Shapley effect application for variance-based sensitivity analysis of the few-group cross-sections

Radaideh, Majdi I.; Surani, Stuti; O’Grady, Daniel; Kozłowski, Tomasz

doi:10.1016/j.anucene.2019.02.002

Cited by 16 publications

(12 citation statements)

References 31 publications

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“…On the basis of their study, the authors confirmed that the technique “D3” in Table in their paper yielded the best performance and results. This D3 technique was described in detail, verified, and applied previously in Radaideh et al A step‐by‐step of the “D3" algorithm is described in Radaideh et al . The inputs to the algorithm are as follows: (a) two independent matrices ( X , X ′ ) sampled from the joint/marginal distribution of the input parameters and (b) the model being evaluated (ie, SOFC model in this study).…”

Section: Methodsmentioning

confidence: 99%

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

Radaideh

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.

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Section: Methodsmentioning

confidence: 99%

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

Radaideh

2020

Int J Energy Res

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“…A variety of SA and UQ methods are used in this framework, and they include, but do not limit to, one-at-a-time (OAT), Morris screening, Monte Carlo UQ, deterministic UQ, partial correlation coefficients, standardized regression coefficients, Sobol indices, and Shapley effect. These methods are investigated and applied in this framework to nuclear data, 67 fundamental delayed neutron data, 49 kinetic parameters, 50 and spent fuel isotopes. 55,68…”

Section: Sa and Uqmentioning

confidence: 99%

“…71 Other tasks such as SA, analysis of variance, parameter screening, and model calibration can be efficiently conducted using the surrogate without worrying about the computational cost. 67,70,72,73 Building the surrogate can be done through a variety of methods based on classical machine learning algorithms, some of them that are related to this framework we highlight here. Polynomial chaos expansion (PCE) is one of the most common and earliest methods used to construct surrogate models, and it is expressed by [74][75][76]…”

Section: Machine Learning Deep Learning and Data Sciencementioning

confidence: 99%

“…The GP is used here on the basis of its high accuracy that we observed before. Sobol indices described in Equations (7) and (8) are estimated using the Monte Carlo algorithm developed and used by Glen and Isaacs 64 and Radaideh et al 67 The final results of the variance decomposition are shown in Figure 10C, which shows that linear heat rate (x 11 ) uncertainty is responsible of 60% of the variance in the maximum fuel centerline temperature. The next influential parameters in order are fuel porosity (x 2 ), clad surface temperature (x 12 ), and fuel roughness (x 9 ).…”

Section: Application 3: Sa and Machine Learning Surrogatesmentioning

confidence: 99%

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

Radaideh

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.

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“…Previously, a data-driven sampling-based UQ framework was developed to quantify the uncertainties in the reactor kinetic parameters [23], which are important for reactor safety. Efforts on global methods and variance decomposition are performed using the Shapley effect and Sobol indices in [24,25,26] with a focus on nuclear data uncertainties. Also various deterministic and stochastic methods have been used to analyze the behaviour of a nuclear spent fuel transportation/storage cask [27,28,29,30].…”

Section: Introductionmentioning

confidence: 99%

Application of Stochastic and Deterministic Techniques for Uncertainty Quantification and Sensitivity Analysis of Energy Systems

Radaideh,

Radaideh

2019

Preprint

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Sensitivity analysis (SA) and uncertainty quantification (UQ) are used to assess and improve engineering models. In this study, various methods of SA and UQ are described and applied in theoretical and practical examples for use in energy system analysis. This paper includes local SA (one-at-a-time linear perturbation), global SA (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. Simple test problems are included to demonstrate the described methods where input parameter interactions, linear correlation, model nonlinearity, local sensitivity, output uncertainty, and variance contribution are explored. Practical applications of analyzing the efficiency and power output uncertainty of a molten carbonate fuel cell (MCFC) are conducted. Using different methods, the uncertainty in the MCFC responses is about 10%. Both SA and UQ methods agree on the importance ranking of the fuel cell operating temperature and cathode activation energy as the most influential parameters. Both parameters contribute to more than 90% of the maximum power and efficiency variance. The methods applied in this paper can be used to achieve a comprehensive mathematical understanding of a particular energy model, which can lead to better performance.

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Shapley effect application for variance-based sensitivity analysis of the few-group cross-sections

Cited by 16 publications

References 31 publications

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

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

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

Application of Stochastic and Deterministic Techniques for Uncertainty Quantification and Sensitivity Analysis of Energy Systems

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