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In nuclear reactor physics, the integral quantities (reaction rates, k e f f , etc.) are estimated by calculation codes (Monte Carlo and deterministic codes). The determination of the bias and uncertainty that may exist between the calculated results and the reality is necessary. These uncertainties are mainly due to the approximations used during modeling, the approximation associated with the calculation method, as well as the uncertainties of the nuclear data. It is necessary to perform the Sensitivity/Uncertainty Analysis using a set of benchmarks in order to provide an overview of nuclear data uncertainty propagation and to identify isotopes and reactions which can contribute to the uncertainty of integral parameters. In this study, a set of benchmarks contained 233 U were selected in order to estimate the impact of the uncertainties related to the reaction of this isotope on k e f f and to validate the ENDF/B-VIII.0 library in comparison to ENDF/B-VII.1 nuclear data. • Study of eigenvalue sensitivity due to the different reactions of 233U isotope using MCNP code. • Analysis of the K eff uncertainty caused by several nuclear data. • Nuclear data uncertainties comparison between ENDF/B-VIII.0 and ENDF/B-VII.1 libraries are performed. • 233U uncertainties of ENDF/B-VIII.0 is significantly reduced compared with that of ENDF/B-VII.1. [ABSTRACT FROM AUTHOR]

• MUSA project aimed at quantifying uncertainties and sensitivities in SA analyses. • WP4 was a joint attempt to apply BEPU to simplified but representative SA scenario. • WP4 provided key insights into BEPU methodology when applied to SA scenarios. The Management and Uncertainties of Severe Accidents (MUSA) project was funded in HORIZON 2020 and is coordinated by CIEMAT (Spain). The project aims at consolidating a harmonized approach for the analysis of uncertainties and sensitivities associated with Severe Accidents (SAs) analysis, focusing on source term figures of merit. The Application of Uncertainty Quantification (UQ) Methods against Integral Experiments (AUQMIE – Work Package 4 (WP4)), led by ENEA (Italy), was devoted to apply and test UQ methodologies adopting the internationally recognized PHEBUS FPT1 test. FPT1 was chosen to test UQ methodologies because, even though it is a simplified SA scenario, it was representative of the in-vessel phase of a severe accident initiated by a break in the cold leg of a PWR primary circuit. WP4 served as a platform to identify and discuss the issues encountered in the application of UQ methodologies to SA analyses (e.g. discuss the UQ methodology, perform the coupling between the SA codes and the UQ tools, define the results post-processing methods, etc.). The purpose of this paper is to describe the MUSA PHEBUS FPT1 uncertainty application exercise with the related specifications and the methodologies used by the partners to perform the UQ exercise. The main outcomes and lessons learned of the analysis are: scripting was in general needed for the SA code and uncertainty tool coupling and to have more flexibility; particular attention should be devoted to the proper choice of the input uncertain parameters; outlier values of figures of merit should be carefully analyzed; the computational time is a key element to perform UQ in SA; the large number of uncertain input parameters may complicate the interpretation of correlation or sensitivity analysis; there is the need for a statistically solid handling of failed calculations. [ABSTRACT FROM AUTHOR]

• Using sensitivity analysis leads to improve cross section evaluation. • High resolution data are needed to derive resonance parameters. • Neutron capture data are of paramount importance in the 233 U evaluation. • Issues on the k eff bias are addressed using IRSN computer tools. The Institut de Radioprotection et de Sûreté Nucléaire (IRSN) is the French public service expert in nuclear and radiation risks with activities that cover all the related scientific and technical issues. IRSN provides expertise in support of radiation protection and nuclear safety risks. A great deal of research work carried out at IRSN concerns the improvement of computational tools and data used on a daily basis by nuclear safety assessment experts. Particularly in this paper the approach used to improve data quality and its uncertainties is presented. Computation tools and nuclear data evaluation methodology are discussed. [ABSTRACT FROM AUTHOR]

