Covariance Library Research Articles

Development of uncertainty quantification module for VVER analysis in STREAM/RAST-V two-step method

This paper introduces the creation of a module for Uncertainty Quantification (UQ) specifically designed for VVER analysis through the implementation of the STREAM/RAST-V two-step approach. The aim was to expand the range of use by developing a UQ module tailored for analyzing VVER. This research presents two innovative computational functionalities: (1) development of a library for the pin-based pointwise energy slowing down method (PSM), and (2) extension of the analysis area to study hexagonal-geometry fuel assemblies. The proposed UQ scheme was evaluated through verification using UAM benchmark, and comparative analysis between codes using SCALE 6.2.2 for. STREAM provides an accuracy comparable to that of SCALE 6.2.2. Additionally, a PSM covariance library was utilized in the calculations, achieving 0.7941% and 0.7907% accuracies in the hot full power and hot zero power calculations, respectively. To assess the UQ sequences in the two-step method, the STREAM/RAST-V calculation scheme was verified using the STREAM lattice code. To conclude, this study furnishes comprehensive insights into the development of the UQ module within the two-step method for VVER analysis, and it validates its performance through utilization of the UAM benchmark.

Uncertainty analysis of UAM TMI-1 benchmark by STREAM/RAST-K

This study rigorously examined uncertainty in the TMI-1 benchmark within the Uncertainty Analysis in Modeling (UAM) benchmark suite using the STREAM/RAST-K two-step method. It presents two pivotal advancements in computational techniques: (1) Development of an uncertainty quantification (UQ) module and a specialized library for the pin-based pointwise energy slowing-down method (PSM), and (2) Application of Principal Component Analysis (PCA) for UQ. To evaluate the new computational framework, we conducted verification tests using SCALE 6.2.2. Results demonstrated that STREAM's performance closely matched SCALE 6.2.2, with a negligible uncertainty discrepancy of ±0.0078% in TMI-1 pin cell calculations. To assess the reliability of the PSM covariance library, we performed verification tests, comparing calculations with Calvik's two-term rational approximation (EQ 2-term) covariance library. These calculations included both pin-based and fuel assembly (FA-wise) computations, encompassing hot zero-power and hot full-power operational conditions. The uncertainties calculated using both the EQ 2-term and PSM resonance treatments were consistent, showing a deviation within ±0.054%. Additionally, the data compression process yielded compression ratios of 88.210% and 92.926% for on-the-fly and data-saving approaches, respectively, in TMI fuel assembly calculations. In summary, this study provides a comprehensive explanation of the PCA process used for UQ calculations and offers valuable insights into the robustness and reliability of newly developed computational methods, supported by rigorous verification tests.

Summary of comparative analysis and conclusions from OECD/NEA LWR-UAM benchmark Phase I

In recent years, large efforts have been devoted to Light Water Reactor (LWR) Uncertainty Quantification (UQ). In 2006, the LWR Uncertainty Analysis in Modeling (UAM) benchmark was launched with an aim to investigate the uncertainty propagation in all modeling stages of the LWRs and guide uncertainty and sensitivity analysis methodology development. This article summarizes the benchmark activities for the standalone neutronics phase (Phase I), which includes three main exercises: Exercise I-1: “Cell Physics,” Exercise I-2: “Lattice Physics,” and Exercise I-3: “Core Physics.” A comparative analysis of the Phase I results is performed in this article for all the considered LWRs types: Three Mile Island – 1 Pressurized Water Reactor (PWR), Peach Bottom – 2 Boiling Water Reactor (BWR), Kozloduy – 6 Water - Water Energetic Reactor (VVER) and a Generation-III reactor. It was found, for all major exercises, that the predicted uncertainty of the system eigenvalue is highly dependent on the choice of the covariance libraries used in the UQ process and is less sensitive to the solution method, nuclear data library and UQ method. For all four reactor types, the observed relative standard deviation across all exercises is approximately 0.5% for the UO2 fuel. In the pin cell and lattice calculations with MOX fuel this uncertainty increases to 1%. The main reason is the larger Pu-239 nu-bar uncertainty compared to the U-235 nu-bar. The largest contributors to the eigenvalue uncertainties are the U-235 nu-bar and the U-238 capture in the UO2 fuel and the Pu-239 nu-bar in the MOX fuel. In the assembly lattice exercises, higher uncertainties are predicted for the fast group than the thermal group constants with differences up to one order of magnitude. This is attributed to the larger uncertainties of most cross-sections at high energies. The obtained correlation matrices share some common major trends but also exhibit strong differences in case by case comparisons indicating an impact of the selected neutronics modeling and nuclear data library. In the core exercises, the predicted relative standard deviation of the radial and axial power, for most of the cores, is below 10%. An exception is the radial power profile of the Generation-III core, when a mixture of UOX/MOX assemblies is considered. Finally, it is important to note that the bias in most of the studies is significant and up to the same order of the estimated uncertainty. This indicates a need for better quantification of the bias/variance through more code to code and code to experiments comparisons.

