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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.

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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Goal-oriented a-posteriori estimation of model error as an aid to parameter estimation

In this work, a Bayesian model calibration framework is presented that utilizes goal-oriented a-posterior error estimates in quantities of interest (QoIs) for classes of high-fidelity models characterized by PDEs. It is shown that for a large class of computational models, it is possible to develop a computationally inexpensive procedure for calibrating parameters of high-fidelity models of physical events when the parameters of low-fidelity (surrogate) models are known with acceptable accuracy. The main ingredients in the proposed model calibration scheme are goal-oriented a-posteriori estimates of error in QoIs computed using a so-called lower fidelity model compared to those of an uncalibrated higher fidelity model. The estimates of error in QoIs are used to define likelihood functions in Bayesian inversion analysis. A standard Bayesian approach is employed to compute the posterior distribution of model parameters of high-fidelity models. As applications, parameters in a quasi-linear second-order elliptic boundary-value problem (BVP) are calibrated using a second-order linear elliptic BVP. In a second application, parameters of a tumor growth model involving nonlinear time-dependent PDEs are calibrated using a lower fidelity linear tumor growth model with known parameter values.

A-posterior estimates↗
DOE OSTI2019

Estimation of Errors in Stress Distributions Computed in Finite Element Simulations of Polycrystals

The accuracy of the stresses predicted from crystal plasticity-based finite element formulation depends on estimation and control of the errors associated with the discretization. In the current work, the errors in the stress distribution are estimated in virtual polycrystalline samples of α-phase titanium (hexagonal close-packed phase of Ti–6Al– 4 V). To estimate the error, the stress field, which does not possess inter-element continuity, is smoothed over a grain using an L 2 projection, thereby providing continuous stress distributions with inter-element continuity. The differences between the continuous (smooth) and discontinuous (raw) stress fields are calculated at individual Gauss quadrature points and used to estimate errors for corresponding elements and grains. Error estimations are performed for a Voronoi-tessellated microstructure, an equiaxed microstructure, and two microstructures with varying grain sizes for tensile loading extending into the fully plastic regime (≈ 5% extension). Magnitudes of the errors are found to depend on microstructural characteristics, particularly the shape and size of grains. Samples having variations in grain size or having less spherical grains exhibited higher errors than samples with uniformly sized, equiaxed grains, with the size variations having a more pronounced effect. In conclusion, errors correlate with proximity to grain boundaries at small (elastic) strains and with deformation-induced features (deformation bands) at large strains.

42 ENGINEERING↗
DOE OSTI2021

Performance Comparison of Circular and Spherical Error Probable Estimators

This report compares the performance of three Circular Error Probable (CEP) estimators: the Grubbs-Patnaik estimator, a new, non-iterative, radial-integration estimator, and a median estimator. It also compares the performance of two Spherical Error Probable (SEP) estimators. The performance of each estimator is assessed in terms of bias, uncertainty, robustness, and computational complexity. Robustness is evaluated with respect to outliers, variations in the underlying statistical distribution characterizing munition impact positions, and impact-position measurement errors. The performance assessments indicate the radial-integration and Grubbs-Patnaik estimators perform nearly identically providing the statistical distribution of impact-position coordinates is jointly normal with zero means. In that case, both estimators outperform the median estimator by about 2% relative to the true CEP in terms of estimator uncertainty. The bias performance of the radial-integration and median estimators is close to zero for jointly normal impacts, however, the Grubbs-Patnaik estimator can be significantly biased for jointly normal impacts with non-zero means. When the statistical distribution characterizing impact positions is known, but not jointly normal, the radial-integration estimator is superior. In this case, the median estimator also outperforms the Grubbs-Patnaik estimator but is not quite as good as the radial-integration estimator. If the statistical distribution characterizing impacts is unknown and not jointly normal, or if distribution parameters are difficult or impractical to estimate, or if test data is corrupted with outliers, then the median estimator dramatically outperforms the other estimators, especially in terms of estimation bias. Unexpectedly, measurement noise did not significantly degrade the performance of any of the estimators, except for cases with signal to noise ratios less than five. Although the Grubbs-Patnaik estimator has remained the gold standard for CEP estimation for over half a century, the performance assessments indicate the new, non-iterative, radial-integration estimator and the median estimator offer significant advantages and, in most practical real-world conditions, are superior estimators. These estimators are also useful for SEP estimation whereas the Grubbs-Patnaik estimator does not extend to three dimensions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Spatially resolved X-ray emission measurements of the residual velocity during the stagnation phase of inertial confinement fusion implosion experiments

