Hybrid Method for Eigenvalue Sensitivity Coefficient Calculations: Part II
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Greene, Travis [ORNL] (ORCID:0000000232144311)↗
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Analyzing Machine Learning Predictions of Passive Microwave Brightness Temperature Spectral Difference Over Snow-Covered Terrain in High Mountain Asia
Snow is an important component of the terrestrial freshwater budget in high mountainAsia (HMA) and contributes to the runoff in Himalayan rivers through snowmelt. Despitethe importance of snow in HMA, considerable spatiotemporal uncertainty exists across the different estimates of snow water equivalent for this region. In order to better estimate snow water equivalent, radiative transfer models are often used in conjunction with microwave brightness temperature measurements. In this study, the efficacy of support vector machines (SVMs), a machine learning technique, to predict passive microwave brightness temperature spectral difference (1Tb) as a function of geophysical variables (snow water equivalent, snow depth, snow temperature, and snow density) is explored through a sensitivity analysis. The use of machine learning (as opposed to radiative transfer models) is a relatively new and novel approach for improving snow water equivalent estimates. The Noah-MP land surface model within the NASALand Information System framework is used to simulate the hydrologic cycle over HMA and model geophysical variables that are then used for SVM training. The SVMsserve as a nonlinear map between the geophysical space (modeled in Noah-MP) andthe observation space (1Tb as measured by the radiometer). Advanced MicrowaveScanning Radiometer-Earth Observing System measured passive microwave brightness temperatures over snow-covered locations in the HMA region are used as training data during the SVM training phase. Sensitivity of well-trained SVMs to each Noah-MP modeled state variable is assessed by computing normalized sensitivity coefficients. Sensitivity analysis results generally conform with the known first-order physics. Input states that increase volume scattering of microwave radiation, such as snow density and snow water equivalent, exhibit a plurality of positive normalized sensitivity coefficients. In general, snow temperature was the most sensitive input to the SVM predictions. The sensitivity of each state is location and time dependent. The signs of normalized sensitivity coefficients that indicate physical irrationality are ascribed to significant cross-correlation between Noah-MP simulated states and decreased SVM prediction capability at specific locations due to insufficient training data. SVM prediction pitfalls do exist that serve to highlight the limitations of this particular machine learning algorithm.
high mountain Asia↗
Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates
Analytic three-dimensional solutions are presented for the coupled thermoelectroelastic response of multilayered hybrid composite plates. The plates consist of a combination of fiber-reinforced cross-ply and piezothermoelastic layers. Both the thermoelectroelastic static response and its sensitivity coefficients are computed. The sensitivity coefficients measure the sensitivity of the response to variations in different mechanical, thermal and piezoelectric material properties of the plate. A linear constitutive model is used, and the material properties are assumed to be independent of the temperature and the electric field. The plates are assumed to have rectangular geometry and special material symmetries. A mixed formulation is used with the fundamental unknowns consisting of the three transverse stress components; three displacement components; transverse component of the electric displacement field; electric potential; transverse heat flux component, and temperature change. Each of the fundamental unknowns is expressed in terms of a double Fourier series in the Cartesian surface coordinates. A state space approach is used to generate the static response and to evaluate the sensitivity coefficients. Extensive numerical results are presented showing the effects of variation in the geometric parameters of the plate on the different response quantities and their sensitivity coefficients.