Uncertainty comparison between ENDF/B-VIII.0 and ENDF/B-VII.1 for fast reactor BN-600 using high-precision sampling method

A method of using small samples to achieve high-precision related variable sequence sampling was proposed. This method mainly uses two techniques: Latin hypercube sampling method for normal distribution and transform the covariance between variables of standard normal distribution sampling samples as unit. Applying this method, the fast reactor uncertainty analysis and sensitivity analysis program, named SUFR1.0, was developed, and conducted verification analysis. Using the NJOY2016 program, 33-group covariance libraries based on ENDF/B-VIII.0 and ENDF/B-VII.1 were developed for uncertainty and sensitivity analysis for fast reactors BN-600. Using the above 33-group covariance libraries, the uncertainty of the effective multiplication factor keff and the uncertainty of the power distribution of core were analyzed. It was found that the covariance matrix values between ENDF/B-VIII.0 and ENDF/B-VII.1, for some nuclides, such as 238U, 239Pu and 56Fe within some neutron energy range, are quite different. At the same time, these relatively different cross section types will also cause a large difference in the relative uncertainty of keff. For the relative uncertainty of power, the calculation result of ENDF/B-VIII.0 is significantly smaller than that of ENDF/B-VII.1.

Augmented ENDF/B-VIII.0 covariance library for SCALE 6.3

There are many challenges associated with the proper assessment, evaluation, interpretation and use of nuclear data covariance. There are even topics on which the international nuclear data community has not reached a consensus as evidenced by the formation of a subgroup of the Working Party for Nuclear Data Evaluation Cooperation (WPEC) under the auspices of the Nuclear Energy Agency (NEA) dedicated to working on problems in nuclear data covariance. One of those issues is directly reflected in the disclaimer published with the ENDF/B-VIII.0 nuclear data library. This paper documents the effort undertaken to produce an augmented ENDF/B-VIII.0 nuclear data covariance library to be distributed and used with the upcoming release of the SCALE 6.3 code package. SCALE has a history of distributing a covariance library that is an edited version of the published ENDF/B release. The demonstrated need, the approach methodology and some preliminary results were published earlier in a pair of ORNL reports. The major contribution of this paper, in the spirit of scientific transparency and reproducibility, is to carefully document the intent and procedure that were used to create the augmented ENDF/BVIII. 0 covariance library for SCALE 6.3 such that the users of SCALE are clearly informed about how the ENDF/B-VIII.0 covariance library was augmented.

BETA EFFECTIVE SENSITIVITY TO NUCLEAR DATA WITHIN THE APOLLO3® NEUTRONIC PLATFORM

In this paper, we present a sensitivity analysis of the beta effective to nuclear data for the UM17x17 experiment that has been performed in the EOLE reactor. This work is carried out using the APOLLO3® platform. Regarding the flux calculation, the standard two-step approach (lattice/core) is used. For what concerns the delayed nuclear data, they are processed to be directly used in the core calculation without going through the lattice one. We use the JEFF-3.1.1 nuclear data library for cross-sections and delayed data. The calculation of k-effective and beta effective is validated against a TRIPOLI4® one while the main sensitivities are validated against direct calculation. Finally, uncertainty propagation is performed using the COMAC-V2.0 covariance library.

