Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis

Abdel-Khalik, Hany S.; Bang, Youngsuk; Wang, Congjian

doi:10.1016/j.anucene.2012.07.020

Cited by 24 publications

(10 citation statements)

References 20 publications

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“…best approaches for optimizing the system economy, and supporting safety analysis calculations. 1,3 At its core, sensitivity analysis is a mathematical approach that allows the analyst to determine how a model's calculated output results are impacted by its input parameters. When sensitivity analysis results are combined with parameter uncertainties, the analyst can determine the uncertainties of the model output results and identify key sources of uncertainties.…”

Section: Background On Sensitivity Analysismentioning

confidence: 99%

“…The literature is replete with many approaches for sensitivity analyses that can be classified in many different ways, e.g., deterministic versus stochastic, local versus global, forward versus adjoint, etc. [2][3][4][5][6] Common to all approaches is the *E-mail: abdelkhalik@purdue.edu NUCLEAR TECHNOLOGY © 2020 American Nuclear Society DOI: https://doi.org/10.1080/00295450.2020.1721407 need to prepare multiple sets of model parameter perturbations, e.g., whereby each set perturbs a single parameter, a group of parameters, or all parameters using deterministic or randomized strategies. For forward-based sensitivity analyses, 1 the perturbed sets of model parameters are employed to execute the model multiple times with the response variations recorded for later extraction of sensitivity measures.…”

Section: Introductionmentioning

confidence: 99%

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Addressing Ambiguities in Constrained Sensitivity Analysis for Reactor Physics Problems

2020

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This paper presents an algorithm for completing sensitivity analysis that respects linear constraints placed on the associated model's input parameters. Any sensitivity analysis (linear or nonlinear, local or global) focuses on measuring the impact of input parameter variations on model responses of interest, which may require the analyst to execute the model numerous times with different model parameter perturbations. With the constraints present, the degrees of freedom available for input parameter variations are reduced, and hence any analysis that changes model parameters must respect these constraints. Focusing here on linear constraints, earlier work has shown that constraints may be respected in many ways, causing ambiguities, i.e., nonuniqueness, in the results of a sensitivity analysis, forcing the analyst to introduce dependencies with downstream analyses, e.g., uncertainty quantification, that employ the sensitivity analysis results. This paper develops the theoretical details for a new algorithm to select model parameter variations that automatically satisfy linear constraints resulting in unique results for the sensitivity analysis, thereby removing any custom dependencies with downstream analyses. To demonstrate the performance of the algorithm, it is applied to solve the multigroup eigenvalue problem for the multiplication factor in a representative CANDU core-wide model. The model parameters analyzed are the group prompt neutron fractions, whose summation must be equal to one over all energy groups. The results indicate that the new algorithm identifies the gradient direction uniquely which represents the direction of maximum change while satisfying the constraints, thus removing any ambiguities resulting from the constraints as identified by earlier work.

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Section: Background On Sensitivity Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Addressing Ambiguities in Constrained Sensitivity Analysis for Reactor Physics Problems

2020

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“…These sufficient summary plots can also be used to examine the variability in the vectors defining the active subspace. In particular, we can use the bootstrap replicateŝ W j from (7). The first eigenvector from each can be used to create pairs for the scatter plot.…”

Section: Visualization With the Active Subspacementioning

confidence: 99%

“…We have applied these methods to several models in aerospace engineering [4][5][6]. Abdel-Khalik has applied similar methods in nuclear engineering applications [7].…”

Section: Introductionmentioning

confidence: 99%

Discovering an active subspace in a single‐diode solar cell model

Constantine

Zaharatos

Campanelli

2015

Statistical Analysis

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Predictions from science and engineering models depend on the values of the model's input parameters. As the number of parameters increases, algorithmic parameter studies like optimization or uncertainty quantification require many more model evaluations. One way to combat this curse of dimensionality is to seek an alternative parameterization with fewer variables that produces comparable predictions. The active subspace is a low-dimensional linear subspace defined by important directions in the model's input space; input perturbations along these directions change the model's prediction more, on average, than perturbations orthogonal to the important directions. We describe a method for checking if a model admits an exploitable active subspace, and we apply this method to a single-diode solar cell model with five input parameters. We find that the maximum power of the solar cell has a dominant one-dimensional active subspace, which enables us to perform thorough parameter studies in one dimension instead of five

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“…In the nuclear field, POD has been successfully applied to neutronics [21][22][23], thermal-hydraulics [24], sensitivity and uncertainty quantification [25,26]. Notwithstanding, there is a lack of literature in the employment in burnup calculations, nevertheless it would be necessary to solve the issue of computational burden previously discussed.…”

Section: Introductionmentioning

confidence: 99%

Development of a Reduced Order Model for Fuel Burnup Analysis

Castagna

Aufiero²,

Lorenzi

et al. 2020

Energies

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Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need to find a compromise between computational cost and solution accuracy is a crucial issue in burnup analysis. To overcome this problem, the present work aims to develop a methodological approach to implement a Reduced Order Model (ROM), based on Proper Orthogonal Decomposition (POD), in fuel burnup analysis. We verify the approach on 4 years of burnup of the TMI-1 unit cell benchmark, by reconstructing fuel materials and burnup matrices over time with different levels of approximation. The results show that the modeling approach is able to reproduce reactivity and nuclide densities over time, where the accuracy increases with the number of basis functions employed.

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Overview of hybrid subspace methods for uncertainty quantification, sensitivity analysis

Cited by 24 publications

References 20 publications

Addressing Ambiguities in Constrained Sensitivity Analysis for Reactor Physics Problems

Addressing Ambiguities in Constrained Sensitivity Analysis for Reactor Physics Problems

Discovering an active subspace in a single‐diode solar cell model

Development of a Reduced Order Model for Fuel Burnup Analysis

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