Xu, Kangming↗
Sensitivity-based Similarity Metrics for New Experiment Design Optimization
The nuclear data used in advanced reactor simulations requires validation. Data from nuclear criticality experiments can provide this validation. New nuclear criticality experiment design requires extensive knowledge and expert judgement such that the experimental design parameters are selected in such a way to keep the experiment subcritical. To aide in this experimental design process, professionals can utilize sensitivity and uncertainty analysis. Sensitivity and uncertainty analysis relies on matching new application experiments with currently existing benchmark experiments. Currently, there is functionality in the Whisper 1.1 software package to calculate a similarity metric based on neutron multiplication factor sensitivity coefficients between a new application designed by the user and existing International Criticality Safety Benchmark Experiment Project (ICSBEP) benchmarks. The Whisper 1.1 software package is included in Monte Carlo N-Particle ® Code Version 6.21 (MCNP ® 6.2). This work is geared toward expanding this capability to new similarity metrics based on beta-effective sensitivity coefficients and reactivity coefficient sensitivity coefficients. While the investigation of these sensitivity coefficients is presented in detail in separate works at this same conference, this work will be primarily focused on studying the similarity metrics in more detail. These similarity metrics will then be incorporated into the optimization algorithms used for experiment design in EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data), which is a Los Alamos National Laboratory (LANL) project designed to constrain nuclear data of interest, such that adjustments can be made to possible inaccuracies. A more detailed optimization can be subsequently performed by breaking down these similarity metrics by isotope, reaction, and energy.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Nuclear data uncertainty propagation applied to the versatile test reactor conceptual design
We report the Versatile Test Reactor (VTR) currently under development is a 300 MWth sodium-cooled fast reactor (SFR) fueled with ternary metal alloy fuel, which aims to accelerate the testing of advanced nuclear fuels, materials, instrumentation, and sensors in high flux environments that are necessary to license the next generation of advanced reactor concepts. To support the VTR design process, uncertainties associated with the nuclear data has been propagated through the reactor core neutronics calculation to global parameters of interest, such as the core multiplication factor, kinetic parameters, and various reactivity feedback coefficients, following the sensitivity based uncertainty propagation approach. By folding the sensitivity coefficients, separately computed by the generalized perturbation theory code PERSENT and Monte Carlo code Serpent 2, with the variance-covariance matrices from COMMARA-2.0, we obtain the reaction-wise, isotope-wise, and overall uncertainties for each response of interest due to nuclear data uncertainty. With Serpent 2, the statistical error of the uncertainty is obtained by propagating the statistical error of the sensitivity coefficients through the same process using a newly developed uncertainty propagation method. From both codes, the overall top uncertainty contributors are found to be the cross section of Fe-56 elastic scattering, Na-23 elastic scattering, and U 238 inelastic scattering. The large contributions of the Fe-56 elastic scattering cross sections to global parameters are due to its relatively large relative uncertainty of 5–10% in nuclear data and the large volume of Fe-containing reflector assemblies in the fairly compact VTR core design. Both codes agreed well for the overall uncertainty estimates of all responses of interest, except the delayed neutron fraction, prompt neutron generation time, and the coolant density feedback coefficient, where Serpent 2 yielded a much larger value than PERSENT due to the large statistical error of sensitivity coefficients. The calculated uncertainties are also compared to those associated with other SFR cores. Another outcome of this study is a variance-covariance matrix of reactivity coefficients, which can be used in the subsequent uncertainty propagation to the system level to investigate the impact of identified uncertainties on system responses in the safety analysis.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Thermomechanical buckling of multilayered composite panels with cutouts
A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.
Noor, Ahmed K.↗
Finite element buckling and postbuckling solutions for multilayered composite panels
A study is made of the buckling and postbuckling responses of flat, unstiffened composite panels subjected to various combinations of mechanical and thermal loads. The analysis is based on a first-order shear deformation von Karman-type plate theory. A mixed formulation is used with the fundamental unknowns consisting of the strain components, stress resultants and the generalized displacements of the plate. The stability boundary, postbuckling response and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented for both solid panels and panels with central circular cutouts. The results show the effects of the variations in the fiber orientation angels, aspect ratio of the panel, and the hole diameter (for panels with cutouts) on the stability boundary, postbuckling response and sensitivity coefficients.
Noor, Ahmed K.↗
Thermomechanical buckling of multilayered composite panels with cutouts
A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.
THERMOMECHANICAL BUCKLING↗
Thermomechanical buckling of multilayered composite panels with cutouts
A study is made of the thermomechanical buckling of flat unstiffened composite panels with central circular cutouts. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. Both the stability boundary and the sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical buckling response and its sensitivity coefficients.
Noor, Ahmed K.↗
Validation of Jezebel Reactivity Coefficients and Sensitivity Analysis
Nuclear data validation is often performed today using criticality measurements. The gold standard for criticality measurements is the International Criticality Safety Benchmark Experiment Project (ICSBEP). The validation specifically focuses on the effective multiplication factor ($k_{eff}$). $K_{eff}$ is a relatively easy parameter to infer and has reduced uncertainty due to being at or above critical. However, while $k_{eff}$ is the most documented parameter and its uncertainties and sensitivities have been evaluated in great detail, it cannot be used as a standalone metric to determine inaccuracies in nuclear data (e.g., cross section data, PFNS, nu), which is based on theory, physics, and differential measurements. The Experiments Underpinned by Computational Learning for Improvements in nuclear Data (EUCLID) project aims to identify compensating errors in specific isotope nuclear data by optimally designing experiments that are, or are not sensitive to a suite of measurement parameters beyond $k_{eff}$. By identifying parameters that are sensitive to each other, oppositely sensitive, or have substantial magnitude differences in sensitivity, experiments can be designed to constrain questionable nuclear data. One sensitivity that is of particular interest to this project includes the sensitivity of reactivity coefficients. Reactivity coefficients compare reactivity, which is related to $k_{eff}$ at two different states therefore being sensitive to small changes in the system. The most common type of reactivity coefficient measurements is comparison to void for a small sample within the assembly. It is key that the sample sizes are small enough to not affect the flux of the full system. Reactivity coefficients were evaluated for many early experiments to better understand transport corrected cross sections. In fact, ICSBEP includes reactivity coefficient results as “Supplemental Measurements” in appendices for a handful of older benchmarks. One of those benchmarks is Jezebel, the bare Pu critical assembly. This paper compares new simulations of reactivity coefficients for Jezebel, and explores the sensitivity of reactivity coefficients to small changes in nuclear data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Thermomechanical postbuckling of multilayered composite panels with cutouts
The results of a study of the detailed thermomechanical postbuckling response characteristics of flat unstiffened composite panels with central circular cutouts are presented. The panels are subjected to combined temperature changes and applied edge loading (or edge displacements). The analysis is based on a first-order shear deformation plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. The postbuckling displacements, transverse shear stresses, transverse shear strain energy density, and their sensitivity coefficients are evaluated. The sensitivity coefficients measure the sensitivity of the post-buckling response to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of the variations in the hole diameter, laminate stacking sequence, fiber orientation, and aspect ratio of the panel on the thermomechanical postbuckling response and its sensitivity to changes in panel parameters.
