Second-order adjoint sensitivity analysis of a general ratio of functionals of the forward and adjoint fluxes in a multiplying nuclear system with source

Cacuci, Dan Gabriel

doi:10.1016/j.anucene.2019.106956

Cited by 12 publications

(28 citation statements)

References 7 publications

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“…In Parts I−V [1][2][3][4][5], which are precursors of this work, the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) conceived by Cacuci [6][7][8][9] has been successfully applied to the subcritical polyethylene-reflected plutonium (acronym: PERP) metal fundamental physics benchmark [10] to compute the exact values of the sensitivities of the PERP's benchmark leakage response with respect to the PERP model parameters, as follows:…”

Section: Introductionmentioning

confidence: 99%

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities on Response Uncertainties

2020

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This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the 1st-order and unmixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity to the isotopic number densities for the two fissionable isotopes have large values, which are comparable to, or larger than, the corresponding sensitivities for the total cross sections. Furthermore, several 2nd-order unmixed sensitivities for the isotopic number densities are significantly larger than the corresponding 1st-order ones. This work also presents results for the first-order sensitivities of the PERP benchmark’s leakage response with respect to the fission spectrum parameters of the two fissionable isotopes, which have very small values. Finally, this work presents the overall summary and conclusions stemming from the research findings for the total of 21,976 first-order sensitivities and 482,944,576 second-order sensitivities with respect to all model parameters of the PERP benchmark, as presented in the sequence of publications in the Special Issue of Energies dedicated to “Sensitivity Analysis, Uncertainty Quantification and Predictive Modeling of Nuclear Energy Systems”.

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Section: Introductionmentioning

confidence: 99%

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities on Response Uncertainties

2020

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“…The Second-Order Adjoint Sensitivity Analysis Methodology (2 nd -ASAM) recently conceived by Cacuci [1] is the only practical method that enables the exact computation of the large number of 2 nd -order sensitivities arising in large-scale problems comprising many parameters. The application of the 2 nd -ASAM to a multiplying nuclear system with source [2] [3] [4] has opened the way for the large-scale application presented in [5]- [10] to a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark [11]. The numerical model of the PERP benchmark includes 21,976 uncertain parameters, as follows: 180 group-averaged total microscopic cross sections, 21,600 group-averaged scattering microscopic cross sections, 120 fission process parameters, 60 fission spectrum parameters, 10 parameters describing the experiment's nuclear sources, and 6 isotopic number densities.…”

Section: Introductionmentioning

confidence: 99%

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

Cacuci¹,

Fang²

2020

AJCM

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This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976) 2 second-order sensitivities of the PERP benchmark's leakage response to all of the benchmark's uncertain parameters, showing that the largest and most consequential 1 stand 2 nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180) 3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3 rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180) 3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark's leakage response.

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“…Of course, if the first-order G-derivatives of the system's response do not exist, the computation of higher-order response sensitivities (G-derivatives) would be moot. Therefore, the conditions described in Equations (15) and (16) will henceforth be considered to be satisfied by the operators underlying the physical system, in which case the partial G-derivatives of ( ) (17) where . and δα is determined by determining the G-differentials of Equations…”

Section: Derivation Of the 1 St -Level Adjoint Sensitivity System (1 mentioning

confidence: 99%

“…Noteworthy, Cacuci [16] [17] has presented methodologies for the exact computation of 1 st -and 2 nd -order sensitivities of responses that are functionals of both the forward and the adjoint fluxes in a multiplying nuclear system with source. However, these works [16] [17] have specifically considered the neutron transport equation (rather than generic linear problems) within precisely known domains, without considering response sensitivities to uncertain domain parameters.…”

Section: Introductionmentioning

confidence: 99%

“…system of equations comprising Equations (20), (21), (26) and (27) are called the "1 st -Level Forward Sensitivity System" (1 st -LFSS). In principle, the 1 st -LFSS could to be solved for each possible vector of parameter variations δα in a neighborhood around 0 be used in Equation(17) to compute the total response sensitivity ( )0 ; R δ e h . Computing the (total) response sensitivity ( )0 ; R δ e h by using the δα -dependent solust -LFSS is called the Forward Sensitivity Analysis Method/Procedure (FSAM).…”

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confidence: 99%

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Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

Cacuci¹

2020

AJCM

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This work presents the "Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2 nd-CASAM)" for the efficient and exact computation of 1 stand 2 nd-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model's response (i.e., model result of interest) is a generic nonlinear function of the model's forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2 nd-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1 st-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2 nd-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (N 2 /2 + 3 N/2) large-scale computations for obtaining all of the first-and second-order sensitivities. This work also shows that constructing and solving the 2 nd-LASS requires very little additional effort beyond the construction of the 1 st-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1 st-LASS and 2 nd-LASS requires the same computational solvers as needed for solving (i.e., "inverting") either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and "solvers" used for solving the original system of equations can also How to cite this paper: Cacuci, D.G.

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Second-order adjoint sensitivity analysis of a general ratio of functionals of the forward and adjoint fluxes in a multiplying nuclear system with source

Cited by 12 publications

References 7 publications

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities on Response Uncertainties

Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark. VI: Overall Impact of 1st- and 2nd-Order Sensitivities on Response Uncertainties

Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework

Second-Order Adjoint Sensitivity Analysis Methodology for Computing Exactly Response Sensitivities to Uncertain Parameters and Boundaries of Linear Systems: Mathematical Framework

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