Search NASA⌕ Search

SEARCH · Search NASA

Results for “methods - statistical”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,189 records · Page 66
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Verification Suite for the Application of the Limiting Surface Density Method to Arrays of 9975 Packages

Criticality Safety Engineering at the Savannah River Site’s K-Area Complex seeks to reduce the computational burden of analysis for the K-Area Complex. By applying an adapted Limiting Surface Density hand calculation method, the need for lengthy detailed Monte Carlo models of the storage arrays may be reduced or eliminated. After promising initial results using models of idealized but heterogeneous packages, application of the method to large arrays of highly heterogeneous 9975 shipping packages is attempted. A SCALE KENO-VI model of the 9975 package, with true dimensions and radial and axial heterogeneity is developed. A suite of array arrangements representing both arrays with equal number of packages per side (package-cubic) and arrays with unequal number of packages per side (non-cubic) are evaluated in SCALE. The cubic arrangements are used to derive the 9975-specific material and geometry constants for the LSD method. These constants are then used to implement the LSD method and compare the LSD- predicted critical mass per package to SCALE-predicted critical mass per package. Sensitivities to certain material and geometric nuances are evaluated for inclusion in the verification suite. Finally, the ability of the method to predict neutron multiplication changes induced by fissile mass changes is examined as a segue for evaluating credible abnormal conditions with the LSD method.

42 ENGINEERING↗
DOE OSTI2017

Verification suite for the application of the limiting surface density method to arrays of 9975 packages

Criticality Safety Engineering at the Savannah River Site's K-Area Complex seeks to reduce the computational burden of analysis for the K-Area Complex. By applying an adapted Limiting Surface Density hand calculation method, the need for lengthy detailed Monte Carlo models of the storage arrays may be reduced or eliminated. After promising initial results using models of idealized but heterogeneous packages, application of the method to large arrays of highly heterogeneous 9975 shipping packages is attempted. A SCALE KENO-VI model of the 9975 package, with true dimensions and radial and axial heterogeneity is developed. A suite of array arrangements representing both arrays with equal number of packages per side (package-cubic) and arrays with unequal number of packages per side (non-cubic) are evaluated in SCALE. The cubic arrangements are used to derive the 9975-specific material and geometry constants for the LSD method. These constants are then used to implement the LSD method and compare the LSD- predicted critical mass per package to SCALE-predicted critical mass per package. Sensitivities to certain material and geometric nuances are evaluated for inclusion in the verification suite. Finally, the ability of the method to predict neutron multiplication changes induced by fissile mass changes is examined as a segue for evaluating credible abnormal conditions with the LSD method. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Investigations about iso-geometric analysis for self-shielding calculations with the subgroup method

The implementation of a self-shielding method for a neutron transport calculation code based on the iso-geometric analysis (IGA) method that can resolve the multi-group neutron transport equation for arbitrary spatial domain, is presented. The self-shielding model based on the subgroup theory is adopted because the subgroup method can be used to perform calculations for any arbitrary geometrical domain which is the main purpose of our IGA code. Some basic theory of the subgroup method is given. A self-shielding calculation based on the PWR fuel pin composed of MOX fuel is presented and compared with a Monte Carlo calculation. The result is that the combination of SN transport theory, IGA and the subgroup method gives correctly shielded cross sections. Validation of the combination of the IGA method and SN neutron transport for subgroup calculations in two steps are presented: the first step is to ascertain the correctness of the IGA solutions compared to a known analytical solution in diffusion theory; the second step is a validation of the IGA solutions compared to a reference calculation in SN transport theory. The relation between the settings for the IGA solver and the accuracy of the results are elucidated. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2020

A least-squares finite element method based on the Helmholtz decomposition for hyperbolic balance laws