• Inverse uncertainty quantification is implemented based MLE and formulation. • Mesh refinement effect on statistical parameters of physical models is investigated. • Methodology implemented for RSTART code based on the BFBT benchmark. • Noticeable effect of mesh refinement on the estimates of the mean was observed. • Estimations based on most refined mesh led to most satisfactory results. Proper quantification of the uncertainties in the input parameters of a thermal-hydraulics code (e.g. physical models) is an essential part of the forward Uncertainty Quantification (UQ) problem. Such quantification can be systematically achieved by solving the Inverse Uncertainty Quantification (IUQ) problem using data from code predictions and experimental measurements. The IUQ problem is highly dependent on several factors such as geometry and discretization. In this paper, we study the effect of mesh refinement on the statistical parameters of three uncertain physical models (interfacial friction coefficient, wall to liquid friction coefficient and critical heat flux). A mathematical framework based on MLE and MAP algorithms is implemented to perform IUQ for the physical models of the thermal-hydraulics code RSTART based on experimental data from the OECD/NEA BWR Full-size Fine-mesh Bundle Test (BFBT) benchmark. Sensitivity analysis required for the IUQ problem was achieved by implementing discrete adjoint methods in the thermal-hydraulics code. The statistical parameters of the three physical models were obtained by implementing the MLE and MAP methods using code predictions that correspond to three different mesh sizes. Results from MLE and MAP showed a noticeable effect of mesh refinement on the estimates of the mean and a negligible effect on the estimates of the variance of the physical models. The compensation of error due to mesh refinement was studied by running the code with perturbation values calculated using the three different mesh sizes. It was shown that the results based on the most refined mesh led to best agreement between experimental data and code prediction. [ABSTRACT FROM AUTHOR]

• A structural method for uncertainty evaluation of constitutive models is proposed. • Several tools for model uncertainty quantification are investigated and discussed. • Uncertainties of important models during the LBLOCA are quantified. • Best estimate plus uncertainty analysis is applied to the LP-02-6 experiment. Best estimate (BE) codes are developed to carry out realistic safety analysis of the nuclear reactor, and generally hundreds of constitutive models are comprised in a BE code. Nevertheless, uncertainties of these constitutive models are often not properly handled in the best estimate plus uncertainty (BEPU) analysis. It is not sufficient to fully evaluate the uncertainties of different sorts of models with only one method. Thereby a structural method for uncertainty quantification (UQ) of constitutive models is proposed and relevant description is presented. Based on the method, constitutive models will be classified into two categories according to the characteristics, namely the independent model and the dependent model, and different methods will be adopted for different sorts of model. Several statistical methods for UQ of constitutive models such as the non-parametric curve estimation method, the Bayesian calibration method and the coverage calibration method are evaluated and the characteristics of these methods are discussed. In addition, several methods for the construction of surrogate model are utilized to reduce the computational cost, and a model selection technique is adopted to opt the optimal model among all alternative models. The large break loss of coolant accident (LBLOCA) experiment LOFT LP-02-6 is utilized to verify the proposed structural method, and the BEPU analysis of the LP-02-6 experiment is carried out. The results show that uncertainty intervals of the identified models obtained through the structural method are reasonable, uncertainties of the peak cladding temperature (PCT) as well as the accumulator injection time (AIT) are quantified, and the sensitivity analysis is carried out to evaluate the influence of different input parameters on the 1st PCT, 2nd PCT and the AIT. [ABSTRACT FROM AUTHOR]

• An integrated methodology for ranking reactor physics uncertainties is presented. • An eigenvalue decomposition of the nuclear data covariance matrix is used. • Perturbed data is propagated through lattice and core calculations. • Comparison to a direct Sobol sample gives consistent results for cases examined. Nuclear data uncertainties lead to substantial uncertainties in the predictions of LWR core calculations. Such problems are typically solved using lattice calculations and nodal codes, such as the WIMS-PANTHER system. It is desirable to derive uncertainties of core simulation output parameters (e.g. enthalpy deposition in an REA) to nuclear data uncertainties for specific nuclide-reaction pairs. This allows the key uncertainty contributions to be identified and ranked and facilitates use of data assimilation techniques. Key challenges in ranking the contributions to uncertainty are (1) the large number of input parameters (2) burnup-dependence of nuclide populations and microscopic cross sections, which challenges the use of adjoint methods (3) propagation of uncertainties through a multi-step calculation sequence. In this paper, an integrated methodology for deriving such uncertainties is presented. This comprises the following steps: (1) sensitivity analysis to identify the key reactions in the problem and exclude insignificant reactions (2) orthogonal decomposition of the nuclear data covariance matrix to calculate and rank eigenvectors (3) direct and consistent perturbation of the microscopic cross sections for the eigenvectors with significant eigenvalues (4) separate lattice (WIMS) and core (PANTHER) calculations with nuclear data perturbed for each eigenvector. This method (which assumes linearity of perturbations) is compared to a direct Sobol sample of the nuclear data and for the cases examined gives consistent results for the importance ranking of reactions, while greatly reducing the number of calculations employed. Hence, it can complement sampling-based approaches in developing an overall understanding of the magnitude, distribution, and contributors to uncertainty in core calculations. Both the linear method and the Sobol sampling method are integrated within the Visual Workshop graphical user environment to automate the process with the WIMS and PANTHER codes. [ABSTRACT FROM AUTHOR]

