Polynomial Chaos Expansion for Uncertainty and Sensitivity Analysis of Integral Experiment Benchmark Evaluations
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Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. Commonly, the uncertainty quantification ignores correlations between experiments that share components. Experiments such as the TEX (Thermal/Epithermal eXperiments) campaigns consist of many shared parts between experiments, such as fuel, which creates a strong correlation in their errors. While these correlations are known to exist, they are often not estimated due to the complexity of such calculations. This paper describes a software package that uses an intuitive method of determining the covariance for each of the experimental components, providing a correlation matrix for each family of parts across the multiple cases examined within a benchmark. The code uses the TEX-HEU campaign as a proof of concept, and we show that the correlations can be calculated with information commonly found in ICSBEP (International Criticality Safety Benchmark Evaluation Project) benchmarks. The estimated covariances are used in χ 2 trending studies to evaluate their impact on nuclear data validation. The covariance determination code can be easily integrated into current benchmark evaluations as well as reevaluating legacy benchmark uncertainties. Uncertainty correlation calculations should become the baseline for criticality safety integral experiment benchmarks and can now be easily calculated with the described software package.
We present an implementation of the direct one-step (D1S) methodology for shutdown dose rate (SDR) calculations in the OpenMC Monte Carlo particle transport code. In addition to being the first fully open-source D1S implementation, it is also the first to require no ad hoc source code or nuclear data library modifications. The code can seamlessly switch between production of prompt and decay photons based on a user input parameter, and the decay data needed for decay photon generation are made available through a depletion chain file, which is already used for OpenMC’s built-in depletion/activation solver. A set of Python functions significantly eases the burden of computing and applying time correction factors needed to properly account for the time dependence of radionuclide activity. To assess the accuracy of the D1S implementation, SDR calculations have been carried out for three problems: a prism of iron irradiated by 14-MeV neutrons, the ITER port plug computational benchmark, and the Frascati Neutron Generator (FNG) ITER dose rate benchmark problem from the Shielding INtegral Benchmark Archive and Database (SINBAD). For each of these problems, comparisons were made to calculations using the rigorous two-step (R2S) method. The results on the iron prism problem illustrate how the D1S method achieves superior spatial resolution compared to the R2S method without the need for spatial discretization of the activation regions. The D1S and R2S results for the ITER port plug benchmark agree well with previously reported results in the literature. While the D1S results are 10% to 15% lower than the R2S results, this may be due to stochastic uncertainty and/or spatial discretization in the R2S calculations. On the FNG dose rate benchmark problem, the D1S method produces dose rate estimates that are within 4% of the dose rates predicted using a cell-based R2S workflow. The D1S estimates of the SDR are also in reasonable agreement with the experimental measurements and show the same basic trends that have been observed in previous works. A qualitative analysis of the execution time and uncertainty for the R2S and D1S workflows suggests that the D1S method would attain a higher figure of merit.
We present the first fully open-source capabilities for shutdown dose rate (SDR) calculations of fusion energy facilities based on the Rigorous 2-Step (R2S) methodology. These capabilities have been implemented in the OpenMC Monte Carlo particle transport code, building on its existing capabilities while also leveraging new features that have been added to the code to support SDR calculations, such as decay photon source generation. Each of the individual physics components in the R2S workflow—neutron transport, activation, decay photon source generation, and photon transport—have been verified through code-to-code comparisons with MCNP6.2 and FISPACT-II 4.0. These comparisons generally demonstrate excellent agreement between codes for each of the physics components. The full cell-based R2S workflow was validated by performing a simulation of the first experimental campaign from the Frascati Neutron Generator (FNG) ITER dose rate benchmark problem from the Shielding INtegral Benchmark Archive and Database (SINBAD). For short cooling times, the dose calculated by OpenMC agrees with the experimental measurements within the stated experimental uncertainties. For longer cooling times, an overprediction of the shutdown dose was observed relative to experiment, which is consistent with previous studies in the literature. Altogether, these features constitute a combination of capabilities in a single, open-source codebase to provide the fusion community with a readily-accessible option for SDR calculations and a platform for rapidly analyzing the performance of fusion technology.
