Systematic Uncertainty Analysis Research Articles

Uncertainty analysis of Transportable Fluoride-salt-cooled High-temperature Reactor (TFHR) using coupled DAKOTA with RELAP-3D method

Reliable systematic uncertainty analysis is of great significance for reactor safety and licensing. In this paper, efforts have been made to quantify uncertainties of computational results. The uncertainty quantification and sensitivity analysis for a 20MWth prismatic Transportable Fluoride-salt-cooled High temperature Reactor (TFHR) proposed by MIT is performed with the DAKOTA code coupled to the best-estimate nuclear system software RELAP5-3D. Eight input parameters are selected with specified variations and probability density functions (PDFs), a total number of 400 steady-state and Unprotected Loss of Flow (ULOF) transient calculations are then conducted in order to statistically obtain the 5% and 95% peaking fuel temperature tolerance intervals with confidence level of 95%. The Latin hypercube sampling (LHS) model in DAKOTA is verified against analytical results and the TFHR RELAP5 modeling is benchmarked based on CFD calculations. It is found that, for the steady-state, the uncertainties of the heat transfer coefficient and helium gap conductivity factor are the most remarkable contributors to the statistical results of peaking fuel temperature. 0.5% of calculated fuel temperatures exceeded the steady-state fuel temperature limit of 1573K. Under ULOF accident condition, no temperature points exceeded the transient fuel failure limit 1873K, but there is a possibility of 0.195 leading to the damage of structural material. Three primary contributors to the uncertainty in peak fuel and outlet coolant temperature are the reactor power, helium gap, and heat transfer coefficient. The findings indicate that there are needs for further reactor design optimization from thermal-hydraulics prospective.

Systematic and quantitative uncertainty analysis for rod ejection accident of pressurized water reactor

A systematic uncertainty analysis strategy based on stochastic sampling method is developed for best estimate analysis of the rod ejection accident in pressurized water reactor (PWR). Self-developed SAMP module and DAKOTA code are used to randomly sample the multigroup nuclear data, important neutronics and thermal-hydraulic (T-H) input parameters respectively. The 3D coupled reactor core model for Almaraz PWR plant is established using RELAP5/PARCS code system and the uncertainties of the core power, fuel enthalpy and local power distribution are obtained. The results indicate that the uncertainties of nuclear data and input parameters can result in large uncertainty on the results which should be carefully considered.

Uncertainty Estimation in the Two-Antenna Gain Measurement of a 4.8-11-GHz Double-Ridged Horn [Measurements Corner

In this article, a rigorous gain measurement campaign is reported for a 4.8-11-GHz wideband double-ridged horn antenna with linear ridges. This work includes a systematic uncertainty analysis in which a detailed description is given for the uncertainty associated with various aspects of the measurement of the gain by means of the twoantenna method.

Recent Progress in the Studies of Neutron-rich and High-$Z$ Systems Within the Covariant Density Functional Theory

The analysis of statistical and systematic uncertainties and their propogation to nuclear extremes has been performed. Two extremes of nuclear landscape (neutron-rich nuclei and superheavy nuclei) have been investigated. For the first extreme, we focus on the ground state properties. For the second extreme, we pay a particular attention to theoretical uncertainties in the description of fission barriers of superheavy nuclei and their evolution on going to neutron-rich nuclei.

JAXA実験用航空機「飛翔」飛行試験で取得された実機空力係数の系統不確かさ解析

Time series data of aerodynamic characteristics obtained by flight tests have large variances compared with data obtained by ground testing tools such as wind tunnel tests and numerical simulations. It is necessary to examine the uncertainty of the data obtained by flight tests in order to minimize random and systematic errors. We investigated on-board measuring instruments of the aircraft, and analyzed systematic uncertainties of the aerodynamic coefficients obtained by the flight tests using the JAXA Flying Test Bed ``Hisho''. This paper discusses the result of the systematic uncertainty analysis and the contributing factors to the uncertainty of aerodynamic coefficients.