Highlights • A more realistic simulation of the ocean conditions was provided. • Uncertain samples related to ocean motions were generated. • An ocean-based thermal hydraulics analysis code has been developed based on RELAP5. • Uncertainty analysis of natural circulation under ocean conditions was carried out. Abstract The stability of natural circulation is more susceptible to the uncertainties involved in the thermal-hydraulic process because the driving force is relatively small. Especially in the marine nuclear power plants, the complex ocean motions will introduce more uncertainties in the natural circulation operation. In this work, the joint probability distribution function of wave parameters was investigated, which provided a more realistic simulation of the ocean conditions. On that basis, it was applied to generate ocean motion parameters as uncertain input via the Metropolis-Hastings algorithm. A thermal-hydraulic code that is capable of simulating system behaviors under ocean conditions was developed to propagate the uncertainties. Additionally, the sensitivity analysis was carried out to identify the parameters that have a significant impact on natural circulation characteristics. Results show that the intense ocean motions will introduce large uncertainties in the natural circulation operation, especially at the startup stage. The rolling amplitude contributes the most on the natural circulation flow rate and the coolant temperature, while the heaving motions have less influence. Uncertainties introduced by the ocean motions will damage the natural circulation ability and stability, which need further considerations during the design optimization. [ABSTRACT FROM AUTHOR]

In this paper, the sensitivity and uncertainty analysis model has been proposed and implemented in the NECP-ONION system, which is capable of performing the 3D online power-distribution monitoring for PWR by applying the harmonics expansion method. A new method called the analytical method is used to quantify the relative sensitivity coefficients of the monitored power distributions with respect to the detector signals; then the “sandwich” rule is used to quantify the uncertainties of the monitored power distributions with the sensitivity-analysis results based on the uncertainty-propagation method. The BEAVRS benchmark is used to verify the sensitivity and uncertainty analysis capability in NECP-ONION. The results of the direct numerical perturbation method are used as reference to verify the sensitivity coefficients calculated with the analytical method. The results of the statistical sampling method and the analytical method are compared to each other for the uncertainty verification. Then, the sensitivity and uncertainty analyses with various expansion orders of harmonics and core burnup levels are carried out. Numerical results show that, the expansion order is the trade-off of the monitoring accuracy and uncertainty, while the sensitivity and uncertainty analysis is useful for the determination of the expansion order. [ABSTRACT FROM AUTHOR]

In this paper, improvements to the multigroup cross-section perturbation model have been proposed and applied in the self-developed UNICORN code, which is capable of performing the total sensitivity and total uncertainty analysis for the neutron-physics calculations by applying the direct numerical perturbation method and the statistical sampling method respectively. The narrow resonance (NR) approximation was applied in the multigroup cross-section perturbation model, implemented in UNICORN. As improvements to the NR approximation to refine the multigroup cross-section perturbation model, an ultrafine-group cross-section perturbation model has been established, in which the actual perturbations are applied to the ultrafine-group cross-section library and the reconstructions of the resonance cross sections are performed by solving the neutron slowing-down equation. The total sensitivity and total uncertainty analysis were then applied to the LWR pin-cells, using both the multigroup and the ultrafine-group cross-section perturbation models. The numerical results show that the NR approximation overestimates the relative sensitivity coefficients and the corresponding uncertainty results for the LWR pin-cells, and the effects of the NR approximation are significant for σ (n,γ) and σ (n,elas) of 238 U. Therefore, the effects of the NR approximation applied in the total sensitivity and total uncertainty analysis for the neutron-physics calculations of LWR should be taken into account. [ABSTRACT FROM AUTHOR]

Environmental contamination subsequent to the atmospheric releases during the Fukushima accident resulted in high radioactive concentrations in feed and foodstuffs. Producing a realistic health risk assessment after severe nuclear accidents, and developing a sufficient understanding of environmental transfer and exposure processes, appears to be a research priority. Specifically, the characterization of uncertainties in the human ingestion pathway, as outlined by the radioecological community, is of great interest. The present work aims to (i) characterize spatial variability and parametric uncertainties raised by the processes involved in the transfer of radionuclides ( 134 Cs and 137 Cs) after atmospheric releases during the Fukushima accident into the terrestrial ecosystems, and (ii) study the impact of these variability and uncertainties on radioactive contamination of leafy vegetables. The implemented approach quantified uncertainties under a probabilistic modelling framework. This resulted in probability distributions derived mainly from Bayesian inference and by performing transfer calculations in the modelling platform SYMBIOSE. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to apply our improved method for calculating sensitivities and uncertainties of reactivity responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The improved method has been used to calculate sensitivity coefficients relative to infinite dilution cross-sections with self-shielding effect taken into account. Two types of reactivities are considered: Doppler reactivity and coolant void reactivity. For each type of reactivity, the sensitivities are calculated for small and large changes of reactivity. The results have demonstrated that the sensitivities are dependent on the changes of reactivity, and the reactivity variation uncertainty is larger than the eigenvalue uncertainty. In addition, the uncertainty of coolant void reactivity is much greater than Doppler reactivity especially for large changes of reactivity because the contribution of U-238 inelastic scattering becomes large. The sensitivity coefficients and uncertainties of both reactivities were verified by comparing with SCALE code results using ENDF/B-VII library and good agreements have been found. [ABSTRACT FROM AUTHOR]

