Uncertainty Analysis in Reactor Physics Modeling

In recent years, the demand to provide best-estimate predictions with confident bounds is increasing for the nuclear reactor performance and safety analysis. The Organisation for Economic Co-operation and Development Nuclear Energy Agency has been developing an international benchmark of the light water reactor (LWR) uncertainty analysis in modeling (UAM) for the examination of uncertainty quantification and propagation methodologies with various modeling and simulation code systems. The objective of the present work is to develop an uncertainty propagation mechanism based on the stochastic sampling method by taking into account the uncertainties of both basic nuclear data and fuel modeling parameters in the simulation of pressurized water reactors (PWRs) that can be incorporated in the conventional LWR simulation approach. More specifically, the Three Mile Island Unit 1–related exercises from the LWR-UAM benchmark have been modeled using the coupled TRACE/PARCS code system in the three-dimensional core representation. The input uncertainties of the neutronics simulation include few-group cross sections and kinetics parameters generated using the Sampler/Polaris sequence of SCALE 6.2.1. Several heat transfer–related variables for the fuel modeling were considered as sources of input uncertainty of the thermal-hydraulics simulations, including the thermal conductivity of fuel and cladding, fuel heat capacity, and the gap conductance. Dakota was used to sample input parameters of the coupled code system and to perform the uncertainty analysis. Two types of simulations were conducted: steady-state calculation at hot full-power condition and transient scenario initiated by the spatially asymmetric rod ejection accident. Quantities of interest for the steady-state calculation, including core multiplication factor and power peaking factors, were calculated with associated uncertainties. For transient calculations, best-estimate plus uncertainty results of the time evolution of core reactivity, core power, and peak fuel temperature were generated and analyzed. The Wilks’ formula was used to determine the necessary sample size to achieve a 95% confidence of the 95% limit of output quantities of interest. Although the uncertainty propagation and quantification method presented in this paper was developed for PWRs, it could be in general applicable to the multiphysics uncertainty quantification of other types of LWR cores.

Quantification and propagation of neutronics uncertainties of the Kozloduy-6 VVER-1000 fuel assembly using SCALE 6.2.1 within the NEA/OECD benchmark for uncertainty analysis in modelling of LWRs

Challenges and progress of uncertainty analysis for the pebble-bed high-temperature gas-cooled reactor

Uncertainty analysis in Modelling (UAM) for Design, Operation and Safety Analysis of Sodium-cooled Fast Reactors (SFRs) has been formed by OECD/NEA to assess the effect of nuclear data uncertainties on parameters of interest in SFR analysis. In this paper, sub-exercises of a medium 1000 MWth metallic core (MET-1000) and a large 3600 MWth oxide core (MOX-3600) are tested by a Monte Carlo code MCS to perform uncertainty analysis. Classical perturbation theory and generalized perturbation theory are used to calculate sensitivity coefficients. Uncertainty is calculated by multiplying the sensitivity coefficients and relative covariance matrix from ENDF/B-VII.1 library.

Nuclear data uncertainty and sensitivity analysis of the VHTRC benchmark using SCALE

To validate new nuclear cross-section evaluations and computational methods, a large number of benchmark experiments were performed in the past. The Organisation for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) launched several projects aiming to collect, preserve, and disseminate the benchmark data in a user-friendly format. Reactor physics benchmarks are covered by the International Reactor Physics Experiments (IRPhE) project. This paper presents the preparation of the IRPhE compilation for the KRITZ-2 critical experiments, consisting of altogether six configurations, both UO2 and mixed oxide, measured at two different temperatures at Studsvik. These configurations were selected for the purpose of the OECD/NEA uncertainty analysis in modeling benchmark activities. Uncertainties due to input data uncertainties, modeling errors, and numerical approximations were studied, with particular emphasis on the uncertainties in the nuclear cross-section data. The SUSD3D sensitivity-uncertainty code with the SCALE-6.0, JENDL-4, and/or JENDL-3.2 covariance data were used in this study. The consistency among the calculated-to-experiment values and the overall computational uncertainties is discussed.