In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is related to the standard notion of a weak solution. This relationship, together with a corresponding connection to negative-norm least-squares, is described in detail. As a consequence, an important numerical conservation theorem is obtained, similar to the famous Lax–Wendroff theorem. The numerical conservation properties of the method in this paper do not fall precisely in the framework introduced by Lax and Wendroff, but they are similar in spirit as they guarantee that when L 2 convergence holds, the resulting approximations approach a weak solution to the hyperbolic problem. The least-squares functional is continuous and coercive in an H -1 -type norm, but not L 2 -coercive. Nevertheless, the L 2 convergence properties of the method are discussed. Convergence can be obtained either by an explicit regularization of the functional, that provides control of the L 2 norm, or by properly choosing the finite element spaces, providing implicit control of the L 2 norm. Numerical results for the inviscid Burgers equation with discontinuous source terms are shown, demonstrating the L 2 convergence of the obtained approximations to the physically admissible solution. The numerical method utilizes a least-squares functional, minimized on finite element spaces, and a Gauss–Newton technique with nested iteration. Finally, we believe that the linear systems encountered with this formulation are amenable to multigrid techniques and combining the method with adaptive mesh refinement would make this approach an efficient tool for solving balance laws (this is the focus of a future study).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Analysis of the shifted boundary method for the Stokes problem

The analysis of stability and accuracy of the shifted boundary method is developed for the Stokes flow equations. The key feature of the shifted boundary method, an embedded finite element method, is the shifting of the location where boundary conditions are applied from the true to a surrogate boundary, and an appropriate modification (shifting) of the value of the boundary conditions. An inf–sup condition is proved for the variational formulation associated to the shifted boundary method and we derive, by way of Strang’s second lemma, an optimal error estimate in the natural SBM norm. Here we also derive an L 2 -error estimate for the velocity field, by means of an extension of the Aubin–Nitsche approach to embedded, non-consistent, mixed finite element methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Mode I tensile fracture behavior of adhesively-bonded metal–metal, metal–CFRP, and CFRP–CFRP bi-material combinations analyzed by size effect method

Understanding the adhesive and interfacial fracture is important for developing and achieving better adhesive jointing in bi-materials, the location which becomes less vulnerable in engineered structure components. Still, to characterize the fracturing behavior of various adhesively-bonded materials, it was shown in this work that the Mode I fracture energies estimated from conventional methods (e.g., work-of-fracture, (modified) compliance calibration method, (modified) beam theory, etc.) can be strongly affected by adherent thickness, adhesive bond length, and material type. Consequently, this hindered the proper understanding of fracturing in adhesive jointing of bi-materials since the estimated fracture energies can exhibit unreasonable difference among various material combinations, thus leading to the confusion in the literature due to the unfair comparison on these non-objective results estimated by leveraging conventional methods on the specimens with different geometries. This work compared size effect method with conventional methods on the calculation of the Mode I fracture energies of metal-metal, metal-CFRP, and CFRP-CFRP material combinations via Double Cantilever Beam (DCB) tests. The results showed that the estimated fracture energies of various material combinations are not dependent on the specimen geometries. This aspect allowed the fair comparison particularly on the interfacial fracturing between metal/adhesive and CFRP/adhesive, and the difference was further explained and correlated with the damage morphology on the material surface after failure identified through three-dimensional profilometer.

36 MATERIALS SCIENCE↗
DOE OSTI2016

An adjoint method for a high-order discretization of deforming domain conservation laws for optimization of flow problems

We report the fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high-order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain is transformed into one on a fixed reference domain by the introduction of a time-dependent mapping that encapsulates the domain deformation and parametrization, resulting in an Arbitrary Lagrangian–Eulerian form of the governing equations. A high-order discontinuous Galerkin method is used to discretize the transformed equation in space and a high-order diagonally implicit Runge–Kutta scheme is used for the temporal discretization. Quantities of interest that take the form of space–time integrals are discretized in a solver-consistent manner. The corresponding fully discrete adjoint method is used to compute exact gradients of quantities of interest along the manifold of solutions of the fully discrete conservation law. These quantities of interest and their gradients are used in the context of gradient-based PDE-constrained optimization. The adjoint method is used to solve two optimal shape and control problems governed by the isentropic, compressible Navier–Stokes equations. The first optimization problem seeks the energetically optimal trajectory of a 2D airfoil given a required initial and final spatial position. The optimization solver, driven by gradients computed via the adjoint method, reduced the total energy required to complete the specified mission nearly an order of magnitude. The second optimization problem seeks the energetically optimal flapping motion and time-morphed geometry of a 2D airfoil given an equality constraint on the x-directed impulse generated on the airfoil. The optimization solver satisfied the impulse constraint to greater than 8 digits of accuracy and reduced the required energy between a factor of 2 and 10, depending on the value of the impulse constraint, as compared to the nominal configuration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A software‐defined networks ‐based measurement method of network traffic for 6G technologies