IMPACT OF VARIOUS SOURCE OF COVARIANCE INFORMATION ON INTEGRAL PARAMETERS UNCERTAINTY DURING DEPLETION CALCULATIONS WITH CASMO-5

This paper describes the effect of input uncertainties on a set of integral parameters (kinf, nuclide compositions) associated with the validation of CASMO-5 against PIE data. The nuclear data under consideration are the cross-sections, fission spectrum and neutron multiplicities and fission yields. Various sources of covariance information are considered, novel ones (ENDFB-VIII.0, JEFF-3.3) as well as more widely distributed ones (JENDL-4.0, ENDF/B-VII.1, Scale 6.1 and Scale 6.2). All possible nuclide reaction pairs (cross sections, fission spectrum and averaged number of neutron per fission) have been perturbed, e.g. all isotopes available in both the respective covariance libraries and the CASMO-5 library. The evolution of the uncertainty estimates with exposure is complemented with sensitivity analysis to determine the main contributors to the uncertainty. The Pearson coefficient defined between the model output and a given input is used in this work to assess the part of the variance in the model output coming from the considered input uncertainty. It is a very promising measure of sensitivity as it is computationally cheap even though it assumes linearity of the output with respect to input perturbations. The evolution of the uncertainty with exposure, both in terms of trends and magnitude are however very different. Sensitivity analysis allows determining why the trends and magnitudes are different.

Sensitivity and uncertainty analyses of a high temperature gas-cooled reactor by using a 44-group covariance library

Sensitivity and uncertainty analyses of the effective neutron multiplication factor (keff) were conducted for the High Temperature Engineering Test Reactor (HTTR) using the ENDF/B-VII.1 nuclear data and the 44-group covariance library provided in the Whisper-1.1. Amongst the criticality benchmark series, the fully-loaded core was selected and analyzed by using a continuous energy Monte Carlo code, MCNP6.2. The top-five positive sensitivity coefficients (+0.1–+0.03) were found to be U-235 (total nu and fission), C-12 (elastic), graphite S(a,b) (elastic and inelastic), while the top-five negative ones (−0.1–−0.003) were U-238 (n,gamma), U-235 (n,gamma), B-10 (n,alpha), C-12 (n,gamma) and Si-28 (n,gamma). The keff uncertainty originated from the nuclear data was calculated using the previously obtained sensitivity coefficients and the 44-group covariance library. In the present S/U analysis, we obtained the keff uncertainty of about 0.5%. The JENDL-4.0 and ENDF/B-VIII.0 nuclear data were also analyzed for comparison.

Best-Estimate Plus Uncertainty Framework for Multiscale, Multiphysics Light Water Reactor Core Analysis

Tremendous work has been done in the Light Water Reactor (LWR) Modelling and Simulation (M&S) uncertainty quantification (UQ) within the framework of the Organization for Economic Cooperation and Development (OECD)/Nuclear Energy Agency (NEA) LWR Uncertainty Analysis in Modelling (UAM) benchmark, which aims to investigate the uncertainty propagation in all M&S stages of the LWRs and to guide uncertainty and sensitivity analysis methodology development. The Best-Estimate Plus Uncertainty (BEPU) methodologies have been developed and implemented within the framework of the LWR UAM benchmark to provide a realistic predictive simulation capability without compromising the safety margins. This paper describes the current status of the methodological development, assessment, and integration of the BEPU methodology to facilitate the multiscale, multiphysics LWR core analysis. The comparative analysis of the results in the stand-alone multiscale neutronics phase (Phase I) is first reported for understanding the general trend of the uncertainty of core parameters due to the nuclear data uncertainty. It was found that the predicted uncertainty of the system eigenvalue is highly dependent on the choice of the covariance libraries used in the UQ process and is less sensitive to the solution method, nuclear data library, and UQ method. High-to-Low (Hi2Lo) model information approaches for multiscale M&S are introduced for the core single physics phase (Phase II). In this phase, the other physics (fuel and moderator), providing feedback to neutronics M&S in a LWR core, and time-dependent phenomena are considered. Phase II is focused on uncertainty propagation in single physics models which are components of the LWR core coupled multiphysics calculations. The paper discusses the link and interactions between Phase II to the multiphysics core and system phase (Phase III), that is, the link between uncertainty propagation in single physics on local scale and multiphysics uncertainty propagation on the core scale. Particularly, the consistency in uncertainty assessment between higher-fidelity models implemented in fuel performance codes and the rather simplified models implemented in thermal-hydraulics codes, to be used for coupling with neutronics in Phase III is presented. Similarly, the uncertainty quantification on thermal-hydraulic models is established on a relatively small scale, while these results will be used in Phase III at the core scale, sometimes with different codes or models. Lastly, the up-to-date UQ method for the coupled multiphysics core calculation in Phase III is presented, focusing on the core equilibrium cycle depletion calculation with associated uncertainties.