Although environmental processes at large scales are to a great degree the resultant of processes at smaller scales, models representing these processes can vary considerably from scale to scale. There are three main reasons for this. Firstly, different processes dominate at different scales, and so different processes are ignored in the simplification step of the model development. Secondly, input data are often absent or of a much lower quality at larger scales, which results in a tendency to use simpler, empirical models at the larger scale. Third, the support of the inputs and outputs of a model changes with change of scale, and this affects the relationships between them. Given these reasons for using different models at different scales, application of a model developed at a specific scale to a larger scale should be treated with care. Instead, models should be modified to suit the larger scale, and for this purpose uncertainty analyses can be extremely helpful. If upscaling disturbed the balance between the contributions of input and model error to the output error, then an uncertainty analysis will show this. Uncertainty analysis will also show how to restore the balance. In practice, application of uncertainty analysis is severely hampered by difficulties in the assessment of input and model error. Knowledge of the short distance spatial variability is of paramount importance to input error assessment with a change of support, but current geographical databases rarely convey this type of information. Model error can only be estimated reliably by validation, but this is not easy because the support of model predictions and validation measurements is usually not the same.

Event Abstract Back to Event Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis Olivia Eriksson1, 2*, Alexandra Jauhiainen1, 3, Sara Maad Sasane4, Anu G Nair5, Carolina Sartorius4 and Jeanette Hellgren Kotaleski2, 5, 6 1 Contributed equally to this work, Sweden 2 Stockholm University, Department of Numerical Analysis and Computer Science, Sweden 3 AstraZeneca AB R&D, Early Clinical Biometrics, Sweden 4 Lund University, Centre for Mathematical Sciences, Sweden 5 KTH Royal Institute of Technology, School of Computer Science and Communication, Sweden 6 Karolinska Institute, Department of Neuroscience, Sweden Computational dynamical models describing intracellular signaling pathways of nerve cells are increasing in size and complexity as more information is obtained from experiments. Models describing protein interactions within neurons can contain over hundred protein reactions [1, 2]. These models are built from knowledge about the interaction topology, inferred from e.g. gene knock-out experiments, as well as from experimental quantitative data describing the input-output relationship of the observed system. The quantitative data are often sparse as compared to the size of the system, and translating the experimental information into dynamical models often results in large uncertainties in the parameter (e.g reaction rates) values. This uncertainty is partly due to the sparseness in experimental time series data (practical unidentifiability), but it is also an intrinsic feature of the modeled system (structural unidentifiability) and could reflect the possibility for biological variation [3]; in many biological systems the same function can be achieved in partly different ways due to degeneracy and redundancy. Here we investigate the extent of this parameter uncertainty, in a model describing calcium (Ca)-dependent activation of Calmodulin (CaM), Protein phosphatase 2B (PP2B) and Ca/CaM-dependent protein kinase II (CamKII) [4], which is an intracellular pathway of importance to synaptic plasticity. We presume that the structure of the model is correct and then characterize the uncertainty in the parameters based on data. This is done by sampling the subspace of parameter values which has an equally good fit to data (corresponding to the “viable space” in [5]), through a statistical approach known as Approximate Bayesian Computation (ABC) with Markov Chain Monte Carlo (MCMC) [6]. ABC has been proposed for parameter estimation in system biology models previously, albeit in slightly different settings, e.g. [7, 8], and can be applied to a wide range of problems. In order to characterize the viable space efficiently with several experimental datasets, we employ multivariate probability distributions called copulas as a part of the ABC sampling. The result is a multivariate posterior distribution for the parameters, which represents how much they are constrained by the data (i.e. the uncertainty) as illustrated in Figure 1 (pairwise plots of viable space for four parameters indicating constraints and dependencies before and after calibration to data). The next step is to look into how the parameter uncertainty is translated to uncertainty of the predictions made from the model. We also investigate the role and importance of different parameters, with respect to different model outputs including the predictions, by means of global sensitivity analysis [9]. Figure 2 illustrates the sensitivity of one of the outputs calculated