Abstract In software‐defined networks (SDN) for 6G technologies, the controller should accurately and efficiently measure the flow traffic in switches for traffic engineering. Fine‐grained flow measurement can more accurately describe the traffic in the network, but it also consumes much more resources. To reduce the overhead incurred in the measurement process and obtain the approximate fine‐grained measurements, we propose a novel lightweight measurement scheme that runs in the controller. The novel lightweight measurement architecture consists of two parts: coarse‐grained measurement and interpolation‐optimization. In the first part, based on the SDN architecture, we use the pull‐based random sampling method to quickly obtain the coarse‐grained measurement of flow traffic through OpenFlow protocol. In the second part, we insert some discrete values into the coarse‐grained measurement with the interpolation theory, then we optimize interpolation results until finding the optimal fine‐grained flow traffic measurement by utilizing the multiconstraint method. We verified the feasibility of the proposed measurement method, and simulation results show that the measurement error of the proposed method is under 25%, but the flow measurement overhead of this method occupies only 3.3% compared with that of the fine‐grained method.

Huo, Liuwei↗
DOE OSTI2016

Variational projection methods for gradient crystal plasticity using Lie algebras

Summary A computational method is developed for evaluating the plastic strain gradient hardening term within a crystal plasticity formulation. While such gradient terms reproduce the size effects exhibited in experiments, incorporating derivatives of the plastic strain yields a nonlocal constitutive model. Rather than applying mixed methods, we propose an alternative method whereby the plastic deformation gradient is variationally projected from the elemental integration points onto a smoothed nodal field. Crucially, the projection utilizes the mapping between Lie groups and algebras in order to preserve essential physical properties, such as orthogonality of the plastic rotation tensor. Following the projection, the plastic strain field is directly differentiated to yield the Nye tensor. Additionally, an augmentation scheme is introduced within the global Newton iteration loop such that the computed Nye tensor field is fed back into the stress update procedure. Effectively, this method results in a fully implicit evolution of the constitutive model within a traditional displacement‐based formulation. An elemental projection method with explicit time integration of the plastic rotation tensor is compared as a reference. A series of numerical tests are performed for several element types in order to assess the robustness of the method, with emphasis placed upon polycrystalline domains and multi‐axis loading. Copyright © 2016 John Wiley & Sons, Ltd.

Truster, Timothy J.↗
DOE OSTI2024

Data‐driven variational method for discrepancy modeling: Dynamics with small‐strain nonlinear elasticity and viscoelasticity

Abstract The effective inclusion of a priori knowledge when embedding known data in physics‐based models of dynamical systems can ensure that the reconstructed model respects physical principles, while simultaneously improving the accuracy of the solution in the previously unseen regions of state space. This paper presents a physics‐constrained data‐driven discrepancy modeling method that variationally embeds known data in the modeling framework. The hierarchical structure of the method yields fine scale variational equations that facilitate the derivation of residuals which are comprised of the first‐principles theory and sensor‐based data from the dynamical system. The embedding of the sensor data via residual terms leads to discrepancy‐informed closure models that yield a method which is driven not only by boundary and initial conditions, but also by measurements that are taken at only a few observation points in the target system. Specifically, the data‐embedding term serves as residual‐based least‐squares loss function, thus retaining variational consistency. Another important relation arises from the interpretation of the stabilization tensor as a kernel function, thereby incorporating a priori knowledge of the problem and adding computational intelligence to the modeling framework. Numerical test cases show that when known data is taken into account, the data driven variational (DDV) method can correctly predict the system response in the presence of several types of discrepancies. Specifically, the damped solution and correct energy time histories are recovered by including known data in the undamped situation. Morlet wavelet analyses reveal that the surrogate problem with embedded data recovers the fundamental frequency band of the target system. The enhanced stability and accuracy of the DDV method is manifested via reconstructed displacement and velocity fields that yield time histories of strain and kinetic energies which match the target systems. The proposed DDV method also serves as a procedure for restoring eigenvalues and eigenvectors of a deficient dynamical system when known data is taken into account, as shown in the numerical test cases presented here.