A computer code, MUSAD was developed for the uncertainty and sensitivity analysis on the DeCART neutron transport calculations for a high temperature gas-cooled reactor. MUSAD is based on a deterministic method in which the sensitivity coefficients of the multiplication factor and the microscopic cross sections are derived using the generalized perturbation theory. Then, the uncertainties of the reactor physics responses are calculated by the product of the covariance matrix and the sensitivity coefficients. MUSAD has been verified against the uncertainty analyses on several benchmark problems including the GODIVA benchmark problem, the PMR-200 pin-cell, and the MHTGR-350 core benchmark problems. A good agreement in comparison with the reference codes, TSUNAMI and McCARD shows the applicability of MUSAD to the uncertainty and sensitivity analyses on the HTGR neutron transport calculations. [ABSTRACT FROM AUTHOR]

SHARKX is a set of Perl-based tools built around the lattice code CASMO-5 which is used to perform sensitivity analysis and uncertainty quantification (UQ). SHARKX has been recently extended to perform UQ on pinpower and representativity analysis (RA). Its aim is to calculate uncertainties due to the nuclear data cross sections on the fission rate of selected pins and to provide a rigorous basis to assess the relevance of an experiment to a given application. The main objective of the work summarised in the present paper is to verify the proper implementation of the SHARKX UQ and RA methodologies. The verification is carried out by comparing the UQ and RA results of SHARKX to the ones of the TSUNAMI code, currently the reference in the field for this kind of calculations. The verification of the proper UQ and RA implementation in SHARKX is performed for a set of test cases relevant to the LWR-PROTEUS experimental campaign. Only nuclear data (cross sections) uncertainty is considered and propagated in the SHARKX and TSUNAMI codes. For various test problems, the comparison with TSUNAMI has shown that the new UQ and RA implementations in the SHARKX methodology are carried out successfully. However, it is found that discrepancies are introduced in sensitivity coefficient calculation of SHARKX by neglecting the perturbation of the resonance self-shielding treatment, the so called “implicit effect”. Such approximation can have significant impact on both UQ and RA especially for Gadolinium doped fuel. The effect of the input uncertainty in UQ and RA is also investigated by comparing the results obtained with the variance–covariance matrix (VCM) of ENDF/B-VII.1, JENDL4.0 and SCALE6. The choice of input VCM is the major source of result discrepancies for UQ on k inf and pinpower. However, for RA, it is found to be of the same order of magnitude than the method discrepancies, i.e. the differences between SHARKX and TSUNAMI coming from the “implicit effect”. [ABSTRACT FROM AUTHOR]

This paper discusses the improvement of a method for calculating sensitivity coefficients of neutronics parameters relative to infinite dilution cross-sections because the conventional method neglects resonance self-shielding effect. In this study, the self-shielding effect is taken into account by using the intermediate resonance approximation in order to get accurate results in both high and low energy groups. The improved method is applied to calculate sensitivity coefficients and uncertainties of eigenvalue responses for UO 2 and MOX ( ThO 2 – UO 2 and PuO 2 – UO 2 ) fueled pressurized water reactor cells. The verification of the improved method was performed by comparing the sensitivities with MCNP6 and TSUNAMI-1D. For uncertainty, calculation comparisons were done with TSUNAMI-1D, and we demonstrate that the differences are caused by the use of different covariance matrices. [ABSTRACT FROM AUTHOR]