by a method based on the decomposition of the variance [10, 11, 12], showing different types of sensitivity measures. Finally, we explore how the sensitivity of different subsets of parameters change as different parts of the viable space are investigated, which is shown in Figure 3, where sensitivity profiles are clustered into groups with different sensitivity characteristics. Figure 1 Figure 2 Figure 3 Acknowledgements This research was supported by funding from the Swedish e-Science Research Centre and the Human Brain Project References [1] Gutierrez-Arenas O, Eriksson O, Hellgren Kotaleski J (2014) Segregation and Crosstalk of D1 Receptor-Mediated Activation of ERK in Striatal Medium Spiny Neurons upon Acute Administration of Psychostimulants. PLoS Comput Biol 10, e1003445. [2] Nair AG, Gutierrez-Arenas O, Eriksson O, Vincent P, and Hellgren Kotaleski J (2015) Sensing Positive versus Negative Reward Signals through Adenylyl Cyclase-Coupled GPCRs in Direct and Indirect Pathway Striatal Medium Spiny Neurons. J. Neuroscience 35, 14017-14030. [3] Marder E, Goeritz ML, Otopalik AG (2015) Robust circuit rhythms in small circuits arise from variable circuit components and mechanisms. Curr Opin Neurobiol 31, 156-163. [4] Nair AG, Gutierrez-Arenas O, Eriksson O, Jauhiainen A, Blackwell KT and Kotaleski, JH (2014). Modeling intracellular signaling underlying striatal function in health and disease. Progress in molecular biology and translational science, 123, 277 [5] Zamora-Sillero E, Hafner M, Ibig A, Stelling J, and Wagner, A. (2011). Efficient characterization of high-dimensional parameter spaces for systems biology. BMC systems biology 5, 142. [6] Marjoram P, Molitor J, Plagnol V, and Tavare S (2003) Markov chain Monte Carlo without likelihoods. Proc. Natl. Acad. Sci. U.S.A. 100, 15324–15328. [7] Toni T, Welch D, Strelkowa N, Ipsen A, and Stumpf MP. Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface, 6, 187–202. [8] Liepe J, Kirk P, Filippi S, Toni T, Barnes CP, and Stumpf MP. A framework for parameter estimation and model selection from experimental data in systems biology using approximate Bayesian computation. Nat Protoc, 9, 439–456. [9] Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Saisana M, Tarantola S Global sensitivity analysis: the primer. In Wiley 2008 New York, NY:Wiley. [10] Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates, Math. Comput. Simul. 55, 271–280. [11] Saltelli A (2002) Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm 145, 280 – 297. [12] Halnes G, Ulfhielm E Ljunggren EE, Kotaleski JH and Rospars JP (2009) Modelling and sensitivity analysis of the reactions involving receptor, G-protein and effector in vertebrate olfactory receptor neurons. Journal of computational neuroscience 27, 471-491. Keywords: sensitivity analysis, Approximate Bayesian Computation, copulas, intracellular signalling, Dynamical Modeling, global sensitivity analysis, Markov chain Monte Carlo, variance decomposition Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Computational neuroscience Citation: Eriksson O, Jauhiainen A, Maad Sasane S, Nair A, Sartorius C and Hellgren Kotaleski J (2016). Statistical uncertainty and sensitivity analysis of intracellular signaling models - through approximate Bayesian computation and variance based global sensitivity analysis. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00014 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 31 May 2016; Published Online: 18 Jul 2016. * Correspondence: PhD. Olivia Eriksson, Contributed equally to this work, Stockholm, Sweden, olivia@kth.se Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Google Scholar Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski PubMed Olivia Eriksson Alexandra Jauhiainen Sara Maad Sasane Anu G Nair Carolina Sartorius Jeanette Hellgren Kotaleski Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Watershed-scale water quality (WWQ) models are now widely used to support management decision-making. However, significant uncertainty in the model outputs remains a largely unaddressed issue. In recent years, Markov Chain Monte Carlo (MCMC), a category of formal Bayesian approaches for uncertainty analysis (UA), has become popular in the field of hydrological modeling, but its applications to WWQ modeling have been rare. This study systematically evaluated the applicability of MCMC in assessing the uncertainty of WWQ modeling, using Differential Evolution Adaptive Metropolis (DREAM(ZS)) and SWAT as the representative MCMC algorithm and WWQ model, respectively. The nitrate pollution in Newport Bay watershed was the case study for numerical experiments. It has been concluded that the efficiency and effectiveness of a MCMC algorithm would depend on some critical designs of the UA, including: (i) how many and which model parameters to be considered as random in the MCMC analysis; (ii) where to fix the non-random model parameters; and (iii) which criteria to stop the Markov Chain. The study results also indicate that the MCMC UA has to be management-oriented, that is, management objectives should be factored into the designs of the UA, rather than be considered after the UA.

