell photoionization cross sections as well as the L-subshell fluorescence production cross sections with significantly lower uncertainties as compared to the established approach.

A high precision VIS/NIR dynamic goniometer-spectrometer

We present a method for measuring the refractive index (RI) and spectral characteristics of transparent triangular prisms based on the minimum deviation technique. The proposed method has been developed to automatically measure RI simultaneously for three different wavelengths to determine the spectral dependence of RI. A high precision dynamic goniometer with a He-Ne ring laser and continuously rotating autocollimation mirror was used to implement the proposed method. A set of reference prisms made of optical glass were experimentally studied and the measurement uncertainty budget was estimated. The obtained values of the expanded measurement uncertainty did not exceed 4.6 × 10−6 for near-infrared and 1.2 × 10−5 for visible wavelength ranges with a coverage factor k = 2 (95% level of confidence). It is shown that this method can be used for high-precision measurements of the RI and determine the spectral characteristics.

Preliminary investigation of an uncertainty budget for uranium isotope ratio analysis using a liquid sampling—atmospheric pressure glow discharge—orbitrap mass spectrometer system

Preliminary investigation of an uncertainty budget for uranium isotope ratio analysis using a liquid sampling—atmospheric pressure glow discharge—orbitrap mass spectrometer system

Application of an intelligent method for hydrogen-based energy hub in multiple energy markets

Use of different energy carriers together, known as an energy hub, has been a hot topic of research. The hub manager manages the energy in the hub and supplies the energy demanded by the consumers. Herein, a multi-carrier energy storage system comprising a thermal energy storage system, ice storage system, and hydrogen storage system is considered for a multi-carrier energy system to exploit their economic benefits. The proposed combined cooling, heating and electricity microgrid not only participates in the electricity, gas and heat market to meet the needs of electricity, heating and cooling, but also can use the new hydrogen power technology used in the hydrogen storage system to increase the efficiency of the whole system participate in the market. In addition, a multi-energy demand response model is used as a new concept of demand response on electrical and thermal loads, which provides more options for multi-energy end users in energy management policies. To cover the uncertainty of the existence of different energy sources in the used model and the price of electricity, a new method has been used. The LHS sampling is used to develop diverse scenarios, and the backward scenario reduction method is adopted to decrease the number of scenarios. To solve the objective function and optimization, the metaheuristic whale algorithm improved by a local search algorithm is utilized. The main goal is to reduce the operation costs of the multi-energy carrier system. The obtained results show that the hydrogen storage utilization and multi-energy demand response can reduce the system operation cost by 6% for the studied experimental system. Furthermore, as the uncertainty budget increased, the total cost of operations increased by 10%. This is because the level of planning conservatism increases with each increase in the uncertainty budget.

Determination of the reactance of rail vehicles wheelsets

The article presents issues related to the determination of resistance, impedance, and reactance of rail vehicles wheelsets in relation to applicable standards and regulations. The methodology of conducting this type of test is discussed, and a configured test stand is presented to measure the resistance and impedance of the wheelsets. The uncertainty budget for this type of testing is discussed. Exemplary measurement results are presented and analyzed.

A robust optimization model for microgrid considering hybrid renewable energy sources under uncertainties.

Hybrid renewable energy sources and microgrids will determine future electricity generation and supply. Therefore, evaluating the uncertain intermittent output power is essential to building long-term sustainable and reliable microgrid operations to fulfill the growing energy demands. To address this, we proposed a robust mixed-integer linear programming model for the microgrid to minimize the day-ahead cost. To validate the proposed model piecewise linear curve is to deal with uncertainties of wind turbine, photovoltaic, and electrical load. The proposed solution is demonstrated through a case study compared under a robust worst-case scenario, deterministic model, and max-min robust optimization that aim to find optimal robustness. So, a piecewise linear curve is considered to obtain uncertain parameters in order to deal with uncertainties and predict the day-ahead cost. This study illustrates how the Uncertainty Budget Set selection used to integrate renewable energy sources into a microgrid, which manages the energy system. Therefore, the model complexity was slightly modified by adjusting the Uncertainty Budget Set to obtain the optimal decision and control the load demand and uncertainty of renewable energy sources. The comparative results demonstrate that the proposed robust optimization can achieve high solutions under microgrid's availability and is intended to confirm that the proposed method is more cost-effective than alternative optimization techniques. Additionally, the effectiveness and advantage of the proposed methodology in the IEEE 33-node system are validated in this case study by comparing it to the existing optimization. The comparison results show that the proposed robust optimization methods illustrate the model's efficiency, concluding remarks, and managerial insights of the research.