Uncertainties in nuclear data are a fundamental source of uncertainty in reactor physics calculations. To determine their contribution to uncertainties in calculated reactor physics parameters, a nuclear data sensitivity and uncertainty study is performed on the Canadian supercritical water reactor (SCWR) concept. The nuclear data uncertainty contributions to the neutron multiplication factor k eff are 6.31 mk for the SCWR at the beginning of cycle (BOC) and 6.99 mk at the end of cycle (EOC). Both of these uncertainties have a statistical uncertainty of 0.02 mk. The nuclear data uncertainty contributions to Coolant Void Reactivity (CVR) are 1.0 mk and 0.9 mk for BOC and EOC, respectively, both with statistical uncertainties of 0.1 mk. The nuclear data uncertainty contributions to other reactivity parameters range from as low as 3% of to as high as ten times the values of the reactivity coefficients. The largest contributors to the uncertainties in the reactor physics parameters are Pu-239, Th-232, H-2, and isotopes of zirconium. [ABSTRACT FROM AUTHOR]

• Sensitivity/Uncertainty analysis using SERPENT 2 and ENDF/B-VIII.0. • Error of k eff of CERCER core was significant and larger than that of CERMET one. • ENDF/B-VIII.0 was found to be insensitive to kinetic parameter simulation results. The reliability of eigenvalue and kinetic parameter calculation results for CERCER and CERMET fueled ADS was investigated by conducting sensitivity and uncertainty analysis by SERPENT 2 and ENDF/B-VIII.0 library. The total error of k eff of CERCER core was found to be 1268.7 pcm and larger than that of CERMET one (609.4 pcm). It mostly comes from cross section uncertainty of 237Np (n,g) – the biggest contributor, 239Pu (n,f), 232Th (n,g) and 237Np (n,f). Therefore, the accuracy of nuclear data of those isotopes is recommended to be improved to achieve more reliable eigenvalue results. For kinetic parameters, the uncertainty of evaluated results mainly originated from the 237Np (n,g), 239Pu (n,inl) and 23Na (n,ela) cross sections. Nevertheless, its impact on simulation accuracy is not significant (less than 1%). Thus, ENDF/B-VIII.0 nuclear data is sufficient to evaluate β eff , l eff, and λ eff and discuss the safety features of ADS. [ABSTRACT FROM AUTHOR]

Highlights: [•] Phenomenological uncertainty analysis has been applied to level 2 PSA. [•] The methodology provides an alternative to simple deterministic analyses and sensitivity studies. [•] A realistic evaluation provides a more complete characterization of risks. [•] Uncertain parameters of MAAP code for the early containment failure were identified. [Copyright &y& Elsevier]

Highlights: [•] An idealisation of the Canadian SCWR is modelled with the code set, TSUNAMI. [•] The SCWR model shows a high sensitivity to contributions from the isotopes H-2, Pu-239, and Th-232. [•] Isotopes of Zr make a large contribution to SCWR modeling uncertainty. [•] Results of this study demonstrate the need for improved nuclear data evaluations for SCWR modeling. [Copyright &y& Elsevier]

• Uncertainty analysis of the Telegrapher's neutron kinetic equations attempted, • Neutron population addressed as the response functional, • Perturbed response functional due to kinetic parameter uncertainty evaluated, • First order variational method employed, • Satisfactory results compared against those of forward perturbation analysis, • The effect of relaxation time on the adjoint system dynamics explored. The work presented herein is an approach to the kinetic uncertainty analysis of the Telegrapher's neutron kinetic equations. The adjoint sensitivity analysis framework has been resorted to meet this end. Burnup induced uncertainty in the value of the delayed neutron fraction is addressed and its impact on the neutron population (as an observable quantity by the way of flux detectors) is investigated. Results compared against those obtained through an exact forward analysis approach confirm quite satisfactory accuracy of the proposed variational method. The effect of relaxation time on the adjoint system dynamics is moreover explored. [ABSTRACT FROM AUTHOR]

Abstract: The uncertainty in the multiplication factor and associated neutron flux is studied for a reflected slab reactor. The uncertainty is introduced into the problem by allowing the cross sections to be simple functions of a random variable, this then leads to a stochastic eigenvalue problem. We use a polynomial chaos expansion to solve this problem but, in contrast to previous workers in this field, we employ a new method that avoids the non-linear equations that normally arise. The fully linear problem is then reduced to a set of deterministic second order differential equations which can be solved very simply. Numerical results are given for the eigenvalue and associated flux in core and reflector. In addition, the sensitivity of the multiplication factor to uncertainty in each cross section is determined thereby enabling the most important areas of uncertainty to be readily identified. [Copyright &y& Elsevier]