Ex. I-2a is Uncertainty Analysis in Modelling (UAM) of stand-alone thermal-hydraulics in steady state. It belongs to IAEA Coordinated Research Project (CRP). In this paper, the work is divided into two steps. Firstly, a single pebble model is developed based on Multiphysics Object Oriented Simulation Environment (MOOSE). The model includes two regions: homogeneous fuel region and shell region. One physical field is concerned: solid temperature field. The field is solved in a Jacobian-free Newton–Krylov (JFNK) way in the MOOSE framework. Secondly, perturbation of thermal parameters is done. In this paper, helium coolant temperature, convective heat transfer coefficient, power density and solid conductivity are the main thermal parameters which are concerned. Different kinds of perturbation of thermal parameters are conducted. Thus, variation of temperature profile across the pebble, Doppler temperature, moderator temperature and maximum temperature could be got.

SCWR (supercritical water cooled reactor) is one of the Generation IV reactors. This review summarizes the results of SCWR design concept development through numerical simulations carried out by the author-led team at the University of Tokyo and Waseda University from 1989 to 2014. They are core design, subchannel analysis, statistical thermal design, fuel rod design, development of fuel integrity criteria, plant system and heat balance, plant dynamics analysis, plant control, startup system, stability analysis, safety principle, safety criteria, safety analysis, transient subchannel analysis and fast reactor SCWR. A brief summary of experimental results on thermal hydraulics, materials and water chemistry follows. Discussion includes SCPR study by Japanese BWR manufacturers, comments on the 2005 INEEL SCWR report, misconceptions about SCWR and commercialization challenges. The SCWR is an innovation in light water reactors based on supercritical coal-fired power plant technology that has been in use worldwide for over half a century. This review covers most of the SCWR design and analysis. For researchers, it is a good subject to understand the design and analysis of light water reactors.

Development Status of Accident-tolerant Fuel for Light Water Reactors in Korea

The sodium-cooled fast reactor (SFR) is a potential candidate for the future production of clean sustainable energy. Some SFR designs planned for construction will use high-assay low-enriched uranium (HALEU) metal fuel enriched up to around 19.75%. However, fast reactor technology faces several criticisms, such as its ability to produce weapons-grade plutonium, the possibility of facility diversion from peaceful use to the production of nuclear weapons–usable materials, and the risk of incentivizing the construction of domestic fuel enrichment programs. To compete with traditional light water reactors (LWRs), SFR technology utilizing HALEU fuel should be developed to be proliferation-resistant and sustainable. In this study, the Serpent 2 Monte Carlo reactor physics code was used to simulate and compare alternative HALEU fuel options that could be implemented to reduce proliferation risk. As part of the comparison, nonpeaceful plutonium diversion pathways were considered. By evaluating its attractiveness for diversion from peaceful use to the production of nuclear weapons–usable material, it was shown that the proliferation resistance of SFR technology utilizing HALEU fuel can be improved. The operation of a once-through fuel cycle SFR utilizing HALEU fuel was simulated, and the performance and material attractiveness of various U-10Zr fuel options were compared. Currently, hundreds of thousands of tons of spent fuel from the operation of LWRs are stored across the world. Most of the heavy metal in this spent nuclear fuel is comprised of reusable uranium and plutonium. Re-enrichment of reprocessed uranium (RepU), with or without the presence of unseparated 237Np, for the production of SFR fuel is one way to simultaneously improve uranium resource utilization and enhance proliferation resistance due to the co-enrichment of 236U and 237Np. The presence of these isotopes in fresh HALEU fuel can increase 238Pu production even at low reactor burnup. Due to its high decay heat and spontaneous neutron emission, 238Pu decreases material attractiveness for nuclear weapons construction. Directly doping fresh fuel with preseparated 237Np requires the separate storage of neptunium, introducing its own nuclear security requirements and proliferation risks. Additionally, due to uncertainty in the separation factor between RepU and neptunium, some neptunium impurities will inevitably remain in RepU following separation. Therefore, this study examined the impact of unseparated 237Np on the production and depletion of U-10Zr fuel. A parametric study comparing fuel options of varying 237Np weight fractions was conducted, and proliferation scenarios considering both clandestine and overt diversion of discharged fuel were considered.