Primary measurement standards for trace moisture in multiple gases: extension of gas species to He and O2

The National Metrology Institute of Japan developed a multi-gas trace-moisture generator which was designed for generating trace water vapor (trace moisture) in multiple gases. Using this system, we previously developed primary measurement standards for trace moisture in N2 (10 nmol mol−1–5 μmol mol−1) and Ar (10 nmol mol−1–1 μmol mol−1). In this study, we have extended the target gas species; trace-moisture standards in He and O2 in the rage of 10 nmol mol−1 − 1 μmol mol−1 were developed. The relative expanded uncertainty (k = 2) of the trace-moisture standard in He was 0.74 %–5.7 %, and that in O2 was 0.78 %–8.9 %. In addition, we have improved stability of the flow rate of the diluent gas by controlling the temperature around the flow measurement/control systems and re-evaluated the uncertainty of the trace-moisture standards in N2 and Ar. The updated relative expanded uncertainty (k = 2) of the trace-moisture standard in N2 and Ar is 0.41 %–2.6 % and 0.73 %–2.6 %, respectively. The uncertainty budgets of the standards in these four gases are presented. The trace-moisture standard in N2 developed using the multi-gas trace-moisture generator was confirmed to be consistent with the standards realized by other generators, whose international comparability were already ensured. A commercial moisture analyzer (MA) based on the cavity ring-down spectroscopy (CRDS) was connected to the multi-gas trace-moisture generator as a device under test, and its performance was evaluated by comparing the readings with the standard values. The MA showed lower accuracy and stability in the measurement of moisture in He when it was used in the default setting, whereas it performed well in N2. This performance difference is related to the pressure-broadening coefficient of water, which depends on the gas species. We estimated the pressure-broadening coefficients of water by N2, Ar, He and O2 and discuss the gas-type dependence of the performance of CRDS-based MAs.

Primary calibration for airborne infrasound utilizing the vertical gradient of the ambient pressure

The demand for reliable and traceable measurements of airborne infrasound has risen, one major application being the International Monitoring System run by the Comprehensive Nuclear-Test-Ban Treaty Organization. However, the current calibration methods do not sufficiently cover the infrasound frequency range. In this paper, we present a calibration method for microphones in this frequency range and its implementation as a measurement setup. The method is based on the vertical gradient of the ambient pressure as a stimulus. A DUT is subjected to an alternating pressure by periodically changing its altitude. The measurement setup realizes such a periodic altitude change by means of a vertically rotating disk and is capable of calibrating measurement microphones in a frequency range from 0.1 Hz to 5 Hz with a planned extension to 10 Hz. A measurement uncertainty of 0.07 dB at maximum could be realized. Particular attention was paid to the mechanics of the measurement setup to ensure that the DUT moves in a precisely determined orbit. We present example calibrations and an uncertainty budget for a Brüel & Kjær 4193 measurement microphone in the frequency range from 0.1 Hz to 5 Hz. Finally, we demonstrate the performance of the calibration method by comparing the acquired results to other calibration techniques showing an agreement better than 0.1 dB.

Primary microvibration standards down to 10−3 m s−2 at low frequency

The reliability of microvibration measurements is important in some applications, such as infrastructure health monitoring. Thus, it is necessary to develop a vibration standard based on ISO16063-11 for microvibrations. In this study, the low-frequency standard vibration calibration system in the National Metrology Institute of Japan was upgraded to be compatible with small input vibrations down to an amplitude of 10−3 m s−2. A low-noise reference vibration measurement system and a precise signal processing method were integrated to reduce the background noise contribution, which is a dominant uncertainty source in the field of microvibration calibration. The developed system could calibrate the sensitivity of a low-noise accelerometer down to 10−3 m s−2, between 0.1 Hz and 100 Hz. This paper reports the calibration demonstration using a servo accelerometer and the evaluated uncertainty budget. The estimated calibration uncertainty was 0.1% for a normal calibration process with an excitation of 10 m s−2, and it was 2.1% for a microvibration calibration process with an excitation of 10−3 m s−2.

Collaborative distribution network design with surging demand and facility disruptions

In this paper, we study a new approach to horizontal collaboration, the so-called coalition configuration among partnering companies through sharing distribution centers in a network design problem. Horizontal collaboration is established by making joint decisions and sharing resources among various parties at the same level of the supply chain which improves operational efficiency and competitiveness. In particular, the question we address is which coalition should be formed in each distribution center while the objective function seeks to minimize the total cost in the network. Beyond that, potential uncertainties, i.e., operational and disruption risks, are considered in the collaborative design phase. Thus, this paper studies a two-stage robust optimization model for collaborative distribution network design under surging demand and facility disruptions. A tailored column-and-constraint generation algorithm is utilized to solve the proposed robust model. Extensive numerical experiments have been conducted to analyze solutions obtained by the model in various situations, e.g., when the grand coalition forms, for decisions ranging from fully centralized to fully decentralized settings, for collaborative approaches versus non-collaborative approaches, and under different amounts of uncertainty budgets. The results demonstrate that the coalition formation mechanism proposes some competitive solutions with savings of the grand coalition. We also find that not only does collaboration always increase the flexibility and resilience of the network but also in collaborative approaches, the average price of robustness is comparatively lower than that of non-collaborative approaches.