Abstract: In activation calculations, there are several approaches to quantify uncertainties: deterministic by means of sensitivity analysis, and stochastic by means of Monte Carlo. Here, two different Monte Carlo approaches for nuclear data uncertainty are presented: the first one is the Total Monte Carlo (TMC). The second one is by means of a Monte Carlo sampling of the covariance information included in the nuclear data libraries to propagate these uncertainties throughout the activation calculations. This last approach is what we named Covariance Uncertainty Propagation, CUP. This work presents both approaches and their differences. Also, they are compared by means of an activation calculation, where the cross-section uncertainties of 239Pu and 241Pu are propagated in an ADS activation calculation. [Copyright &y& Elsevier]

Abstract: Best estimate accident analysis with uncertainty evaluation is being encouraged in the present licensing scenarios of nuclear power plants. This paper deals with uncertainty and sensitivity analysis for station blackout in PSB VVER integral test facility under the framework of coordinated research project of IAEA. Nodalization was developed using best estimate system code RELAP5/MOD3.2 and its steady state and transient level qualifications are achieved. Sampling based approaches are used to carry out uncertainty and sensitivity/importance analysis. The objective of the analysis is to get confidence for uncertainty methodology by comparing with the experimental results and extend its applicability to NPPs. Uncertainty analysis is carried out by selecting nine important input parameters with specified ranges and its uniform distributions. A design matrix of 45×9 is generated for variations of input parameters with the Latin Hypercube Sampling and 45 code runs were taken. Linear regression was also carried out to quantify the effect of each individual input parameter on output parameters in terms of standard rank regression coefficients. Uncertainty band in output parameters is defined between 95th and 5th percentile value. It is observed that most of the experimental values and code calculated reference values are lying within the uncertainty band. For most of the parameters, width of uncertainty band increases with transient progression time. [Copyright &y& Elsevier]

Abstract: The XT-ADS, an accelerator-driven system for an experimental demonstration, has been investigated in the framework of IP EUROTRANS FP6 project. In this study, the sensitivity and uncertainty analyses were performed to comprehend the reliability of the XT-ADS neutronic design. For the sensitivity analysis, it was found that the sensitivity coefficients were significantly different by changing the geometry models and calculation codes. For the uncertainty analysis, it was confirmed that the uncertainties deduced from the covariance data varied significantly by changing them. The uncertainties deduced from the covariance data for the XT-ADS criticality were 0.94%, 1.9% and 1.1% by the SCALE 44-group, TENDL-2009 and JENDL-3.3 data, respectively. When the target accuracy of 0.3%Δk for the criticality was considered, the uncertainties did not satisfy it. To achieve this accuracy, the uncertainties should be improved by experiments under an adequate condition. [Copyright &y& Elsevier]

• We analyse the most recent MSFR design using a high-fidelity coupled reactor model. • We use non-intrusive Polynomial Chaos Expansion as a fast and accurate meta-model. • Polynomial Chaos Expansion enables detailed S&U analysis of the full solution field. • We shows the heat-exchanger design to be crucial to ensure safe operating conditions. In this work, we present the results of a preliminary uncertainty quantification and sensitivity analysis study of the Molten Salt Fast Reactor (MSFR) behavior at steady-state performed by applying a non-intrusive Polynomial Chaos Expansion (PCE) approach. An in-house high-fidelity multi-physics simulation tool is used as reactor reference model. Considering several thermal-hydraulics and neutronics parameters as stochastic inputs, with a limited number of samples we build a PCE meta-model able to reproduce he reactor response in terms of effective multiplication factor, maximum, minimum, and average salt temperatures, and complete salt temperature distribution. The probability density functions of the responses are constructed and analyzed, highlighting strengths and issues of the current MSFR design. The sensitivity study highlights the relative importance of each input parameter, thus providing useful indications for future research efforts. The analysis on the whole temperature field shows that the heat exchanger can be a critical component, so its design requires particular care. [ABSTRACT FROM AUTHOR]