Noor, Ahmed K.↗
Sensitivity Calculations for Systems with Polyethylene Reflector Materials Using CLUTCH
The SCALE 6.2.4 code package contains four sequences for calculating $k_{eff}$ sensitivity coefficients. Two of these sequences use deterministic transport solvers: a one-dimensional (1D) capability based on XSDRN, and a two-dimensional (2D) capability based on NEWT. These sequences are restricted to the multigroup (MG) treatment of neutron energy. The three-dimensional (3D) sequences use the KENO V.a or KENO-VI Monte Carlo transport codes and can be used to calculate sensitivity coefficients with either MG or continuous-energy (CE) transport. The 3D sensitivities are ultimately reported in an MG structure, regardless of the method used in the transport calculations. If desired, the sensitivity coefficients can be reported with very fine energy resolution from a CE calculation, but they are calculated only in the MG library structure in the MG mode. CE TSUNAMI methods are available in SCALE starting in SCALE version 6.2. Sensitivity coefficients were generated using the 3D sequences as part of the generation of the SCALE 6.2.2 Validation Report; difficulties encountered when using the CLUTCH method for thick, fissionable-material reflectors were discussed and investigated as documented in a previous paper. This paper discusses the difficulties encountered in generating accurate sensitivity coefficients using the CLUTCH technique for polyethylene reflectors for two fast spectrum benchmarks. Direct perturbation (DP) calculations were performed to confirm the accuracy of the total sensitivity coefficient for important isotopes with large sensitivities in the system. Discrepancies were detected for CLUTCH-calculated sensitivity coefficients in the reflector of a critical experiment with a radial polyethylene reflector. A simple polyethylene-reflected plutonium sphere was then used to further investigate the discrepancy. Calculations performed using the iterated fission probability (IFP) method generated accurate sensitivity coefficients in both cases. The results of this study emphasize the need to confirm CLUTCH sensitivity results with DP calculations. IFP calculations are generally less efficient but more reliable than CLUTCH calculations. Improvements to the CLUTCH methodology that retain the greater efficiency but address identified difficulties are therefore potentially useful to analysts.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Nonlinear vibrations of thin-walled composite frames
A reduced basis technique and a computational procedure are presented for generating the nonlinear vibrational response, and evaluating the first-order sensitivity coefficients of thin-walled composite frames. The sensitivity coefficients are the derivatives of the nonlinear frequency with respect to the material and lamination parameters of the frame. A mixed formulation is used with the fundamental unknowns consisting of both the generalized displacements and stress resultants in the frame. The flanges and webs of the frames are modeled by using geometrically nonlinear two-dimensional shell and plate finite elements. The computational procedure can be conveniently divided into three distinct steps. The first step involves the generation of various-order perturbation vectors, and their derivatives with respect to the material and lamination parameters of the frame, using the Linstedt-Poincare perturbation technique. The second step consists of using the perturbation vectors as basis vectors, computing the amplitudes of these vectors and the nonlinear frequency of vibration, via a direct variational procedure. The third step consists of using the perturbation vectors, and their derivatives, as basis vectors and computing the sensitivity coefficients of the nonlinear frequency via a second application of the direct variational procedure. Numerical results are presented for semicircular thin-walled frames with I and J section, showing the convergence of the nonlinear frequency and the sensitivity coefficients obtained by both the reduced-basis and perturbation techniques.