The Critical Unresolved Region Integral Experiment (CURIE) critical experiment was performed at the National Criticality Experiments Research Center (NCERC) at the Device Assembly Facility (DAF) at the Nevada Nuclear Security Sites (NNSS) in 2020. The objective of CURIE was to improve the quality of integral nuclear data in the uranium-235 ( 235 U) unresolved resonance region (URR) by performing benchmark integral experiments that were sensitive to the URR energy ranges. The CURIE experiment was evaluated for the International Criticality Safety Benchmark Evaluation Project (ICSBEP) handbook and the benchmark evaluation was accepted in 2022. The URR is a region within the intermediate neutron energy range (the intermediate energy ranges from 0.7 eV to 100 keV). The observed resonance structure in neutron cross sections is due to discrete energy levels in the nucleus and are characterized by resonance parameters. In the URR region, the resonance parameters are only partially resolved as the resolution of the experiment techniques becomes comparable to the average width of the resonances themselves, and the resonances are so close to one another that the structure cannot be determined empirically. The ENDF/B-VIII.0 and JEFF-3.3 nuclear data libraries define the URR as beginning at 2.25 keV and continuing until 25 keV. There are minimal intermediate neutron energy benchmarks available in the ICSBEP benchmark handbook, and aside from CURIE there are none that are highly sensitive in the URR energy region. There is a current need for additional experiments sensitive to the URR energy region. There is a new proposed subgroup for the Organization for Economic Co-operation and Development and Nuclear Energy Agency (OECD NEA) Working Party on International Nuclear Data Evaluation Cooperation (WPEC), so any new models or information will need experimental validation and testing. The NEA Working Party on Nuclear Criticality Safety (WPNCS) recent experimental needs and priority list includes intermediate energy 235 U and 238 U experiments, as does the recent Integral Experiments to Address Nuclear Criticality Safety Needs Meeting (May 2023). A variant on the original CURIE experiment called the Multiple Critical Unresolved Region Integral Experiment (MCURIE) is proposed to provide further investigation of the intermediate and URR energy region for uranium. MCURIE will utilize existing fuels at NCERC but use alternative moderators and reflectors to modify the neutron absorption, scattering, and fission spectra of the experiments, allowing for precise targeting of nuclear data sensitivities. The overall goal of MCURIE is to develop a framework for designing and performing integral benchmark experiments with high sensitivities in the intermediate and URR energy regions for nuclear data validation.
Integral benchmarks for criticality safety and nuclear data validation require expensive uncertainty quantification studies. Commonly, the uncertainty quantification ignores correlations between experiments that share components. Experiments such as the TEX (Thermal/Epithermal eXperiments) campaigns consist of many shared parts, such as fuel, which create a strong correlation in their uncertainties. While these correlations are known to exist, they are often not estimated due to the complexity of such calculations. This paper describes a software package that uses an intuitive method of determining the covariance for each of the experimental components, providing a correlation matrix for each family of parts across the multiple cases examined within a benchmark. The code uses the TEX-HEU campaign as a proof of concept, and we show that the correlations can be calculated with information commonly found in ICSBEP (International Criticality Safety Benchmark Evaluation Project) benchmarks. The estimated covariances are used in χ 2 trending studies to evaluate their impact on nuclear data validation. Without covariances, χ 2 per degree of freedom was calculated as 2.203 and with covariances it was 1.179. The difference shows that omitting covariance information may cause overly pessimistic bias quantifications. The covariance determination code can be easily integrated into current benchmark evaluations as well as reevaluating legacy benchmark uncertainties. Uncertainty correlation calculations should become the baseline for criticality safety integral experiment benchmarks and can now be easily calculated with the described software package.