• Overview of the dual number (DN) arithmetic and DN automatic differentiation (DNAD). • Dual number arithmetic is applied in solving infinite homogeneous diffusion problem. • Two methods based on the DNAD are used for uncertainty propagation. • Utilising dual number arithmetic yielded results for k-inf correct to 3 pcm. • DNAD is a viable additional method for sensitivity analysis in nuclear engineering. Automatic differentiation (AD) is a set of techniques which allows the numeric evaluation of derivatives of functions calculated by a computer program. In recent years, interest in AD has grown significantly in many disciplines, especially in the context of gradient-based optimization algorithms. Sensitivity analysis is another natural application area for AD methods. However, despite the large body of sensitivity and uncertainty (S/U) analysis publications produced in the field of nuclear reactor science and engineering in the last decade, the use of AD by the community has been very limited. The purpose of the present paper is to fill this gap and to demonstrate how AD can be employed in conjunction with some traditionally used sensitivity analysis and uncertainty propagation techniques. Specifically, the forward mode of AD based on dual number arithmetic was considered in the study. We provide a short overview of dual number algebra and dual number automatic differentiation (DNAD) methods, as well as of the tools available for the practical implementation of DNAD, followed by a discussion of its application to S/U analysis. As illustration, we solve a simplistic example of an infinite, homogeneous diffusion problem using parameters that correspond to a plate-type, Material Testing Reactor fuel assembly. Homogenized cross-sections and uncertainty (covariance) data for the test problem are generated with the SCALE code in six energy groups. The diffusion problem is solved through the power iteration algorithm with the algebra of dual matrices, which yields sensitivity information for use in the sandwich formula. DNAD is also used to calculate partial derivatives of the production and loss operators in the perturbation formula in the context of the adjoint-weighted technique. Both of these methods yield uncertainty values for the multiplication factor that are within three pcm of the reference value. Automatic differentiation can, therefore, be useful for uncertainty propagation in the framework of local sensitivity analysis in addition to traditionally employed sampling methods or in conjunction with the perturbation method. [ABSTRACT FROM AUTHOR]

• Improvement of uncertainty evaluation of the closure models in uncertainty methods. • Improvement of sensitivity analysis method and framework of the uncertainty methods. • Development of an optimized uncertainty method. • Application of the improved uncertainty method to the CPR1000 LBLOCA. Best estimate plus uncertainty methodology is an advanced technology for licensing application of the nuclear power plants, but some aspects can still be improved in the conventional input-driven methodologies. For instance, uncertainties of the closure models are not properly handled; local sensitivity analysis methods not suitable for complex nuclear systems are still widely utilized; the sensitivity analysis process needs to be performed again every time new parameters are identified. Optimization researches were carried out in the study. A structural method was proposed to quantify the uncertainties of the closure models, and a low-cost moment-independent global sensitivity analysis method was developed to improve the sensitivity analysis framework. By integrating the improvements into the conventional input-driven framework, an uncertainty method with model treatment and improved sensitivity analysis was obtained. Finally, the method was validated through a large break loss of coolant accident in a three-loop pressurized water reactor. [ABSTRACT FROM AUTHOR]

• Uncertainty Sensitivity Analyses for LOCA Simulation of PHEBUS Experiment. • SUNSET software is coupled with ASTEC code for computing U&S during severe accident condition. • Modifying the SUNSET post-processing step to evaluate the uncertainty for the whole period of the transient. • The main safety parameters are very sensitive to the change in power during the severe accident. • Linear regression model failed to predict the source variables due to no/non-linear correlation of the model. One task of the regulatory body during the review and assessment process is the quantification of uncertainty and sensitivity (U&S) during normal and accident conditions. Nowadays there are many codes having the capability of estimating U&S, but few of them can estimate uncertainty and sensitivity during severe accident conditions. The IRSN uncertainty propagation and sensitivity analysis tool named SUNSET is considered one of the most important tools used in U&S analysis, where it is coupled with ASTEC software package (Accident Source Term Evaluation Code) for computing U&S during severe accident condition. Unfortunately, the SUNSET tool cannot perform U&S analyses during all the transient time. The SUNSET software can only calculate U&S parameters for maximum, minimum, and last output values, therefore it was necessary to modify the SUNSET tool to calculate U&S during the whole transient time. The main objective of this study is to develop a Python script to replace the SUNSET post-processing step, extract the results, and perform U&S analysis. ASTEC code has been used for the simulation of a loss of coolant accident in the cold leg of the primary circuit of the FPT-1 test. The obtained results indicate the efficiency of the modified SUNSET tools to calculate the uncertainty during severe accidents. In general, it was found that the code is capable to model the main severe accident phenomena. SUNSET package shows good agreement with the experimental data, for the whole calculation period, until thermocouples failure moment. The obtained results show that the main safety parameters are very sensitive to the power multiplier. [ABSTRACT FROM AUTHOR]

• Uncertainty of input parameters do not cause unsafe behavior during transient. • Margins of the reactivity feedback parameters are very large. • Increasing pump coastdown time eliminates instability during transient. A sensitivity and uncertainty analysis was performed on a small lead cooled reactor for two types of transients: an unprotected loss of flow (ULOF) and unprotected transient overpower (UTOP). Transients were simulated with the code BELLA, which is a point-kinetics and lumped-parameter model. A Monte Carlo based method was used with 5000 simulations. Input parameters are reactor dimensions, neutronics properties, material properties and thermal hydraulic properties. Outputs are maximum temperatures (clad, coolant and fuel), mass flow disturbance, natural convection mass flow, maximum power and energy deposition. For ULOF, it was found that the most sensitive parameters were the gap between fuel and clad, the flow area in the core, the friction factors in core and steam generator and the pump coastdown time. A deeper analysis recommends increasing pump coastdown time to avoid mass flow disturbances during coastdown. For UTOP, the most sensitive parameters are the gap between fuel and clad, the reactivity feedback coefficients, and to a lesser extent, fuel conductivity and fuel heat capacity. In any case, the uncertainties never bring the reactor beyond safety limits. [ABSTRACT FROM AUTHOR]

