Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics
This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-orde...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Journal of Nuclear Engineering |
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| Online Access: | https://www.mdpi.com/2673-4362/2/2/12 |
| _version_ | 1797521201380196352 |
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| author | Dan G. Cacuci |
| author_facet | Dan G. Cacuci |
| author_sort | Dan G. Cacuci |
| collection | DOAJ |
| description | This paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters. |
| first_indexed | 2024-03-10T08:09:14Z |
| format | Article |
| id | doaj.art-e1166d29ebc44676a2b211582a9b3cbb |
| institution | Directory Open Access Journal |
| issn | 2673-4362 |
| language | English |
| last_indexed | 2024-03-10T08:09:14Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Nuclear Engineering |
| spelling | doaj.art-e1166d29ebc44676a2b211582a9b3cbb2023-11-22T10:51:06ZengMDPI AGJournal of Nuclear Engineering2673-43622021-04-012211412310.3390/jne2020012Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor PhysicsDan G. Cacuci0Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USAThis paper illustrates the relative importance of the largest first- and second-order sensitivities of the leakage response of an OECD/NEA reactor physics benchmark (a polyethylene-reflected plutonium sphere) to the benchmark’s underlying total cross sections. It will be shown that numerous 2nd-order sensitivities of the leakage response with respect to the total cross sections are significantly larger than the largest corresponding 1st-order sensitivities. In particular, the contributions of the 2nd-order sensitivities cause the mean (expected) value of the response to differ appreciably from its computed value and also cause the response distribution to be skewed towards positive values relative to the mean. Neglecting these large 2nd-order sensitivities would cause very large non-conservative errors by under-reporting the response’s variance and expected value. The results presented in this paper also underscore the need for obtaining reliable cross section covariance data, which are currently unavailable. Finally, comparing the CPU-times needed for computations, this paper demonstrates that the Second-Order Adjoint Sensitivity Analysis Methodology is the only practical method for computing 2nd-order sensitivities exactly, without introducing methodological errors, for large-scale systems characterized by many uncertain parameters.https://www.mdpi.com/2673-4362/2/2/12polyethylene-reflected plutonium sphere (PERP) benchmark2nd-order adjoint sensitivity analysis1st- and 2nd-order sensitivitiestotal cross sectionsexpected valuevariance and skewness of PERP response |
| spellingShingle | Dan G. Cacuci Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics Journal of Nuclear Engineering polyethylene-reflected plutonium sphere (PERP) benchmark 2nd-order adjoint sensitivity analysis 1st- and 2nd-order sensitivities total cross sections expected value variance and skewness of PERP response |
| title | Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics |
| title_full | Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics |
| title_fullStr | Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics |
| title_full_unstemmed | Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics |
| title_short | Illustrating Important Effects of Second-Order Sensitivities on Response Uncertainties in Reactor Physics |
| title_sort | illustrating important effects of second order sensitivities on response uncertainties in reactor physics |
| topic | polyethylene-reflected plutonium sphere (PERP) benchmark 2nd-order adjoint sensitivity analysis 1st- and 2nd-order sensitivities total cross sections expected value variance and skewness of PERP response |
| url | https://www.mdpi.com/2673-4362/2/2/12 |
| work_keys_str_mv | AT dangcacuci illustratingimportanteffectsofsecondordersensitivitiesonresponseuncertaintiesinreactorphysics |