Nuclear data sensitivity and uncertainty analysis of critical VENUS-F cores with the Serpent Monte Carlo code

In the framework of the FP7 Euratom project FREYA, the Serpent Monte Code was used to characterize a number of critical VENUS-F core configurations. Several neutronic parameters calculated by Serpent were compared to the available experimental data and reported in a previous study. Although a generally reasonable agreement between the calculated and experimental values was obtained, the study also revealed some important issues related to the modeling results such as a systematic overestimation of reactivity and a systematic underestimation of U238 to U235 fission rate ratio (designated as F28/F25 spectral index).The objective of the current follow-up study is to assess the impact of nuclear data uncertainties on the Monte Carlo estimates of reactivity and spectral indices. The analysis is carried out for two critical VENUS-F cores using a recently upgraded version of Serpent which is capable to perform sensitivity analysis, based on the collision history method and to propagate and quantify nuclear data uncertainties using multi-group covariance libraries in an automated way. The criticality calculations were performed using the ENDV/B-VII.1 based cross sections while the uncertainties due to nuclear data were obtained using 56-group neutron cross section covariance library from the SCALE-6.2 package.The estimated uncertainties due to nuclear data are of the order of 2200 pcm and 8% on k-eff and F28/F25 spectral index, respectively. It was found that the major contributor to the k-eff uncertainty is the capture cross section of U235. In the F28/F25 case, the total uncertainty is dominated by inelastic scattering cross section of U238, fission spectrum of U235, and capture cross section of U235.

Covariance comparisons between ENDF/B-VII.1 and ENDF/B-VIII.0 with application for the UAM-LWR exercises

In this study, the nuclear-data covariance data have been compared between ENDF/B-VII.1 and ENDF/B-VIII.0. Using NJOY2016.34, the multigroup cross-section covariance libraries based on ENDF/B-VII.1 and ENDF/B-VIII.0 have been generated respectively. From the direct comparisons of the covariance data between ENDF/B-VII.1 and ENDF/B-VIII.0, very notable differences can be observed in the uncertainties and correlations. Based on the multigroup cross-section covariance libraries generated from ENDF/B-VII.1 and ENDF/B-VIII.0, our home-developed UNICORN code has been applied for the uncertainty analysis. The exercises proposed by UAM-LWRs in Phase I have been chosen as the analysis exercises, including the UOX fuel pin-cells, UOX fuel assembly and MOX fuel assembly. The relative uncertainties of the eigenvalues, two-group constants and burnup-related parameters have been quantified and compared, quantifying the uncertainty differences of covariance data in ENDF/B-VII.1 and ENDF/B-VIII.0. Through analysis, the conclusions can be given that more reliable, not smaller nuclear-data covariance data can be provided in ENDF/B-VIII.0.

Nuclear-data uncertainty propagation in transient simulation for the C5G7-TD benchmark problem

In this study, uncertainty analysis has been performed to the time-dependent transient simulation of the C5G7-TD benchmark problem, propagating the nuclear-data uncertainties to the key parameters of interest. The detailed material compositions and geometries of C5G7-TD have been applied for the time-dependent transient simulation. For uncertainty analysis of the transient simulation, multigroup cross-section covariance library has been generated based on ENDF/B-VII.1 using the NJOY code. Our home-developed uncertainty-analysis code named UNICORN has been utilized for the uncertainty analysis, using the statistical sampling method. For the steady-state and transient simulations, our home-developed high-fidelity neutronics code NECP-X has been utilized. The relative uncertainties of the fuel-assembly normalized power and pin-wise power have been quantified as function of time. The numerical results show that the maximum relative uncertainties for the assembly normalized power can up to be about 2.14% and the value for the pin-wise power distributions can be about 3.54%.

