A new framework for sampling-based uncertainty quantification of the six-group reactor kinetic parameters

Kozłowski

2019

Int J Energy Res

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Summary A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction.

Section: Nuclear Datamentioning

confidence: 99%

Section: Nuclear Datamentioning

confidence: 99%

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

Kozłowski

2019

Int J Energy Res

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“…neutron flux [12]. TRITON, which is a lattice physics code in the SCALE code system, calculates the adjoint/fissionweighted kinetic parameters for a given material composition using a 2-energy-group structure.…”

Section: Mathematical Definitionsmentioning

confidence: 99%

“…The DND random libraries are written in humanreadable format which means that the user can easily replace them by other data libraries generated using other DND sources or sampling methods. The user can increase the number of libraries/samples to larger than 1000, even though the convergence study reported in [12] showed that 200-300 random samples of DND are more than sufficient for convergence. The only restriction is that the user-generated libraries (name, directory, and format) should be consistent with the original libraries.…”

Section: Implementation and Test Modelsmentioning

confidence: 99%

“…Therefore, our focus will be on the 6group Keepin's model. A framework to propagate the uncertainty of delayed neutron data (DND) and neutron cross-sections into the homogenized kinetic parameters was developed previously by Radaideh et al [12] in the SCALE code system [13]. The framework methodology is described in detail in that paper, where a set of DND for 7 actinides was collected and used in the UQ process.…”

Section: Introductionmentioning

confidence: 99%

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Data-Driven and Precursor-Group Uncertainty Propagation of Lattice Kinetic Parameters in UAM Benchmark

Science and Technology of Nuclear Installations

Kozłowski

Wieselquist

et al. 2019

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A new data-driven sampling-based framework was developed for uncertainty quantification (UQ) of the homogenized kinetic parameters calculated by lattice physics codes such as TRITON and Polaris. In this study, extension of the database for the delayed neutron data (DND) is performed by exploring more delayed neutron experiments and adding additional isotopes/actinides to the data libraries. Afterwards, the framework is utilized to obtain a deeper knowledge of the kinetic parameters’ sensitivity and uncertainty. The kinetic parameters include precursor-group-wise delayed neutron fraction (DNF) and decay constant. Input uncertainties include nuclear data (i.e., cross-sections) and DND (i.e., precursor group parameters and fractional delayed neutron yield). It is found that kinetic parameters, especially DNFs, have large uncertainties. The DNF uncertainty is driven by the cross-section uncertainties for LWR designs, while decay constant uncertainty is dominated by the DND uncertainties. The usage of correlated U-235 thermal DND in the UQ process significantly reduces the DND uncertainty contribution on the kinetic parameters. Large void fraction and presence of neutron absorber (e.g., control rod) increase the DNF uncertainty due to the hardening of neutron spectrum. High correlation between the DNF groups (β1,..,β6) is observed, while the decay constant groups (λ1,..,λ6) show weak correlation to each other and also to DNF groups. The DNF uncertainties of the dominant precursor group 4 for PWR, BWR, and VVER are about 7.5%, 9.4%, and 7.6%, respectively. The DNF uncertainty grows to larger values after fuel burnup. Kinetic parameters’ values and uncertainties provided here can be efficiently used in subsequent core calculations, point reactor kinetics, and other applications.

Efficient analysis of parametric sensitivity and uncertainty of fuel cell models with application to SOFC

2020

Int J Energy Res

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Summary Sensitivity analysis (SA) and uncertainty quantification (UQ) are used to assess and improve engineering models. SA of fuel cell models can be challenging because of the large number of design parameters to optimize. Following the regular approach of manually testing the fuel cell outputs under changing each design parameter one at a time can be tedious. In this work, a framework of SA and UQ methods is applied with a purpose of efficiently analysing fuel cell models. The SA and UQ methods are also compared to increase the confidence in the results. In this methodology, all design parameters and their effects can be analysed in an integrated form, where model variance, sensitivity, linearity/nonlinearity, parameter interactions, and importance ranking can be assessed. This paper highlights and compares between local SA (one‐at‐a‐time linear perturbation), parameter screening (Morris screening), variance decomposition (Sobol indices), and regression‐based SA. For UQ, stochastic methods (Monte Carlo sampling) and deterministic methods (using SA profiles) are used. All methods are applied to solid oxide fuel cell (SOFC) to analyse the power output and system efficiency under 21 uncertain design parameters. Using different methods, the uncertainty in the SOFC responses (maximum power and efficiency) is about 11%, when the current density is about 13 200 A m−2. In addition, analysis shows that operating temperature (T), length of grain contact (X), grain size (Ds), porosity (ϵ), and electrolyte thickness (Le) contribute to more than 97% of the SOFC's maximum power variance, with individual contributions as follows: 63.3%, 13.1%, 12.5%, 5.4%, and 3.6%, respectively. The previous conclusions are subjective to the simplified SOFC model used in this study to demonstrate the methods. Benchmarking the UQ methods in capturing the response uncertainty and the SA methods in raking the design parameters demonstrate very good agreement between them. The methods applied in this paper can be used to achieve a comprehensive mathematical understanding of more advanced fuel cell or energy models, which can lead to better performance.