Masud, Arif↗
DOE OSTI2017

Fabrication of oriented crystals as force measurement tips via focused ion beam and microlithography methods

Detailed knowledge of the forces between nanocrystals is very crucial for understanding many generic (e.g., random aggregation/assembly and rheology) and specific (e.g., oriented attachment) phenomena at macroscopic length scales, especially considering the additional complexities involved in nanocrystals such as crystal orientation and corresponding orientation-dependent physicochemical properties. Because there are a limited number of methods to directly measure the forces, little is known about the forces that drive the various emergent phenomena. Here we report on two methods of preparing crystals as force measurement tips used in an atomic force microscope (AFM): the focused ion beam method and microlithography method. The desired crystals are fabricated using these two methods and are fixed to the AFM probe using platinum deposition, ultraviolet epoxy, or resin, which allows for the orientation-dependent force measurements. These two methods can be used to attach virtually any solid particles (from the size of a few hundreds of nanometers to millimeters). We demonstrate the force measurements between aqueous media under different conditions such as pH.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2018

Fast Decomposition of Three-Component Spectra of Fluorescence Quenching by White and Grey Methods of Data Modeling

‘White’ and ‘grey’ methods of data modeling have been employed to resolve the heterogeneous fluorescence from a fluorophore mixture of 9-cyanoanthracene (CNA), 10-chloro-9-cyanoanthracene (ClCNA) and 9,10-dicyanoanthracene (DCNA) into component individual fluorescence spectra. The three-component spectra of fluorescence quenching in methanol were recorded for increasing amounts of lithium bromide used as a quencher. The associated intensity decay profiles of differentially quenched fluorescence of single components were modeled on the basis of a linear Stern-Volmer plot. These profiles are necessary to initiate the fitting procedure in both ‘white’ and ‘grey’ modeling of the original data matrices. ‘White’ methods of data modeling, called also ‘hard’ methods, are based on chemical/physical laws expressed in terms of some well-known or generally accepted mathematical equations. The parameters of these models are not known and they are estimated by least squares curve fitting. ‘Grey’ approaches to data modeling, also known as hard-soft modeling techniques, make use of both hard-model and soft-model parts. In practice, the difference between ‘white’ and ‘grey’ methods lies in the way in which the ‘crude’ fluorescence intensity decays of the mixture components are estimated. In the former case they are given in a functional form while in the latter as digitized curves which, in general, can only be obtained by using dedicated techniques of factor analysis. In the paper, the initial values of the Stern-Volmer constants of pure components were evaluated by both ‘point-by-point’ and ‘matrix’ versions of the method making use of the concept of wavelength dependent intensity fractions as well as by the rank annihilation factor analysis applied to the data matrices of the difference fluorescence spectra constructed in two ways: from the spectra recorded for a few excitation lines at the same concentration of a fluorescence quencher or classically from a series of the spectra measured for one selected excitation line but for increasing concentration of the quencher. The results of multiple curve resolution obtained by all types of the applied methods have been scrutinized and compared. In addition, the effect of inadequacy of sample preparation and increasing instrumental noise on the shape of the resolved spectral profiles has been studied on several datasets mimicking the measured data matrices. .

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2019

Leapfrog Time-Stepping for Hermite Methods

We introduce here Hermite-leapfrog methods for first order linear wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors et al. (Math Comput 75(254):595–630, 2006). The new schemes stagger field variables in both time and space and are high-order accurate for equations with smooth solutions and coefficients. We provide a detailed description of the method and demonstrate that the method conserves variable quantities. Higher dimensional versions of the method are constructed via tensor products. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Optimization of Pineapple Leaf Fibre Extraction Methods and Their Biodegradabilities for Soil Cover Application

Cellulosic natural fibres from pineapple leaves are considered as a green alternative to the conventional polyethylene (PE) soil cover in agro-industry. The use of pineapple leaf fibres (PALFs) soil cover can overcome the disposal problem of the conventional plastic covers which take hundreds of years to degrade. This research was undertaken to study the effectiveness methods of extracting the PALFs. The mechanical method utilized ‘roller and bladder system’, where the chemical method involved the extraction with 6% NaOH, 20% aqueous acetone, and pineapple juice solution. The semi-mechanical method was a combination of “roller and bladder” system and a chemical retting process using 6% NaOH alkaline solutions. The characteristics of the extracted fibers were determined using X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR). Kappa number test of the fibres extracted with semi-mechanical method showed the lowest percentage of lignin (3.39%). Based on XRD results, the highest percentage of crystallinity was recorded when PALF was extracted using the semi-mechanical method. A remarkable change on the morphological surface the biodegraded PALF soil cover was observed after 90 days of soil burial test. Biodegradability of soil cover made from PALF was higher than the commercial degradable soil cover i.e. PE/starch (80 wt% PE/ 20 wt% starch). Meanwhile, the growing rate and the soil fertility of chili tree that used PALFs soil cover showed better results than the chili tree that used conventional PE/starch soil cover.