Informal benchmarking using personal or professional networks has taken place for many years at the Kennedy Space Center (KSC). The National Aeronautics and Space Administration (NASA) recognized early on, the need to formalize the benchmarking process for better utilization of resources and improved benchmarking performance. The need to compete in a faster, better, cheaper environment has been the catalyst for formalizing these efforts. A pioneering benchmarking consortium was chartered at KSC in January 1994. The consortium known as the Kennedy Benchmarking Clearinghouse (KBC), is a collaborative effort of NASA and all major KSC contractors. The charter of this consortium is to facilitate effective benchmarking, and leverage the resulting quality improvements across KSC. The KBC acts as a resource with experienced facilitators and a proven process. One of the initial actions of the KBC was to develop a holistic methodology for Center-wide benchmarking. This approach to Benchmarking integrates the best features of proven benchmarking models (i.e., Camp, Spendolini, Watson, and Balm). This cost-effective alternative to conventional Benchmarking approaches has provided a foundation for consistent benchmarking at KSC through the development of common terminology, tools, and techniques. Through these efforts a foundation and infrastructure has been built which allows short duration benchmarking studies yielding results gleaned from world class partners that can be readily implemented. The KBC has been recognized with the Silver Medal Award (in the applied research category) from the International Benchmarking Clearinghouse.
SuperMC is a general purpose, intelligent and multifunctional, continuous energy Monte Carlo program for the design and safety evaluation of nuclear systems. It is designed to perform the comprehensive neutronics calculation, taking the radiation transport as the core and including the depletion, radiation source term/dose/biohazard, material activation and transmutation, etc. The latest version of SuperMC can perform the simulation of neutron, photon and coupled neutron and photon transport, and also equipped with the functions of automatic modeling and visualization. SuperMC has been verified by more than 2000 benchmark models and experiments including the handbook of International Criticality Safety Benchmark Evaluation Project (ICSBEP), the Shielding Integral Benchmark Archive Database (SINBAD), etc. The fusion reactor (ITER benchmark model, FDS Fusion Reactors), fast reactors (BN600, CLEAR-I), PWR reactors (HM, BEAVRS) and cases from the International Reactor Physics handbook Evaluation Program (IRPhEP) were employed for validating the comprehensive capability for reactor applications. In this paper, the validation of SuperMC based on the handbook of ICSBEP will be presented. ICSBEP, released by OECD/NEA, contains criticality safety benchmark specifications derived from experiments that were performed at various nuclear critical facilities around the world, which was widely used to verify neutronic codes and associated nuclear data libraries for criticality safety analysis. (authors)
Benchmark experiments can serve several purposes and the availability of suitable experimental data is fundamental to ensure that modelling tools meet the requirements of nuclear industry and licensing needs. Essentially, they are used for: - validation of nuclear cross-section data, - validation of nuclear codes and models used, - qualification and training of users through benchmarking and code comparison exercises. The Shielding Integral Benchmark Archive and Database (SINBAD) project was started in the early 1990's at the OECD Nuclear Energy Agency Data Bank (NEA DB) and the Radiation Safety Information Computational Center (RSICC) as a collection of quality experiments for validating and benchmarking computer codes and data for radiation transport and shielding applications. Currently, the SINBAD database comprises over 100 benchmark compilations and evaluations of relevance to: - reactor shielding, pressure vessel dosimetry (48); - fusion blanket neutronics (31); - accelerator shielding (23). In order to facilitate their use, the data are organized in the standardized format structure. The index and the master document (called abstract) use the Hyper Text Markup Language (HTML) format with links to text files, figures, Portable Document Format (pdf) documents and computer code inputs. The format allows easy access and forward/backward navigation among the data and has proved to be suitable, general enough and above all easy (and low-cost) to maintain. In addition to the characterization of the radiation source, description of the shielding set-up, the instrumentation and the relevant detector measurements, most sets in SINBAD contain also the deterministic or Monte Carlo radiation transport computer model used for the interpretation of the experiment and, where available, results from uncertainty analysis. The set of primary documents used for the benchmark compilation and evaluation are provided in computer readable form. The database is intended for different types of users, including nuclear data evaluators, computer code developers, experiment designers and university students. SINBAD is available from the NEA Data Bank and RSICC (see https://www.oecdnea.org/science/wprs/shielding/sinbad/). Up to now several hundreds of SINBAD packages were distributed from the NEA DB and RSICC. Since 2011 the maintenance and further development of the database is coordinated in the scope of the OECD NEA Nuclear Science Committee (NSC) Working Party on Scientific Issues of Reactor Systems (WPRS) Expert Group on Radiation Transport and Shielding (EGRTS). A key objective of the group is to identify, evaluate and preserve experimental data on shielding benchmarks. The Expert Group maintains close links with the International Reactor Physics Experiment Evaluation (IRPhE) and International Criticality Safety Benchmark Evaluation (ICSBEP) projects, as well as in co-ordination with the JEFF and EFF NEA Data Bank projects and with the SATIF community of accelerator shielding specialists. In the last years, much effort was devoted to the quality review of the available benchmark information.