Uncertainty evaluation of an on-machine chromatic confocal measurement system

On-machine optical measurement receives growing attention as a viable quality assurance technique to satisfy the increasingly critical requirements for dimensional accuracy and surface finish upon precision components. It preserves the temporal and spatial consistency between manufacturing and measurement activities, allowing for a substantial productivity improvement and a great opportunity for on-line quality control. However, additional uncertainty can be introduced under the harsh on-machine measuring environment degrading the measurement quality. The explicit research on the on-machine measurement uncertainty is therefore essential but rarely carried out to date. To fill this gap, this paper presents the uncertainty investigation of an on-machine areal measuring instrument based on the chromatic confocal scanning principle. The vibration transmitted from neighboring machine tools is found to strengthen the drive vibration and to cause an overestimation of the roughness in the static noise test. The motion-induced disturbance and subdivisional error are recognized as artefacts in the flatness map influencing the evaluation of the flatness deviation, though they can be attenuated by the notch filter. Based on further evaluation on the roughness parameters, the uncertainty contributions from the noise and the corrected flatness deviation are found to be 18nm and 50nm respectively in Sz for the rough surface (pulse energy=250μJ). An uncertainty budget concerning all these influencing factors enables a systematic uncertainty quantification for the on-machine measurement.

A practical method for assigning uncertainty and improving the accuracy of alpha-ejection corrections and eU concentrations in apatite (U–Th) ∕ He chronology

Abstract. Apatite (U–Th) / He (AHe) dating generally assumes that grains can be accurately and precisely modeled as geometrically perfect hexagonal prisms or ellipsoids in order to compute the apatite volume (V), alpha-ejection corrections (FT), equivalent spherical radius (RFT), effective uranium concentration (eU), and corrected (U–Th) / He date. It is well-known that this assumption is not true. In this work, we present a set of corrections and uncertainties for V, FT, and RFT aimed (1) at “undoing” the systematic deviation from the idealized geometry and (2) at quantifying the contribution of geometric uncertainty to the total uncertainty budget for eU and AHe dates. These corrections and uncertainties can be easily integrated into existing laboratory workflows at no added cost, can be routinely applied to all dated apatite, and can even be retroactively applied to published data. To quantify the degree to which real apatite deviates from geometric models, we selected 264 grains that span the full spectrum of commonly analyzed morphologies, measured their dimensions using standard 2D microscopy methods, and then acquired 3D scans of the same grains using high-resolution computed tomography (CT). We then compared our apatite 2D length, maximum width, and minimum width measurements with those determined by CT, as well as the V, FT, and RFT values calculated from 2D microscopy measurements with those from the “real” 3D measurements. While our 2D length and maximum width measurements match the 3D values well, the 2D minimum width values systematically underestimate the 3D values and have high scatter. We therefore use only the 2D length and maximum width measurements to compute V, FT, and RFT. With this approach, apatite V, FT, and RFT values are all consistently overestimated by the 2D microscopy method, requiring correction factors of 0.74–0.83 (or 17 %–26 %), 0.91–0.99 (or 1 %–9 %), and 0.85–0.93 (or 7 %–15 %), respectively. The 1σ uncertainties in V, FT, and RFT are 20 %–23 %, 1 %–6 %, and 6 %–10 %, respectively. The primary control on the magnitude of the corrections and uncertainties is grain geometry, with grain size exerting additional control on FT uncertainty. Application of these corrections and uncertainties to a real dataset (N=24 AHe analyses) yields 1σ analytical and geometric uncertainties of 15 %–16 % in eU and 3 %–7 % in the corrected date. These geometric corrections and uncertainties are substantial and should not be ignored when reporting, plotting, and interpreting AHe datasets. The Geometric Correction Method (GCM) presented here provides a simple and practical tool for deriving more accurate FT and eU values and for incorporating this oft neglected geometric uncertainty into AHe dates.

Production of a reference material for seawater pHT measurements by a National Metrology Institute

Measurements of seawater pH on the total scale, noted pHT, contribute to the assessment of ocean acidification and its impact on the marine environment if a sufficient data quality is achieved. In order to achieve this, reference materials known as TRIS buffers (equimolal buffer of 2-Amino-2-(hydroxymethyl)-1,3-propanediol (TRIS) and TRIS hydrochloride (TRIS.HCl) in artificial seawater of salinity 35) have been developed and commercialised in the last decades. This paper describes, for the first time, the production of this reference material according to the ISO guide 35 and ISO standard 17034 guidelines that includes a thorough uncertainty budget evaluation carried out following the Guide to the expression of Uncertainty in Measurement (GUM). Characterization with Harned Cells at three temperatures as well as homogeneity and long-term stability assessments were performed and taken into account in the final uncertainty budget. The global standard uncertainty budget of the produced reference material for seawater pHT measurements is of 0.0025, 0.0024 and 0.0022 at, respectively, 15 °C, 25 °C and 30 °C for a shelf life of six months. The level of uncertainty obtained meets the requirements of the “climate” quality objective requested by the Global Ocean Acidification Observing Network (GOA-ON) for the monitoring of ocean acidification.