• Modelling and simulation of the CPR1000 SBLOCA transient. • Transient analysis of the CPR1000 SBLOCA at different break sizes. • Uncertainty and sensitivity analysis of the CPR1000 SBLOCA. The best estimate plus uncertainty (BEPU) is an advanced method which has been widely adopted in nuclear power plant safety analysis. In order to investigate the transient behaviors of the pressurized water reactor CPR1000 during the cold leg small break loss of coolant accident (SBLOCA) at different break sizes, BEPU analysis of the SBLOCA was carried out in this study, and the sizes of the break were 0.2%, 0.4%, 0.6%, 0.8% and 1.0% of the cross-sectional area of the cold leg, respectively. The minimum collapsed level (MCL) in the active core section was determined to be the figure of merit (FOM). The base case calculations, uncertainty propagation calculations and sensitivity analysis calculations were performed with the NUSOL-SYS code. Based on the results, the transient behaviors were analyzed, the lower 95/95 tolerance limits of the MCL at different break sizes were quantified, and the important input parameters were determined. [ABSTRACT FROM AUTHOR]

• Nuclear data uncertainty propagation through reactor transient analysis. • Random sampling-based method XSUSA for generation of varied cross section sets. • Analysis of control rod withdrawal transients of PWR mini-core with DYN3D-ATHLET. • Wilks tolerance limit as a robust uncertainty measure to complex output time series. • Sensitivity analysis to identify important nuclide reactions to power uncertainty. The impact of nuclear data uncertainties is studied for the reactor power and the reactivity during control rod withdrawal transients with reactivity insertions of 0.5 $ and 0.97 $ , respectively, for a PWR mini-core model. Multi-group cross sections, the multiplicities of both prompt and delayed neutrons, and fission spectra are varied by the application of the random sampling-based method XSUSA with covariance data of SCALE 6.1 supplemented by JENDL-4.0. The varied multi-group data are used by TRITON/NEWT to generate varied 2-group cross sections, which are then applied in neutron-kinetic/thermal-hydraulic calculations with DYN3D-ATHLET. A significant impact on both the reactivity uncertainty and the power uncertainty is observed. Since the distributional properties of the output time series vary across the problem time, the distribution-free Wilks tolerance limit is applied as a robust uncertainty measure to complex time series patterns. The most contributing nuclide reactions to the power uncertainty are identified via sensitivity analysis. [ABSTRACT FROM AUTHOR]

• Vessel breach due to penetration failure is predicted to occur first by MELCOR code. • User defined solid debris ejection mode has the dominant effect on MELCOR results. • Probability of vessel lower head wall failure depends on the mode of debris ejection. • Melt release characteristics depend on the mode of debris ejection from the vessel. Nordic boiling water reactors (BWR) employ ex-vessel debris coolability as a severe accident management (SAM) strategy. Melt release mode into a deep water pool located in the lower drywell is a major source of uncertainty for success of such strategy. The main goal of this work is to identify the major contributors to the uncertainty in prediction of vessel failure mode, timing and melt release conditions in Nordic BWR using MELCOR severe accident analysis code. There is a forest of control rod guide tubes (CRGTs) and instrumentation guide tubes (IGTs) in the lower head of a BWR. Failure of the penetrations is considered in this work along with the gross creep rupture of the vessel lower head. Modelling of penetrations failure in MELCOR code is based on parametric models, allowing a user to select different assumptions, such as temperature threshold for penetrations failure, modelling of penetrations assembly and respective failure modes, mode of solid and liquid debris ejection from the vessel. In this work we perform sensitivity analysis to the MELCOR modelling options and sensitivity parameters in unmitigated station blackout scenario (SBO). Results of analysis suggest that (i) vessel breach due to penetration failure is predicted to occur before creep-rupture failure of the vessel lower head, (ii) the mode of debris ejection from the vessel has the dominant effect on the likelihood of creep-rupture failure of the vessel lower head and debris ejection rate from the vessel. [ABSTRACT FROM AUTHOR]