Objective: The relationship between health level (status) and economic level is an important research area in health economics literature, and countries with above-average health status indicators that have healthy economic indicators as well are generally accepted. The aims of the present study were to determine the position of countries based on their health status and economic indicators, to rank the performance of countries with respect to both groups of indicators, to observe the changes in and the relationship between health and economic performance ranking, and to examine the relationship between health and macroeconomic performance scores using correlation analysis. Materials and methods: Multidimensional scaling was used to determine the countries’ position, and the Technique for Order of Preference by Similarity to Ideal Solution method was used to rank the country’s net performance according to health status and economic indicators. The study uses horizontal data for 2016. Economic data were obtained from the International Monetary Fund, and each of the country’s health status indicators was obtained from the World Health Organization and Organisation for Economic Co-operation and Development (OECD) Health Data Bank. Results: Macroeconomic performance ranking results showed that while Ireland performed best, Turkey performed worst among OECD countries. Health status performance ranking results ranked Japan as first and Turkey as last. Additionally, a positive, moderately significant correlation between macroeconomic and health status indicators was obtained. Conclusion: Currently, especially with aging populations, various problems have arisen in the health status of societies, affecting the general level of health in the society and economic structure. Therefore, health services for the elderly can play a role in improving health status and economic level. Cite this article as: Özsarı H, Boz C. Comparison of Health Status and Macroeconomic Indicators in Organization for Economic Cooperation and Development Countries Using Multidimensional Scaling and TOPSIS. Journal of Health Science and Profession 2019; 6(3): 545-54.

The paper provides a brief historical background on the formation and development of ecotoxicology as a science, reflects the main modern methods and principles for studying the acute toxicity of xenobiotics for representatives of aquatic and terrestrial ecosystems recommended by the OECD (Organization for Economic Cooperation and Development). The classification of acute ecotoxicity of chemicals for land and water test systems is given. Further perspective development of the unit, which will be aimed at expanding ecotoxicological research in accordance with international OECD methods and GLP requirements, has been outlined. Aim. Revealing the main methods and principles recommended by the OECD for determining acute toxicity for biological objects of aquatic and terrestrial ecosystems and putting these methods and principles into practice of the Scientific Centre. Materials and Methods. The work was based on the implementation of international OECD standards and GLP principles. The OECD public electronic library of methods, particularly section 2 of the Instructions for Testing Chemicals, was used and analysed. Results and Conclusions. International methods for determining the acute toxicity of pollutants for non-target environmental objects were put into practice in the Scientific Centre, such as OECD 201 (Freshwater Alga and Cyanobacteria, Growth Inhibition Test); OECD 202 (Daphnia sp. Acute Immobilisation Test); OECD 203 (Fish, Acute Toxicity Test); OECD 207 (Earthworm, Acute Toxicity Tests); OECD 213 (Honeybees, Acute Oral Toxicity Test); OECD 216 (Soil Microorganisms: Nitrogen Transformation Test); OECD 217 (Soil Microorganisms: Carbon Transformation Test); OECD 223 (Avian Acute Oral Toxicity Test). Systems for the quality and control of ecotoxicological studies have been developed, which made it possible to obtain national and international accreditation for the conduct of the above studies. Further activities of the department will be aimed at expanding ecotoxicological research using international OECD methods and compliance with GLP requirements, which will contribute to the development of ecotoxicological research both in the Scientific Centre and in Ukraine as a whole. Key Words: ecotoxicology, pesticides and agrochemicals, biological test systems, OECD methods, good laboratory practice (GLP).