Measurement of High-Energy Neutron Flux Above Ground Utilizing a Spallation Based Multiplicity Technique

Cosmogenic high-energy neutrons are a ubiquitous, difficult to shield, poorly measured background. Above ground the high-energy neutron energy-dependent flux has been measured, with significantly varying results. Below ground, high-energy neutron fluxes are largely unmeasured. Here we present a reconstruction algorithm to unfold the incident neutron energy-dependent flux measured using the Multiplicity and Recoil Spectrometer (MARS), simulated test cases to verify the algorithm, and provide a new measurement of the above ground high-energy neutron energy-dependent flux with a detailed systematic uncertainty analysis. Uncertainty estimates are provided based upon the measurement statistics, the incident angular distribution, the surrounding environment of the Monte Carlo model, and the MARS triggering efficiency. Quantified systematic uncertainty is dominated by the assumed incident neutron angular distribution and surrounding environment of the Monte Carlo model. The energy-dependent neutron flux between 90 MeV and 400 MeV is reported. Between 90 MeV and 250 MeV the MARS results are comparable to previous Bonner sphere measurements. Over the total energy regime measured, the MARS result are located within the span of previous measurements. These results demonstrate the feasibility of future below ground measurements with MARS.

Optimization of a flexible multi-generation system based on wood chip gasification and methanol production

Flexible multi-generation systems (FMGs) consist of integrated and flexibly operated facilities that provide multiple links between the different sectors of the energy system. The present study treated the design optimization of a conceptual FMG which integrated a methanol-producing biorefinery with an existing combined heat and power (CHP) unit and industrial energy utility supply in the Danish city of Horsens. The objective was to optimize economic performance and minimize total CO2 emission of the FMG while it was required to meet the local district heating demand plus the thermal utility demand of the butchery. The design optimization considered: Selection, dimensioning, location and integration of processes; operation optimization with respect to both hourly variations in operating conditions over the year as well as expected long term energy system development; and uncertainty analysis considering both investment costs and operating conditions.Applying a previously developed FMG design methodology, scalable models of the considered processes were developed and the system design was optimized with respect to hourly operation over the period 2015–2035. The optimal design with respect to both economic and environmental performance involved a maximum-sized biorefinery located next to local industry rather than in connection with the existing CHP unit. As the local industry energy demands were limited when compared to the biorefinery dimensions considered, process integration synergies were found to be marginal when compared to the economic and environmental impact of the biorefinery for the present case.Assessing the impact of uncertainties on the estimated FMG performances, the net present value (NPV) of the optimal design was estimated to vary within the range 252.5–1471.6M€ in response to changes of ±25% in investment costs and methanol price, and considering two different electricity price scenarios. In addition, a change in the interest rate from 5% to 20% was found to reduce the lower bound of the NPV to 181.3M€ for reference operating conditions. The results suggest that the applied interest rate and operating conditions, in particular the methanol price, would have a much higher impact on the economic performance of the designs than corresponding uncertainties in investment costs. In addition, the study outcomes emphasize the importance of including systematic uncertainty analysis in the design optimization of FMG concepts.

Structured Singular-Value Analysis of the Vega Launcher in Atmospheric Flight

Using the structured singular value , an independent control law assessment is presented for the Vega launcher thrust vector control system. A systematic uncertainty modeling and analysis process is illustrated to retrieve and structure driving perturbation combinations affecting competing control system design requirements. It is demonstrated how analysis not only complements and generalizes classical frequency-domain stability assessments but also how it applies naturally as a performance indicator to manage the requirements tradeoff space. The proposed methodology is shown to be reliable and computationally more efficient than widespread verification and validation techniques that rely on random sampling via Monte–Carlo analysis. Although not meant as a replacement of these traditional approaches, analysis effectively complements and enhances the verification and validation tasks by guiding the analyst toward worst-case convergence over the uncertain parameter search space. The attitude dynamics in atmospheric flight of Europe’s lightweight Vega launcher is assumed throughout the paper. Comparative robustness analysis results are shown between pre- and postflight assessments.