Nuclear data-induced uncertainty quantification of prompt neutron decay constant based on perturbation theory for ADS experiments at KUCA

ABSTRACTIn experimental benchmarks of the accelerator-driven system (ADS) conducted at the Kyoto University Critical Assembly (KUCA), the prompt neutron decay constant was measured using two types of pulsed neutron sources, i.e. a D-T neutron source and a spallation neutron source driven by a 100-MeV proton beam. The measurement results of are useful information to validate the numerical results predicted by the prompt -eigenvalue calculation. In this study, the numerical analysis of using a multi-energy group SN neutron transport code was carried out for the uranium-lead zoned experimental cores. To reduce the discretization error owing to the deterministic code, the KUCA geometry was modelled in detail as a three-dimensional heterogeneous plate-by-plate geometry, and an improved variant of EON quadrature was utilized. In addition, the sensitivity coefficients of with respect to nuclear data were efficiently evaluated by first-order perturbation theory, followed by nuclear data-induced uncertainty quantification based on the 56 neutron-energy group SCALE covariance library. Consequently, the numerical results of were validated successfully by the experimental results of the pulsed neutron source method, compared with the range of the nuclear data-induced uncertainties.

Uncertainty quantification for the first-cycle modeling and simulations of the BEAVRS benchmark problem

In this paper, the uncertainty quantification has been implemented to the first-cycle modeling and simulations for the BEAVRS benchmark problem, propagating the nuclear-data uncertainties to the key core parameters. NJOY has been applied to generate the nuclear-data covariance library based on ENDF/B-VII.1 in the research. The statistical sampling method has been utilized for the uncertainty quantification, based on the conventional “two-step” scheme. First, the nuclear-data uncertainties are propagated to the few-group constants through the lattice modeling and simulations; and then the uncertainties of the key core parameters are quantified through the reactor modeling and simulations. As interests, the uncertainties have been quantified to the critical boron concentrations, axial-power offset and radial assembly-power distributions through the whole life of first cycle. From the numerical results, it can be observed that for the critical boron concentration, the nuclear-data introduced uncertainties can up to be 51 ppm as maximum; for the axial-power offset, the relative uncertainties vary within 1.3% and for the radial assembly-power distributions, the maximum relative uncertainties is about 3.8% at BOL and 0.8% at EOL.

Quantification and mechanism analysis of the kinf uncertainty propagated from nuclear data for the TRISO particle fuel pebble

To give a more clear picture of uncertainty propagation and quantification in the pebble bed high temperature reactor (HTR), an explicit fuel pebble model with regular lattice model of TRISO particles was built in the SCALE 6.2.1 code system to quantify the uncertainty of the infinite multiplication factor propagated from nuclear data. Based on this lattice model, a “step-by-step comparison scheme” was designed to fully understand the mechanism of the contributions of nuclear data to the total uncertainty of the infinite multiplication factor. Then the contribution difference arose from uranium loading, enrichment, temperature, material composition, position in a realistic reactor and covariance library was quantified. Some valuable observations were further drawn from the mechanism analysis. Numerical results show that the average number of neutrons emitted per fission event of 235U is the most significant contributors to the total uncertainty. Same as the light water reactor, increasing temperature leads to a decreasing multiplication factor but an increasing uncertainty. Especially that 239Pu will play a more and more important role to total uncertainty, and also the contribution of 135Xe is also not negligible, when the depletion is considered. For the realistic reactor core, the position of fuel pebble in the core not only has a significant effect on the multiplication factor and spectrum, but also on the uncertainty propagation. Finally, the difference derives from libraries is also not to be ignored.

Sensitivity methods for effective delayed neutron fraction and neutron generation time with summon

Accurate and reliable tools for sensitivity analysis and uncertainty quantification are needed to estimate the uncertainties in reactor key parameters (keff, βeff, Λeff, safety coefficients, …) and to identify possible nuclear data weaknesses. A Sensitivity and Uncertainty Methodology for MONte carlo codes (SUMMON) has been developed to calculate the sensitivities of the criticality safety parameters as well as their uncertainties due to uncertainties in nuclear data, addressing limitations of existing tools. The methodology is currently based on the use of the KSEN card of MCNP6 code to perform the eigenvalue sensitivity calculations, although any Monte Carlo code that can provide sensitivity coefficients can be used. The sensitivity coefficients of a reactivity response are calculated using the eigenvalue definition of reactivity, which is equivalent to applying the Equivalent Generalized Perturbation Theory. Moreover, the effective delayed neutron fraction sensitivity coefficients are derived from Bretscher’s approximation, whereas the sensitivity coefficients of the effective neutron generation time are obtained using the 1/v insertion method and the Equivalent Generalized Perturbation Theory. Uncertainties are propagated using the “Sandwich Rule” of the “Propagation of Moments” method employing state-of-the-art covariance libraries. The implementation in SUMMON of Bretscher’s approximation and the 1/v insertion method has been validated using integral experiments from ICSBEP and IRPhE databases, while the methods for calculating the sensitivity coefficients have been verified against consolidated codes, such as SCALE, SUSD3D, SERPENT and XSUSA and good agreement has been obtained.