For safe and reliable use of computer codes by the community, accuracy must be clearly evaluated. In particular, the nuclear reactor engineering and licensing field needs accurate tools for radiation shielding modeling. Monaco with Automated Variance Reduction using Importance Calculations (MAVRIC) is one such tool, with built-in variance reduction methods distributed within the SCALE code, and its validity is demonstrated in this report for the released version 6.2.4. Representative benchmarks corresponding to shielding analysis are selected for the validation study. Typical experimental results analyzed from those benchmarks include neutron fluxes, detector count rates, detector energy response functions, neutron and gamma doses, foil neutron activation rates and activities, neutron leakage fluxes, and skyshine dose rates. Thousands of points of comparison between experiment and calculation are presented in this work. Other than rare outliers typically explained by either a lack of information or large uncertainties in the experiment conditions, material, or dimensions, MAVRIC agrees well with the experiment results. MAVRIC is also compared to Monte Carlo N-Particle (MCNP) calculations when available, and both codes generally produce good agreements within estimated uncertainties. The selected benchmarks are obtained from reliable sources such as the International Criticality Safety Benchmark Evaluation Project Handbook (ICSBEP Handbook), the Shielding Integral Benchmark Archive & Database (SINBAD), and other shielding validation work found in the literature. Additional datapoints and benchmarks will be added to future versions of this report to incrementally expand the shielding validation suite incrementally.
Two projects sanctioned by the Organisation for Economic Co-operation and Development (OECD) Nuclear Energy Agency (NEA) have over two decades of experience established comprehensive data sets in handbooks supporting criticality safety and reactor physics. The International Criticality Safety Benchmark Evaluation Project (ICSBEP), and later the International Reactor Physics Experiment Evaluation Project (IRPhEP) that was patterned after the success of the ICSBEP, serves as an example of quality and excellence in preserving our nuclear data heritage and establishing benchmark standards upon which current and future modeling, validation, and safety efforts can be supported. Many of the best practices and lessons learned from these benchmark projects can be adopted and adapted for use with the Shielding Integral Benchmark Archive and Database (SINBAD) to prepare higher quality shielding benchmark data to effectively expand the availability of qualified experimental data available to the nuclear community. The unique experiments performed and aggregated within SINBAD represent characteristic measurements, techniques, and applications not captured with the specificity of nuclear criticality safety or traditional reactor physics applications. Application of evaluated SINBAD benchmark data would challenge and enhance our current nuclear data and modeling and simulation strategies. (authors)
From the countless critical experiments performed in the world during the past century, high-quality integral benchmarks experiments have been collected and gathered into the International Handbook of Evaluated Criticality Safety Benchmark Experiments (ICSBEP Handbook), managed by the International Criticality Safety Benchmark Evaluation Project (ICSBEP) Working Group. This information preservation and dissemination effort is crucial for reactor licensing as well as criticality and radiation transport modeling validation. This summary reports on the status of a tentative benchmark addition to the ICSBEP Handbook. The proposed benchmark arises from legacy operation data of the Oak Ridge National Laboratory (ORNL) Health Physics Research Reactor (HPRR). The HPRR was a small, unmoderated, unshielded fast burst reactor that was used for research in health physics and radiobiology as well as teaching and training. As part of a comprehensive investigation of the available HPRR operation data and characteristics, different possibilities for use of the valuable results were studied. A critical experiment benchmark evaluation was performed, analyzing data coming from sub-critical and critical operation of the HPRR during operator training, steady-state irradiation of samples