scholarly journals Illustrative Application of the 2<sup>nd</sup>-Order Adjoint Sensitivity Analysis Methodology to a Paradigm Linear Evolution/Transmission Model: Point-Detector Response

2020 ◽  
Vol 10 (03) ◽  
pp. 355-381
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Transmission Model ◽  
Detector Response ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Linear Evolution ◽  
Analysis Methodology ◽  
Point Detector ◽  
Model Point ◽  
Illustrative Application

scholarly journals The nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (nth-CASAM-L): II. Illustrative Application

Energies ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 8315
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Closed Form ◽  
Linear Systems ◽  
Predictive Modeling ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Third Order ◽  
Analysis Methodology ◽  
Illustrative Application

This work illustrates the application of the nth-order comprehensive adjoint sensitivity analysis methodology for response-coupled forward/adjoint linear systems (abbreviated as “nth-CASAM-L”) to a paradigm model that describes the transmission of particles (neutrons and/or photons) through homogenized materials, as encountered in radiation protection and shielding. The first-, second-, and third-order sensitivities of responses that depend on both the forward and adjoint particle fluxes are obtained exactly, in closed-form, underscoring the principles and methodology underlying the nth-CASAM-L. The results presented in this work underscore the fundamentally important role of the nth-CASAM-L in the quest to overcome the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: V. Computation of Mixed 2nd-Order Sensitivities Involving Isotopic Number Densities

Energies ◽  
2020 ◽  
Vol 13 (10) ◽  
pp. 2580 ◽  
Author(s):  
Ruixian Fang ◽  
Dan G. Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Cross Sections ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Number Density ◽  
Reactor Physics ◽  
Adjoint Sensitivity ◽  
Energy Group ◽  
Analysis Methodology

This work applies the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to compute the mixed 2nd-order sensitivities of a polyethylene-reflected plutonium (PERP) benchmark’s leakage response with respect to the benchmark’s imprecisely known isotopic number densities and the other benchmark imprecisely known parameters, including: (i) the 6 × 180 mixed 2nd-order sensitivities involving the total microscopic cross sections; (ii) the 6 × 21,600 mixed 2nd-order sensitivities involving the scattering microscopic cross sections; (iii) the 6 × 60 mixed 2nd-order sensitivities involving the fission microscopic cross sections; and (iv) the 6 × 60 mixed 2nd-order sensitivities involving the average number of neutrons produced per fission. It is shown that many of these mixed 2nd-order sensitivities involving the isotopic number densities have very large values. Most of the large sensitivities involve the isotopic number density of 239Pu, and the microscopic total, scattering or fission cross sections for the 12th or 30th energy groups of 239Pu or 1H, respectively. The 2nd-order mixed sensitivity of the PERP leakage response with respect to the isotopic number density of 239Pu and the microscopic total cross section for the 30th energy group of 1H is the largest of the above mentioned sensitivities, attaining the value −94.91.

scholarly journals First-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Critical Points in Coupled Nonlinear Systems. II: Application to a Nuclear Reactor Thermal-Hydraulics Safety Benchmark

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 34
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Heat Conduction ◽  
Critical Points ◽  
Adjoint Sensitivity Analysis ◽  
Thermal Hydraulics ◽  
Reactor Safety ◽  
Adjoint Sensitivity ◽  
Computational Tools ◽  
First Order ◽  
Analysis Methodology

Responses defined at critical points are particularly important for reactor safety analyses and licensing (e.g., the maximum fuel and/or clad temperature). The novel mathematical framework of the first-order comprehensive adjoint sensitivity analysis methodology for critical points (1st-CASAM-CP) is applied in this work to develop a reactor safety thermal-hydraulics benchmark model which admits exact closed-form expressions for the adjoint functions and for the first-order sensitivities of responses defined at critical points (maxima, minima, saddle points) in physical systems characterized by imprecisely known parameters, external and internal boundaries. This benchmark model is designed for verifying the capabilities and accuracies of computational tools for modeling numerically thermal-hydraulics systems. The unique and extensive capabilities of the 1st-CASAM-CP methodology are demonstrated in this work by considering two responses of paramount importance in reactor safety, namely, (i) the maximum rod surface temperature, which occurs at the imprecisely known interface between the subsystem that models the heat conduction inside the heated rod and the subsystem modeling the heat convection process surrounding the rod; and (ii) the maximum temperature inside the heated rod, which has a critical point with two components, one located at a precisely known boundary of the subsystem that models the heat conduction inside the heated rod, while the other component depends on an imprecisely known boundary (i.e., the rod length). The exact analytical expressions developed in this work for the sensitivities of the maximum internal rod temperature and maximum rod surface temperature, as well as for the sensitivities of the locations where these respective maxima occur, provide exact benchmarks for verifying the accuracy of thermal-hydraulics computational tools. The sensitivities of such responses and of their critical points with respect to model parameters enable the quantification of uncertainties induced by uncertainties stemming from the system’s parameters and boundaries in the respective responses and their underlying critical points.

scholarly journals Comprehensive Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) Applied to a Subcritical Experimental Reactor Physics Benchmark: IV. Effects of Imprecisely Known Source Parameters

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1431 ◽  
Author(s):  
Ruixian Fang ◽  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Source Parameters ◽  
Second Order ◽  
Adjoint Sensitivity Analysis ◽  
Response Distribution ◽  
Adjoint Sensitivity ◽  
Scattering Cross ◽  
Analysis Methodology ◽  
Scattering Cross Sections

By applying the Second-Order Adjoint Sensitivity Analysis Methodology (2nd-ASAM) to the polyethylene-reflected plutonium (PERP) benchmark, this work presents results for the first- and second-order sensitivities of this benchmark’s leakage response with respect to the spontaneous fission source parameters. The numerical results obtained for these sensitivities indicate that the 1st-order relative sensitivity of the leakage response to the source parameters for the two fissionable isotopes in the benchmark are all positive, signifying that an increase in the source parameters will cause an increase in the total neutron leakage from the PERP sphere. The 1st- and 2nd-order relative sensitivities with respect to the source parameters for 239Pu are very small (10−4 or less). In contradistinction, the 1st-order and several 2nd-order relative sensitivities of the leakage response with respect to the source parameters of 240Pu are large. Large values (e.g., greater than 1.0) are also displayed by several mixed 2nd-order relative sensitivities of the leakage response with respect to parameters involving the source and: (i) the total cross sections; (ii) the average neutrons per fission; and (iii) the isotopic number densities. On the other hand, the values of the mixed 2nd-order relative sensitivities with respect to parameters involving the source and: (iv) the scattering cross sections; and (v) and the fission cross sections are smaller than 1.0. It is also shown that the effects of the 1st- and 2nd-order sensitivities of the PERP benchmark’s leakage response with respect to the benchmark’s source parameters on the moments (expected value, variance and skewness) of the PERP benchmark’s leakage response distribution are negligibly smaller than the corresponding effects (on the response distribution) stemming from uncertainties in the total, fission and scattering cross sections.

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