Mechanism analysis of the contribution of nuclear data to the keff uncertainty in the pebble bed HTR

As one part of IAEA CRP on HTGR UAM, mechanism analysis of the contributions of nuclear data on the keff uncertainty for the pebble bed HTR core has been studied through a “step-by-step comparison scheme” and HTR-10 is chosen as the representative core model. Within this scheme, three main types of HTR-10 core states including initial critical configuration, initial core and equilibrium core, have been established by using the continuous energy module named Tsunami-3D-K6 in SCALE6.2.1 to quantify the uncertainty of keff propagated from nuclear data. Then, the mechanism of the keff uncertainty difference deriving from the core models, temperature distributions, material compositions and different covariance libraries are analyzed in-depth. Meanwhile, some valuable observations have been made through the mechanism analysis and also the most significant contributors to the total keff uncertainty have been figured out for HTR-10.

Checking, processing and verification of nuclear data covariances

The aim of this paper is to present the activities carried out by NEA Data Bank on checking, processing and verification of JEFF-3.3T4 covariances. A picture of the completeness and status of the JEFF-3.3T4 covariances is addressed. The verification of JEFF-3.3T4 covariances is performed with nuclear data sensitivity tool providing thekeffuncertainty as a function of the contributing nuclide-reaction pairings including cross-reaction covariances. A total number of 4501 ICSBEP benchmarks is used in this analysis. This exercise is also extended to covariance libraries such as JENDL-4.0 updated files, ENDF/B-VII.1, SCALE-6.2rev8 and ENDF/B-VIII.0β5, allowing comparison of these results with both the experimental criticality benchmark and different methodologies of evaluation.

A stochastic method to propagate uncertainties along large cores deterministic calculations

Deterministic uncertainty propagation methods are certainly powerful and time-sparing but their access to uncertainties related to the power map remains difficult due to a lack of numerical convergence. On the contrary, stochastic methods do not face such an issue and they enable a more rigorous access to uncertainty related to the PFNS. Our method combines an innovative transport calculation chain and a stochastic way of propagating uncertainties on nuclear data: first, our calculation scheme consists in the calculation of assembly self-shielded cross sections and a pin-by-pin flux calculation on the whole core. Validation was done and the required CPU time is suitable to allow numerous calculations. Then, we sample nuclear cross sections with consistent probability distribution functions with a correlated optimized Latin Hypercube Sampling. Finally, we deduce the power map uncertainties from the study of the output response functions. We performed our study on the system described in the framework of the OECD/NEA Expert Group in Uncertainty Analysis in Modelling. Results show the 238U inelastic scattering cross section, the 235U PFNS, the elastic scattering cross section of 1H and the 56Fe cross sections as major contributors to the total uncertainty on the power map: the power tilt between central and peripheral assemblies using COMAC-V2 covariance library amounts to 5.4% (1σ) (respectively 7.4% (1σ) using COMAC-V0).

Uncertainty in the delayed neutron fraction in fuel assembly depletion calculations

This study presents uncertainty and sensitivity analyses of the delayed neutron fraction of light water reactor and sodium-cooled fast reactor fuel assemblies. For these analyses, the sampling-based XSUSA methodology is used to propagate cross section uncertainties in neutron transport and depletion calculations. Cross section data is varied according to the SCALE 6.1 covariance library. Since this library includes nu-bar uncertainties only for the total values, it has been supplemented by delayed nu-bar uncertainties from the covariance data of the JENDL-4.0 nuclear data library. The neutron transport and depletion calculations are performed with the TRITON/NEWT sequence of the SCALE 6.1 package. The evolution of the delayed neutron fraction uncertainty over burn-up is analysed without and with the consideration of delayed nu-bar uncertainties. Moreover, the main contributors to the result uncertainty are determined. In all cases, the delayed nu-bar uncertainties increase the delayed neutron fraction uncertainty. Depending on the fuel composition, the delayed nu-bar values of uranium and plutonium in fact give the main contributions to the delayed neutron fraction uncertainty for the LWR fuel assemblies. For the SFR case, the uncertainty of the scattering cross section of U-238 is the main contributor.