Noor, Ahmed K.↗
Buckling and postbuckling of composite panels with cutouts subjected to combined edge shear and temperature change
The results of a detailed study of the buckling and postbuckling responses of composite panels with central circular cutouts are presented. The panels are subjected to combined edge shear and temperature change. The panels are discretized by using a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the panel. The fundamental unknowns consist of the average mechanical strains through the thickness and the displacement components. The effects of geometric nonlinearities and laminated anisotropic material behavior are included. The stability boundary, postbuckling response and the hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the buckling and postbuckling responses to variations in the panel stiffnesses, and the material properties of both the individual layers and the constituents (fibers and matrix). Numerical results are presented for composite panels with central circular cutouts subjected to combined edge shear and temperature change, showing the effects of variations in the hole diameter, laminate stacking sequence and fiber orientation, on the stability boundary and postbuckling response and their sensitivity to changes in the various panel parameters.
Noor, Ahmed K.↗
Analysis of Curved Sandwich Panels Subjected to Combined Temperature Gradient and Mechanical Loads
The results of a detailed study of the nonlinear response of curved sandwich panels with composite face sheets and subjected to a temperature gradient through-the-thickness combined with mechanical loadings are presented. The analysis is based on a first-order shear-deformation Sanders-Budiansky type theory with the effects of large displacements, moderate rotations, transverse shear deformation and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, the effective properties of the face sheet layers and the core, and the micromechanical parameters. Numerical results are presented for cylindrical panels subjected to combined pressure loading, edge shortening or extension, edge shear and a temperature gradient through the thickness. The results show the effects of variations in the loading and the panel aspect ratio, on the nonlinear response and its sensitivity to changes in the various panel, effective layer and micromechanical parameters.
Noor, Ahmed K.↗
Analysis of Composite Panels Subjected to Thermo-Mechanical Loads
The results of a detailed study of the effect of cutout on the nonlinear response of curved unstiffened panels are presented. The panels are subjected to combined temperature gradient through-the-thickness combined with pressure loading and edge shortening or edge shear. The analysis is based on a first-order, shear deformation, Sanders-Budiansky-type shell theory with the effects of large displacements, moderate rotations, transverse shear deformation, and laminated anisotropic material behavior included. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the panel. The nonlinear displacements, strain energy, principal strains, transverse shear stresses, transverse shear strain energy density, and their hierarchical sensitivity coefficients are evaluated. The hierarchical sensitivity coefficients measure the sensitivity of the nonlinear response to variations in the panel parameters, as well as in the material properties of the individual layers. Numerical results are presented for cylindrical panels and show the effects of variations in the loading and the size of the cutout on the global and local response quantities as well as their sensitivity to changes in the various panel, layer, and micromechanical parameters.
Noor, Ahmed K.↗
Thermomechanical buckling and postbuckling of multilayered composite panels
A study is made of the thermomechanical buckling and postbuckling responses of flat unstiffened composite panels. The panels are subjected to combined temperature change and applied edge displacement. The analysis is based on a first-order shear deformation, von Karman type nonlinear plate theory. A mixed formulation is used with the fundamental unknowns consisting of the generalized displacements and the stress resultants of the plate. An efficient multiple-parameter reduction method is used in conjunction with mixed finite element models, for determining the stability boundary and postbuckling response. The reduction method is also used for evaluating the sensitivity coefficients which measure the sensitivity of the buckling and postbuckling responses to variations in the different lamination and material parameters of the panel. Numerical results are presented showing the effects of variations in the laminate stacking sequence, fiber orientation, number of layers and aspect ratio of the panels on their thermomechanical buckling and postbuckling responses and their sensitivity coefficients.
Noor, Ahmed K.↗
Sensitivity analysis for large-deflection and postbuckling responses on distributed-memory computers
A computational strategy is presented for calculating sensitivity coefficients for the nonlinear large-deflection and postbuckling responses of laminated composite structures on distributed-memory parallel computers. The strategy is applicable to any message-passing distributed computational environment. The key elements of the proposed strategy are: (1) a multiple-parameter reduced basis technique; (2) a parallel sparse equation solver based on a nested dissection (or multilevel substructuring) node ordering scheme; and (3) a multilevel parallel procedure for evaluating hierarchical sensitivity coefficients. The hierarchical sensitivity coefficients measure the sensitivity of the composite structure response to variations in three sets of interrelated parameters; namely, laminate, layer and micromechanical (fiber, matrix, and interface/interphase) parameters. The effectiveness of the strategy is assessed by performing hierarchical sensitivity analysis for the large-deflection and postbuckling responses of stiffened composite panels with cutouts on three distributed-memory computers. The panels are subjected to combined mechanical and thermal loads. The numerical studies presented demonstrate the advantages of the reduced basis technique for hierarchical sensitivity analysis on distributed-memory machines.
Watson, Brian C.↗