A technique for measuring residual motion during the stagnation phase of an indirectly driven inertial confinement experiment has been implemented. This method infers a velocity from spatially and temporally resolved images of the X-ray emission from two orthogonal lines of sight. This work investigates the accuracy of recovering spatially resolved velocities from the X-ray emission data. A detailed analytical and numerical modeling of the X-ray emission measurement shows that the accuracy of this method increases as the displacement that results from a residual velocity increase. For the typical experimental configuration, signal-to-noise ratios, and duration of X-ray emission, it is estimated that the fractional error in the inferred velocity rises above 50% as the velocity of emission falls below 24 μm/ns. By inputting measured parameters into this model, error estimates of the residual velocity as inferred from the X-ray emission measurements are now able to be generated for experimental data. Details of this analysis are presented for an implosion experiment conducted with an unintentional radiation flux asymmetry. The analysis shows a bright localized region of emission that moves through the larger emitting volume at a relatively higher velocity towards the location of the imposed flux deficit. This technique allows for the possibility of spatially resolving velocity flows within the so-called central hot spot of an implosion. This information would help to refine our interpretation of the thermal temperature inferred from the neutron time of flight detectors and the effect of localized hydrodynamic instabilities during the stagnation phase. Across several experiments, along a single line of sight, the average difference in magnitude and direction of the measured residual velocity as inferred from the X-ray and neutron time of flight detectors was found to be ∼13 μm/ns and ∼14°, respectively.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Measurement Error Variance Estimation in Gamma-Spectroscopy Data using FRAM

The FRAM gamma-ray isotopic analysis code has recently been applied to four Pu data sets and four U data sets, each with relatively well-characterized standard items, in order to estimate the variances of random errors and of item-specific systematic errors. Assay results are available for Pu238, Pu239, Pu240, Pu241, Pu242 (operator entered, not independently measured), Am241, Specific Power, and Pu240eff. For the four U data sets, results are available for the measurands U234, U235, U236 (operator entered, not independently measured), and U238. For example, in Pu data set 1, there are 33 standard reference Pu items, which have well-known nominal/true values (except for a few items). FRAM was used to make approximately 15 repeat measurements for each of the 33 items, so empirical standard deviations can be calculated. In addition, FRAM internally estimates its random error variance using propagation of variance. This paper applies analysis of variance (ANOVA) to separately estimate the repeatability standard deviation and the standard deviation of the item-specific biases δ s in each of the 8 data sets.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Modeling mechanical behavior of an additively manufactured metal structure with local texture variations: a study on model form error

Here, the repetitive rapid solidification that occurs in metal additive manufacturing (AM) processes creates microstructures distinctly different from wrought materials. Local variability in AM microstructures (either by design or unintentional) raises questions as to how AM structures should be modeled at the part-scale to minimize modeling error. The key goal of this work is to demonstrate a posteriori error estimation applied to an AM part. It is assumed that the actual microstructure is unknown and an approximate, spatially uniform material model is used. Error bounds are calculated for many reference models based on AM microstructures with elongated grain morphology and localized or global fiber textures during a post-processing step. The current findings promote confidence that a posteriori model form error estimation could be used effectively in mechanical performance simulations of AM parts to quickly obtain quantitative error metrics between an approximate model result and many microstructure-based reference models. The a posteriori error estimation introduces significant time savings compared to computing the full reference model solutions. Tight bounds on model form error are obtained when texture variations in the reference models occur on large length scales. For materials with property variation at small length scales, multi-scale error estimation techniques are needed to properly account for the many interfaces present between areas with different properties.