and before critical bursts. The results of the evaluation do not satisfy for the ICSBEP standards as the benchmark relative standard uncertainty is of about 4% for k eff , and the relative difference between sample calculations and expected k eff results is of about 1.5%. Due to those unsatisfactory results, it was decided not to pursue critical experiments evaluation of the HPRR presently and to focus instead on shielding type data for the creation of a criticality accident alarm system (CAAS) and shielding category benchmark, which is currently very scarce in the ICSBEP handbook—especially concerning critical, pulsed assembly, or reactor operation data. Several dosimetry and shielding experiments from HPRR burst operation were evaluated, with different benchmark metrics as sulfur fluence, Element 57 dose, or neutron fluence at different distances and under different shield materials conditions. An evaluation focusing on the Element 57 neutron dose as a benchmark metric was submitted to the ICSBEP Technical Review Group (TRG) meeting in October 2021, and the inclusion of the evaluation in the ICSBEP Handbook was deferred. The main change proposed by the international experiment evaluation experts is to use the neutron fluence measured by Bonner spheres as a benchmark metric. This represents a quantity closer to that actually measured by the experimentalists of the HPRR compared to the Element 57 dose, which adds another step of data transformation, thus potentially adding uncertainty to the benchmark. The evaluation has been updated and will be submitted to the 2022 ICSBEP TRG meeting for inclusion in the 2023 edition of the ICSBEP Handbook. The evaluation is performed using the KENO and MAVRIC combination from the SCALE 6.2.4 code suite which was previously used in similar CAAS benchmarks to allow for the use of variance reduction techniques.
The measurements of neutron spectra compiled inside the NEA-1517/82 package from the Shielding Integral Benchmark Archive and Database (SINBAD) are chosen as benchmark cases to validate the variance reduction technique based on weight window in Monte Carlo Code MCS. A full 3D model for fixed source mode calculation with hexagonal lattice source definition is developed to simulate total of 6 points of measurements at the vicinity of the reactor and the reactor pressure vessel region. A code/code comparison against MCNP6 code is first conducted as verification element for the mesh-based weight window capability in MCS. Finally, the validation results are presented against measurements. The verification against MCNP6 code gives good agreement in addition of the insight to the importance of user understanding to determine proper reference point and reference lower weight bound for scaling which is not required in MCS code due to its capability of automatic scaling. The comparison of neutron spectra between MCS and measurements shows good agreement within 3 standard deviations for all of six detector positions.
This report presents a review of available radiochemical assay data and shielding benchmarks applicable to spent nuclear fuel (SNF) shielding calculations. The relevant information reviewed herein includes the Spent Fuel Composition (SFCOMPO) database, the Shielding Integral Benchmark Archive and Database (SINBAD), the International Handbook of Evaluated Criticality Safety Benchmark Experiments, and published measurements of external dose rates of casks loaded with SNF. The relevant experimental data identified in this report may be used to support verification and validation of computer codes used in SNF cask/transport shielding applications, as well as development of calculation uncertainties. It should be noted that a relatively small subset of the identified experimental data (e.g., criticality alarm experiments) is available in a standard format established by the international community participating in experimental isotopic and shielding data evaluations. An effort of the SFCOMPO Technical Review Group (TRG) is underway to publish first isotopic evaluations of individual assay data using a standard data evaluation format. The SINBAD TRG has recently initiated benchmark evaluations and modernization of the database. Therefore, more relevant information is expected in the future that will enable users to select quality experimental data in depletion code and shielding code validations for SNF applications.