Global sensitivity analysis of a three-dimensional nutrients-algae dynamic model for a large shallow lake

Sensitivity analysis is a primary approach used in mathematical modeling to identify important factors that control the response dynamics in a model. In this paper, we applied the Morris sensitivity analysis method to identify the important factors governing the dynamics in a complex 3-dimensional water quality model. The water quality model was developed using the Environmental fluid dynamics code (EFDC) to simulate the fate and transport of nutrients and algal dynamics in Lake Dianchi, one of the most polluted large lakes in China. The analysis focused on the response of four water quality constituents, including chlorophyll-a, dissolved oxygen, total nitrogen, and total phosphorus, to 47 parameters and 7 external driving forces. We used Morris sensitivity analysis with different sample sizes and factor perturbation ranges to study the sensitivity with regard to different output metrics of the water quality model, and we analyzed the consistency between different sensitivity scenarios. In addition to the analysis with aggregate outputs, a spatiotemporal variability analysis was performed to understand the spatial heterogeneity and temporal distribution of sensitivities. Our results indicated that it is important to consider multiple characteristics in a sensitivity analysis, and we have identified a robust set of sensitive factors in the water quality model that will be useful for systematic model parameter identification and uncertainty analysis.

Impact of nuclear data on sodium-cooled fast reactor calculations

Neutron transport and depletion calculations are performed in combination with various nuclear data libraries in order to assess the impact of nuclear data on safety-relevant parameters of sodium-cooled fast reactors. These calculations are supplemented by systematic uncertainty analyses with respect to nuclear data. Analysed quantities are the multiplication factor and nuclide densities as a function of burn-up and the Doppler and Na-void reactivity coefficients at begin of cycle. While ENDF/B-VII.0 / -VII.1 yield rather consistent results, larger discrepancies are observed between the JEFF libraries. While the newest evaluation, JEFF-3.2, agrees with the ENDF/B-VII libraries, the JEFF-3.1.2 library yields significant larger multiplication factors.

Measurement of the cosmic ray all-particle and light-component energy spectra with the ARGO-YBJ experiment

ARGO-YBJ preliminary results of the measurements of the all-particle and light-component (i.e. protons and helium) cosmic ray energy spectra between approximately 5 TeV and 5 PeV are reported and discussed. The resulting all-particle spectrum (measured in the energy range 100TeV - 3PeV) is in good agreement with both theoretical parametrizations and previous measurements. The light-component (i.e. p + He) has been measured with high resolution up to about 5 PeV. The preliminary result is in agreement with direct measurements and then show a clear indication of a bending below 1PeV. Improvements of event selection/reconstruction with the full statistics and a complete analysis of systematic uncertainties is currently under way.

Uncertainty Analysis of Multi-Model Flood Forecasts

This paper demonstrates, by means of a systematic uncertainty analysis, that the use of outputs from more than one model can significantly improve conditional forecasts of discharges or water stages, provided the models are structurally different. Discharge forecasts from two models and the actual forecasted discharge are assumed to form a three-dimensional joint probability density distribution (jpdf), calibrated on long time series of data. The jpdf is decomposed into conditional probability density distributions (cpdf) by means of Bayes formula, as suggested and explored by Krzysztofowicz in a series of papers. In this paper his approach is simplified to optimize conditional forecasts for any set of two forecast models. Its application is demonstrated by means of models developed in a study of flood forecasting for station Stung Treng on the middle reach of the Mekong River in South-East Asia. Four different forecast models were used and pairwise combined: forecast with no model, with persistence model, with a regression model, and with a rainfall-runoff model. Working with cpdfs requires determination of dependency among variables, for which linear regressions are required, as was done by Krzysztofowicz. His Bayesian approach based on transforming observed probability distributions of discharges and forecasts into normal distributions is also explored. Results obtained with his method for normal prior and likelihood distributions are identical to results from direct multiple regressions. Furthermore, it is shown that in the present case forecast accuracy is only marginally improved, if Weibull distributed basic data were converted into normally distributed variables.

Matching Pion-Nucleon Roy-Steiner Equations to Chiral Perturbation Theory.

We match the results for the subthreshold parameters of pion-nucleon scattering obtained from a solution of Roy-Steiner equations to chiral perturbation theory up to next-to-next-to-next-to-leading order, to extract the pertinent low-energy constants including a comprehensive analysis of systematic uncertainties and correlations. We study the convergence of the chiral series by investigating the chiral expansion of threshold parameters up to the same order and discuss the role of the Δ(1232) resonance in this context. Results for the low-energy constants are also presented in the counting scheme usually applied in chiral nuclear effective field theory, where they serve as crucial input to determine the long-range part of the nucleon-nucleon potential as well as three-nucleon forces.