36 MATERIALS SCIENCE↗
DOE OSTI2018

On the convergence and convergence order of finite volume gradient schemes for oblique derivative boundary value problems

This work is an improvement of the previous note (Bradji in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) which dealt with the convergence analysis of a finite volume scheme for the Poisson’s equation with a linear oblique derivative boundary condition. The formulation of the finite volume scheme given in Bradji (in: Fuhrmann et al., Finite volumes for complex applications VII–methods, theoretical aspects. Proceedings of the FVCA 7, Berlin, 2014) involves the discrete gradient introduced recently in Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010). In this paper, we consider the convergence analysis of finite volume schemes involving the discrete gradient of Eymard et al. (IMA J Numer Anal 30(4):1009–1043, 2010) for elliptic and parabolic equations with linear oblique derivative boundary conditions. Linear oblique derivative boundary conditions arise for instance in the study of the motion of water in a canal, cf. Lesnic (Commun Numer Methods Eng 23(12):1071–1080, 2007). We derive error estimates in several norms which allow us to get error estimates for the approximations of the exact solutions and its first derivatives. In particular, we provide an error estimate between the gradient of the exact solutions and the discrete gradient of the approximate solutions. Convergence of the family of finite volume approximate solutions towards the exact solution under weak regularity assumption is also investigated. In the case of parabolic equations with oblique derivative boundary conditions, we develop a new discrete a priori estimate result. The proof of this result is based on the use of a discrete mean Poincaré–Wirtinger inequality. Thanks to the stated a priori estimate and to a comparison with an appropriately chosen auxiliary finite volume scheme, we derive the convergence results. This work can be viewed as a continuation of the previous work (Bradji and Gallouët in Int J Finite Vol 3(2):1–35, 2006) where a convergence analysis for a finite volume scheme, based on the admissible mesh of Eymard et al. (In: Ciarlet and Lions, Handbook of numerical analysis, North-Holland, Amsterdam, 2000), for the Poisson’s equation with a linear oblique derivative boundary conditions is given. The obtained convergence results do not require any relation between the mesh sizes of the spatial and time discretizations. Some numerical tests are presented for both elliptic and parabolic equations. In particular, we present three methods to compute the discrete solution.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Investigation of the effect of noise parameters of a 3D lidar on the error in estimating relief signatures of distant objects from 2D field intensity distributions of reflected radiation

We consider the influence of noise parameters of a 3D lidar and external background radiation on the error in estimating the relief signatures of distant objects from 2D field intensity distributions of the reflected radiation. A physical and mathematical model is developed to analyse the effect of noise. The dependence of the error in estimating the relief signatures at various signal-to-noise ratios is investigated taking into account the parameters of real multi-element photodetectors (MEPDs). The obtained results indicate the possibility of evaluating relief signatures of distant objects with high accuracy based on standard MEPDs simultaneously for a large number of points on the object’s surface with a signal-to-noise ratio of more than 4. (paper)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Simulation Evaluation of a Large-Scale Implementation of Virtual-Phase Link-Based Model Predictive Control