Evaluations of nuclear reaction data for the major uranium isotopes 238 U and 235 U were performed within the scope of the CIELO Project on the initiative of the OECD/NEA Data Bank under Working Party on Evaluation Co-operation (WPEC) Subgroup 40 coordinated by the IAEA Nuclear Data Section. Both the mean values and covariances are evaluated from 10 -5 eV up to 30 MeV. The resonance parameters of 238 U and 235 U were re-evaluated with the addition of newly available data to the existing experimental database. The evaluations in the fast neutron range are based on nuclear model calculations with the code EMPIRE–3.2 Malta above the resonance range up to 30 MeV. 235 U(n,f), 238 U(n,f), and 238 U(n,γ) cross sections and 235 U(n th ,f) prompt fission neutron spectrum (PFNS) were evaluated within the Neutron Standards project and are representative of the experimental state-of-the-art measurements. The Standards cross sections were matched in model calculations as closely as possible to guarantee a good predictive power for cross sections of competing neutron scattering channels. 235 U(n,γ) cross section includes fluctuations observed in recent experiments. 235 U(n,f) PFNS for incident neutron energies from 500 keV to 20 MeV were measured at Los Alamos Chi-Nu facility and re-evaluated using all available experimental data. While respecting the measured differential data, several compensating errors in previous evaluations were identified and removed so that the performance in integral benchmarks was restored or improved. Covariance matrices for 235 U and 238 U cross sections, angular distributions, spectra and neutron multiplicities were evaluated using the GANDR system that combines experimental data with model uncertainties. Unrecognized systematic uncertainties were considered in the uncertainty quantification for fission and capture cross sections above the thermal range, and for neutron multiplicities. Evaluated files were extensively benchmarked to ensure good performance in reactor calculations and fusion-related systems. New comprehensive evaluations show excellent agreement with available differential data and integral performance better than current evaluated data libraries, and represent a step forward in a quest for better nuclear data for applications.
A myriad of opportunities is available to collaborate via international benchmark exercises and experimental data preservation activities. Many such opportunities abound under the auspices of the Nuclear Science Committee of the Organisation for Economic Co-operation and Development Nuclear Energy Agency (NEA). Key projects and activities of relevance to the development of advanced reactors design include the International Criticality Safety Benchmark Evaluation Project (ICSBEP), the International Reactor Physics Experiment Evaluation Project (IRPhEP), the International Assay Data of Spent Nuclear Fuel Database (SFCOMPO), the Shielding Integral Benchmark and Archive Database (SINBAD), and The International Experimental Thermal HYdraulicS Database (TIETHYS), and various cooperative benchmark exercises. Interested participants are encouraged to contact the leadership and secretariat of the various Technical Working Groups and Working Parties to become more engaged. This paper provides a summary of the current benchmark exercises and experimental databases available for international participation.
The intent of this work is to highlight the role of differential and integral data evaluation to address issues in connection with criticality safety applications. Demonstration is made by using, as an example, differential data measurements and evaluation, and the benchmark integral experiments for titanium. Energy differential data are measured analyzed and evaluated to produce nuclear data libraries for criticality safety applications. Alternatively, integral experiments are performed at critical facilities, small experimental reactors, and play an important part in the validation of the differential nuclear data. The demonstration provided here for titanium gives its importance to criticality safety. Titanium is an effective neutron absorber that serves as baseline material for chemical separation in high-activity waste solutions in US. Titanium has not been considered for use in nuclear applications such as reactor design and analysis. Rather, it appears as a structural material that may be present in fuel cycle facilities or canisters for transport and disposition of nuclear waste. Criticality safety evaluations of systems in which titanium is present require an understanding of the nuclear data and its uncertainty.
The OECD Nuclear Energy Agency (NEA) Working Party on International Nuclear Data Evaluation Cooperation (WPEC) was established in 1989 to facilitate collaboration in nuclear data activities. Over its thirty year history, different Subgroups have been created to address topics in nearly every aspect of nuclear data, including: experimental measurements, evaluation, validation, model development, quality assurance of databases and the development of software tools. WPEC has recently completed activities on fission yield evaluation, the general nuclear database structure (GNDS) to replace the ENDF-6 format, methods to provide feedback to evaluation, studies of specific capture cross sections, new methods in thermal scattering kernel evaluation and the Collaborative International Evaluated Library Organisation (CIELO) Pilot Project. Ongoing activities in GNDS application programming interface (API) development, methods for covariance evaluation and quality assurance in nuclear data validation using the International Criticality Safety Benchmark Evaluation Project (ICSBEP) database are complemented by the work of two Expert Groups that oversee the High-Priority Request List (HPRL) for Nuclear Data and the continuous development of the GNDS. New activities on the use of integral experiments for nuclear data validation and adjustment, as well as the use of the Shielding Integral Benchmark Archive and Database (SINBAD) for validation have begun and will be coordinated alongside future Subgroups. After three decades we will review the status of WPEC, how it integrates other collections and activities organised by the NEA and how it dovetails with the initiatives of the IAEA and other bodies to effectively coordinate international activities in nuclear data.