Optimization of the GSFC TROPOZ DIAL retrieval using synthetic lidar returns and ozonesondes – Part 1: Algorithm validation

Abstract. The main purpose of the NASA Goddard Space Flight Center TROPospheric OZone DIfferential Absorption Lidar (GSFC TROPOZ DIAL) is to measure the vertical distribution of tropospheric ozone for science investigations. Because of the important health and climate impacts of tropospheric ozone, it is imperative to quantify background photochemical ozone concentrations and ozone layers aloft, especially during air quality episodes. For these reasons, this paper addresses the necessary procedures to validate the TROPOZ retrieval algorithm and confirm that it is properly representing ozone concentrations. This paper is focused on ensuring the TROPOZ algorithm is properly quantifying ozone concentrations, and a following paper will focus on a systematic uncertainty analysis. This methodology begins by simulating synthetic lidar returns from actual TROPOZ lidar return signals in combination with a known ozone profile. From these synthetic signals, it is possible to explicitly determine retrieval algorithm biases from the known profile. This was then systematically performed to identify any areas that need refinement for a new operational version of the TROPOZ retrieval algorithm. One immediate outcome of this exercise was that a bin registration error in the correction for detector saturation within the original retrieval was discovered and was subsequently corrected for. Another noticeable outcome was that the vertical smoothing in the retrieval algorithm was upgraded from a constant vertical resolution to a variable vertical resolution to yield a statistical uncertainty of <10 %. This new and optimized vertical-resolution scheme retains the ability to resolve fluctuations in the known ozone profile, but it now allows near-field signals to be more appropriately smoothed. With these revisions to the previous TROPOZ retrieval, the optimized TROPOZ retrieval algorithm (TROPOZopt) has been effective in retrieving nearly 200 m lower to the surface. Also, as compared to the previous version of the retrieval, the TROPOZopt had an overall mean improvement of 3.5 %, and large improvements (upwards of 10–15 % as compared to the previous algorithm) were apparent between 4.5 and 9 km. Finally, to ensure the TROPOZopt retrieval algorithm is robust enough to handle actual lidar return signals, a comparison is shown between four nearby ozonesonde measurements. The ozonesondes are mostly within the TROPOZopt retrieval uncertainty bars, which implies that this exercise was quite successful.

Experimental Determination of the Uncertainty of the Absorption Coefficient of Crystalline Silicon

Based on a combined analysis of spectroscopic ellipsometry, reflectance and transmittance measurements as well as spectrally resolved luminescence measurements and spectral responsivity measurements, we present data of the coefficient of band-to-band absorption of crystalline silicon at 295K in the wavelength range 250 – 1450nm. A systematic measurement uncertainty analysis according to the “Guide to the Expression of Uncertainty in Measurements” (GUM) is carried out for each method, showing that the relative uncertainty of the absorption coefficient data so determined is of the order of 0.3% at 300nm, 1% at 900nm, 10% at 1200nm and 180% at 1450nm. The data are consolidated by comparison of measurements carried out independently at different institutions. The uncertainty of solar cell energy conversion predictions by means of simulations due to the uncertainty of the absorption coefficient data is shown to be of the order of 0.1% relative.

A systematic uncertainty analysis for liner impedance eduction technology

The so-called impedance eduction technology is widely used for obtaining acoustic properties of liners used in aircraft engines. The measurement uncertainties for this technology are still not well understood though it is essential for data quality assessment and model validation. A systematic framework based on multivariate analysis is presented in this paper to provide 95 percent confidence interval uncertainty estimates in the process of impedance eduction. The analysis is made using a single mode straightforward method based on transmission coefficients involving the classic Ingard–Myers boundary condition. The multivariate technique makes it possible to obtain an uncertainty analysis for the possibly correlated real and imaginary parts of the complex quantities. The results show that the errors in impedance results at low frequency mainly depend on the variability of transmission coefficients, while the mean Mach number accuracy is the most important source of error at high frequencies. The effect of Mach numbers used in the wave dispersion equation and in the Ingard–Myers boundary condition has been separated for comparison of the outcome of impedance eduction. A local Mach number based on friction velocity is suggested as a way to reduce the inconsistencies found when estimating impedance using upstream and downstream acoustic excitation.