Traffic congestion is a serious problem in the US, and traffic signal control is one of the effective solutions to congestion. Previous research on model predictive control (MPC)-based traffic signal control showed substantial benefits over conventional methods. This study focused on implementing MPC over a large-scale network with complex intersections and the impact of cycle length, network size, and imperfect state estimation on performances. This study implemented a virtual phase link (VPL)-based model predictive control method which used the number of vehicles in each VPL as input state variables and was suitable for National Electrical Manufacturing Association (NEMA) ring-barrier control. To test the impact of network size, the performance of distributed MPC (36 intersections in the network are divided into five subnetworks) was compared with that of MPC over the full network for a set of cycle lengths. To test the impact of imperfect state estimation, we synthetically infused estimation error and developed two scenarios, MPC-error and MPC-error narrow, which had higher and lower estimation errors, respectively. The performance of these MPC methods was compared with that of the existing time-of-day (TOD) method and an offline method that used Webster's method for split and MULTIBAND for cycle length and offset optimization. Trajectory and linkwise signal performance measures were collected from the simulation to evaluate performance. The distributed MPC method with perfect state estimation had the lowest delay and highest energy efficiency of all the methods. The performance of MPC decreased as the prediction inaccuracy increased. MPC-error had 7% and 11% more delay than MPC-error narrow in the morning and evening peaks, respectively. Overall, simulation results suggest that even with imperfect state estimation, MPC methods will outperform offline methods significantly.

large-scale simulation↗
DOE OSTI2020

Variable-fidelity multipoint aerodynamic shape optimization with output-based adapted meshes

This work presents a method to control the discretization error in multipoint aerodynamic shape optimization using output-based adapted meshes. The meshes are adapted via adjoint-based error estimates, taking into account both the objective and constraint output errors. A multi-fidelity optimization framework is then developed by taking advantage of the variable fidelity offered by adaptive meshes. The objective functional and its sensitivity at each design point (operating condition) are first evaluated on the same initial coarse mesh, which is then subsequently adapted for each design point individually as the shape optimization proceeds. The effort to set up the optimization is minimal since the initial mesh can be fairly coarse and easy to generate. As the shape approaches the optimal design, the mesh at each design point becomes finer, in regions necessary for that particular operating condition. The multi-fidelity framework is tightly coupled with the objective error estimation to ensure the optimization accuracy at each fidelity. Computational savings arise from a reduction of the mesh size when the design is far from optimal and avoiding an exhaustive search on low-fidelity meshes. The proposed method is demonstrated on multipoint drag minimization problems of a transonic airfoil with lift and area constraints. Improved accuracy and efficiency are shown compared to traditional fixed-fidelity optimization with a fixed computational mesh.

42 ENGINEERING↗
DOE OSTI2016

Proton radius from electron scattering data

Background: The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. The discrepancy has become known as the proton radius puzzle. Purpose: In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. Methods: We make use of stepwise regression techniques using the F-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. Results: Starting with the precision, low four-momentum transfer (Q 2 ) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the F-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on GE from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-Q 2 data on G E to select functions which extrapolate to high Q 2 , we find that a Pad´e (N = M = 1) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, G E (Q 2 ) = (1 + Q 2 /0.66 GeV 2 ) -2 . Conclusions: Rigorous applications of stepwise regression techniques and multivariate error estimates result in the extraction of a proton charge radius that is consistent with the muonic hydrogen result of 0.84 fm; either from linear extrapolation of the extreme low-Q 2 data or by use of the Pad´e approximant for extrapolation using a larger range of data. Thus, based on a purely statistical analysis of electron scattering data, we conclude that the electron scattering result and the muonic hydrogen result are consistent. Lastly, it is the atomic hydrogen results that are the outliers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

On the time growth of the error of the DG method for advective problems

Abstract In this paper we derive a priori $L^{\infty }(L^{2})$ and L2(L2) error estimates for a linear advection–reaction equation with inlet and outlet boundary conditions. The goal is to derive error estimates for the discontinuous Galerkin method that do not blow up exponentially with respect to time, unlike the usual case when Gronwall’s inequality is used. While this is possible in special cases, such as divergence-free advection fields, we take a more general approach using exponential scaling of the exact and discrete solutions. Here we use a special scaling function, which corresponds to time taken along individual pathlines of the flow. For advection fields, where the time that massless particles carried by the flow spend inside the spatial domain is uniformly bounded from above by some $\widehat{T}$, we derive $\mathcal{O}$(hp+1/2) error estimates where the constant factor depends only on $\widehat{T}$, but not on the final time T. This can be interpreted as applying Gronwall’s inequality in the error analysis along individual pathlines (Lagrangian setting), instead of physical time (Eulerian setting).