36 MATERIALS SCIENCE↗
DOE OSTI2018

The Influence of Fabrication Methods on Structure and Microwave Absorption Property of Fe{sub 3}O{sub 4}/rGO Composites

In this study, flake graphite is used as raw material and oxidized to produce graphene oxide (GO), and then two kinds of ferroferric oxide/reduced graphene oxide (Fe{sub 3}O{sub 4}/rGO) composites are fabricated with one-step and two-step methods, respectively. The influence of composite methods on structure and performance is investigated by FT-IR, XRD, SEM, TEM, and testing of electromagnetic parameters. The results show that there are many advantages in the one-step method for fabrication of Fe{sub 3}O{sub 4}/rGO composite, such as the composite process is simplified, the time is shortened, and the Fe{sub 3}O{sub 4}/rGO composite fabricated with the one-step method has the best microwave impedance matching property in the frequency range of 2.5–6 GHz. At the same time, it can be found that there is the Fe–O–C bond in Fe{sub 3}O{sub 4}/rGO composites fabricated with the one-step method, which results in two ways of physical recombination and chemical bonding between Fe{sub 3}O{sub 4} and rGO sheet particulates. In addition, when the mass ratio of GO and FeCl{sub 3} is 1:10, the R{sub L} value of the Fe{sub 3}O{sub 4}/rGO composite fabricated with the one-step method is minimum, and the increase of sample thickness is beneficial to improve the impedance matching property of Fe{sub 3}O{sub 4}/rGO composite in the frequency range of 2.5–6 GHz.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Effect of Zn, Ga and Gd Doping on Structural and Magnetic Properties of Nanonickel Ferrite Prepared by Two Different Methods

Zn/Ga/Gd-substituted NiFe{sub 2}O{sub 4} was formed by solid state reaction and citrate methods. The influence of substitutions on phase formation, the strain, crystallize size, cations distribution and magnetic properties have been examined by X-ray diffraction, Mössbauer effect spectrometer, Fourier-transform infrared, and vibrating sample magnetometer. Zn/Ga/Gd substituted NiFe{sub 2}O{sub 4} samples prepared by solid state method showed that as gadolinium introduced into the system, a second phase was formed with a small percentage while samples prepared by citrate method exhibited a single phase. The distributions of different cations between different sites were determined by both Mössbauer effect spectroscopy, modified Bertaut and Rietveld analysis. Mössbauer technique at room temperature showed that samples synthesized by the ceramic method have a magnetic order while samples prepared by citrate method have a superparamagnetic nature. The canting angle between magnetic ions was increased by increased the amount of Zn in samples prepared by both methods.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

A relative radiometric correction method for airborne SWIR hyperspectral image using the side-slither technique

Stripe noise still remains in airborne short-wave infrared (SWIR) hyperspectral (HS) images after laboratory calibration due to the stray light of HS imager, nonlinear response of infrared focal plane array, and the distinct difference of equivalent color temperature between the integrating sphere and the sun. It is difficult to get a sun-like radiation source, and we apply the side-slither technique for relative radiometric correction of HS images. The calibration data corresponding to different irradiance were obtained by the side-slither technique of imager. Then, the two-point multi-section method is used for relative radiometric correction of HS images. This paper presents the principle, the experimental results, and the analysis of the proposed method. To validate the effectiveness of this method, it was compared with other methods and evaluated by quantitative quality indices. The results reveal that this method has a good performance in relative radiometric correction of HS image and is superior to the laboratory calibration based on integrating sphere. Consequently, the proposed method can successfully eliminate the adverse effect caused by the difference of equivalent color temperature between radiation sources, and also can improve the accuracy of HS applications such as absolute radiation correction and target recognition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