Uncertainty analysis for the coefficient of band-to-band absorption of crystalline silicon

We analyze the uncertainty of the coefficient of band-to-band absorption of crystalline silicon. For this purpose, we determine the absorption coefficient at room temperature (295 K) in the wavelength range from 250 to 1450 nm using four different measurement methods. The data presented in this work derive from spectroscopic ellipsometry, measurements of reflectance and transmittance, spectrally resolved luminescence measurements and spectral responsivity measurements. A systematic measurement uncertainty analysis based on the Guide to the expression of uncertainty in measurement (GUM) as well as an extensive characterization of the measurement setups are carried out for all methods. We determine relative uncertainties of the absorption coefficient of 0.4% at 250 nm, 11% at 600 nm, 1.4% at 1000 nm, 12% at 1200 nm and 180% at 1450 nm. The data are consolidated by intercomparison of results obtained at different institutions and using different measurement approaches.

Applying Fuzzy and Probabilistic Uncertainty Concepts to the Material Flow Analysis of Palladium in Austria

AbstractMaterial flow analysis (MFA) is a widely applied tool to investigate resource and recycling systems of metals and minerals. Owing to data limitations and restricted system understanding, MFA results are inherently uncertain. To demonstrate the systematic implementation of uncertainty analysis in MFA, two mathematical concepts for the quantification of uncertainties were applied to Austrian palladium (Pd) resource flows and evaluated: (1) uncertainty ranges expressed by fuzzy sets and (2) uncertainty ranges defined by normal distributions given as mean values and standard deviations. Whereas normal distributions represent the traditional approach for quantifying uncertainties in MFA, fuzzy sets may offer additional benefits in relation to uncertainty quantification in cases of scarce information. With respect to the Pd case study, the fuzzy representation of uncertain quantities is more consistent with the actual data availability in cases of incomplete databases, and fuzzy sets serve to highlight the effect of uncertainty on resource efficiency indicators derived from the MFA results. For both approaches, data reconciliation procedures offer the potential to reduce uncertainty and evaluate the plausibility of the model results. With respect to Pd resource management, improved formal collection of end‐of‐life (EOL) consumer products is identified as a key factor in increasing the recycling efficiency. In particular, the partial export of EOL vehicles represents a substantial loss of Pd from the Austrian resource system, whereas approximately 70% of the Pd in the EOL consumer products is recovered in waste management. In conclusion, systematic uncertainty analysis is an integral part of MFA required to provide robust decision support in resource management.

Uncertainty evaluation of the diffusive gradients in thin films technique.

Although the analytical performance of the diffusive gradients in thin films (DGT) technique is well investigated, there is no systematic analysis of the DGT measurement uncertainty and its sources. In this study we determine the uncertainties of bulk DGT measurements (not considering labile complexes) and of DGT-based chemical imaging using laser ablation - inductively coupled plasma mass spectrometry. We show that under well-controlled experimental conditions the relative combined uncertainties of bulk DGT measurements are ∼10% at a confidence interval of 95%. While several factors considerably contribute to the uncertainty of bulk DGT, the uncertainty of DGT LA-ICP-MS mainly depends on the signal variability of the ablation analysis. The combined uncertainties determined in this study support the use of DGT as a monitoring instrument. It is expected that the analytical requirements of legal frameworks, for example, the EU Drinking Water Directive, are met by DGT sampling.

An integrated systematic analysis of uncertainties in UK energy transition pathways

Policy goals to transition national energy systems to meet decarbonisation and security goals must contend with multiple overlapping uncertainties. These uncertainties are pervasive through the complex nature of the system, the long term consequences of decisions, and in the models and analytical approaches used. These greatly increase the challenges of informing robust decision making. Energy system studies have tended not to address uncertainty in a systematic manner, relying on simple scenario or sensitivity analysis. This paper utilises an innovative UK energy system model, ESME, which characterises multiple uncertainties via probability distributions and propagates these uncertainties to explore trade-offs in cost effective energy transition scenarios. A linked global sensitivity analysis is used to explore the uncertainties that have most impact on the transition. The analysis highlights the strong impact of uncertainty on delivering the required emission reductions, and the need for an appropriate carbon price. Biomass availability, gas prices and nuclear capital costs emerge as critical uncertainties in delivering emission reductions. Further developing this approach for policy requires an iterative process to ensure a complete understanding and representation of different uncertainties in meeting mitigation policy objectives.