Mathematics↗
DOE OSTI2019

Solution-Based Adaptivity as a Paradigm for Computational Fluid Dynamics

This is the final report for the DOE Early Career award. Through innovation in error estimation and solution-based adaptation methods we strive to dramatically improve the efficiency and robustness of computational science and engineering simulations. By solution-based error estimation and adaptation we refer to techniques for estimating numerical error and efficiently reducing it through targeted discretization changes. In such a setting, high-order methods play a key role, though they are just one mechanism for efficient accuracy improvement. Other mechanisms include well known mesh size and stretching optimization, as well as less-practiced mesh motion and basis optimization. With additional work on the latter, we are integrating these techniques into one adaptive suite that maximizes efficiency and robustness of Computational Fluid Dynamics (CFD) calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Processing Aleatory and Epistemic Uncertainties in Experimental Data From Sparse Replicate Tests of Stochastic Systems for Real-Space Model Validation

This paper presents a practical methodology for propagating and processing uncertainties associated with random measurement and estimation errors (that vary from test-to-test) and systematic measurement and estimation errors (uncertain but similar from test-to-test) in inputs and outputs of replicate tests to characterize response variability of stochastically varying test units. Also treated are test condition control variability from test-to-test and sampling uncertainty due to limited numbers of replicate tests. These aleatory variabilities and epistemic uncertainties result in uncertainty on computed statistics of output response quantities. The methodology was developed in the context of processing experimental data for “real-space” (RS) model validation comparisons against model-predicted statistics and uncertainty thereof. The methodology is flexible and sufficient for many types of experimental and data uncertainty, offering the most extensive data uncertainty quantification (UQ) treatment of any model validation method the authors are aware of. It handles both interval and probabilistic uncertainty descriptions and can be performed with relatively little computational cost through use of simple and effective dimension- and order-adaptive polynomial response surfaces in a Monte Carlo (MC) uncertainty propagation approach. A key feature of the progressively upgraded response surfaces is that they enable estimation of propagation error contributed by the surrogate model. Sensitivity analysis of the relative contributions of the various uncertainty sources to the total uncertainty of statistical estimates is also presented. Finally, the methodologies are demonstrated on real experimental validation data involving all the mentioned sources and types of error and uncertainty in five replicate tests of pressure vessels heated and pressurized to failure. Simple spreadsheet procedures are used for all processing operations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A kriging and entropy-based approach to raingauge network design

Highlights: • A kriging and entropy theory-based approach is developed for gauge network design. • The method considers both minimum estimating error andoptimum rainfall information. • The best combination is verified to be effectiveto achieve final goals. Hydrological data, such as precipitation, is fundamental for planning, designing, developing, and managing water resource projects as well as for hydrologic research. An optimal raingauge network leads to more accurate estimates of mean or point precipitation at any site over the watershed. Some studies in the past have suggested increasing gauge network density for reducing the estimation error. However, more stations mean more cost of installation and monitoring. This study proposes an approach on the basis of kriging and entropy theory to determine an optimal network design in the city of Shanghai, China. Unlike the past studies using kriging interpolation and entropy theory for network design, the approach developed in the current study not only used the kriging method as an interpolator to determine rainfall data at ungauged locations but also incorporated the minimum kriging standard error (KSE) and maximum net information (NI) content. The approach would thus lead to an optimal network and would enable the reduction of kriging standard error of precipitation estimates throughout the watershed and achieve an optimum rainfall information. This study also proposed an NI-KSE-based criterion which is dependent on a single-objective optimization. To evaluate the final optimal gauge network, areal average rainfall was estimated and its accuracy was compared with that obtained with the existing rain gauge network.

54 ENVIRONMENTAL SCIENCES↗