SEARCH · Search NASA

Results for “extrapolation method”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

NASA NTRS1981

Comparison of three thrust calculation methods using in-flight thrust data

The gross thrust of an experimental airplane was determined by each method using the same flight maneuvers and generally the same data parameters. Coefficients determined from thrust stand calibrations for each of the three methods were then extrapolated to cruise flight conditions. The values of total aircraft gross thrust calculated by the three methods for cruise flight conditions agreed within + or - 3 percent. The disagreement in the values of thrust calculated by the different techniques manifested itself as a bias in the data. There was little scatter (0.5 percent) for the thrust levels examined in flight.

Hughes, D. L.↗

NASA NTRS1994

Sonic boom predictions using a solution-adaptive full-potential code

The TranAir full-potential code, which utilizes a solution-adaptive, unstructured Cartesian grid, was used to compute near-field pressure signatures of three generic geometries: (1) a cone-cylinder; (2) a low aspect ratio rectangular wing; and (3) a delta-wing/body. Pressure signatures computed by TranAir are extrapolated to near- and midfield distances using a quasilinear extrapolation technique. Results are compared with wind-tunnel data and, where possible, with extrapolated wind-tunnel data and Whitham-method results. In general, extrapolated TranAir data is in good agreement with experimental and Whitham-method pressure signatures, but peak pressures are slightly underpredicted. It is felt that data computed too close to the model caused some of the discrepancies. The flowfield grid structure was also found to be an important issue in obtaining accurate off-body data. Results were encouraging enough to proceed with the application of TranAir to conceptual configurations in support of the NASA high speed research program (HSRP).

Madson, Michael D.↗

NASA NTRS1995

Accurate Evaluation of Quantum Integrals

Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schrodinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

Galant, D. C.↗

NASA NTRS1994

Accurate Evaluation of Quantum Integrals

Combining an appropriate finite difference method with Richardson's extrapolation results in a simple, highly accurate numerical method for solving a Schr\"{o}dinger's equation. Important results are that error estimates are provided, and that one can extrapolate expectation values rather than the wavefunctions to obtain highly accurate expectation values. We discuss the eigenvalues, the error growth in repeated Richardson's extrapolation, and show that the expectation values calculated on a crude mesh can be extrapolated to obtain expectation values of high accuracy.

Galant, David C.↗

DOE OSTI2021

Constrained Extrapolation Problem and Order-Dependent Mappings

In this work, we consider the problem of extrapolating the perturbation series for the dilute Fermi gas in three dimensions to the unitary limit of infinite scattering length and into the BEC region, using the available strong-coupling information to constrain the extrapolation problem. In this constrained extrapolation problem (CEP) the goal is to find classes of approximants that give well converged results already for low perturbative truncation orders. First, we show that standard Padé and Borel methods are too restrictive to give satisfactory results for this CEP. A generalization of Borel extrapolation is given by the so-called Maximum Entropy extrapolation method (MaxEnt). However, we show that MaxEnt requires extensive elaborations to be applicable to the dilute Fermi gas and is thus not practical for the CEP in this case. Instead, we propose order-dependent-mapping extrapolation (ODME) as a simple, practical, and general method for the CEP. Here, we find that the ODME approximants for the ground-state energy of the dilute Fermi gas are robust with respect to changes of the mapping choice and agree with results from quantum Monte Carlo simulations within uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗

NASA NTRS1987

An algorithm for a generalization of the Richardson extrapolation process

The paper presents a recursive method, designated the W exp (m)-algorithm, for implementing a generalization of the Richardson extrapolation process. Compared to the direct solution of the linear sytems of equations defining the extrapolation procedure, this method requires a small number of arithmetic operations and very little storage. The technique is also applied to solve recursively the coefficient problem associated with the rational approximations obtained by applying a d-transformation to power series. In the course of development a new recursive algorithm for implementing a very general extrapolation procedure is introduced, for solving the same problem. A FORTRAN program for the W exp (m)-algorithm is also appended.

Ford, William F.↗

NASA NTRS1992

Modifications to Encke's method for long arc orbit determination solutions

An expanded model is developed that permits the extrapolation of Encke's method for the determination of orbits with long arcs, and the model is used to determine a solution for the Lageos trajectory. Encke's method is reviewed emphasizing the nature of the growth of the Encke ratio and the reliability of extrapolated reference trajectories. The reference-orbit formulation is improved by including parameters that accommodate drag and large-amplitude perodic variations in the orbital elements. The proposed Long Arc Model is expected to provide a maximum Encke ratio that is an order of magnitude more reliable than that given by the secularly precessing ellipse. The computational cost of using the Long Arc Model is shown to compare favorably with that of the true force model, and the long arc solutions are useful for current orbit-determination needs.

Lundberg, J. B.↗

NASA NTRS1981

MEGA16 - Computer program for analysis and extrapolation of stress-rupture data

The computerized form of the minimum commitment method of interpolating and extrapolating stress versus time to failure data, MEGA16, is described. Examples are given of its many plots and tabular outputs for a typical set of data. The program assumes a specific model equation and then provides a family of predicted isothermals for any set of data with at least 12 stress-rupture results from three different temperatures spread over reasonable stress and time ranges. It is written in FORTRAN 4 using IBM plotting subroutines and its runs on an IBM 370 time sharing system.

Ensign, C. R.↗

NASA NTRS1995

Enhancing Images By Nonlinear Extrapolation In Frequency

Improved method of enchancing edges in image involves nonlinear filter operation creating image-intensity components having spatial frequencies higher than those present in input image and locked in phase to lower-frequency input components. In comparison with other edge-enhancement methods involving mostly strengthening of higher-frequency components already present in input, this method computationally simpler and yields better results. Better suited to real-time applications like high-definition television and compression of image data.

Anderson, Charles H.↗

NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Two advances in the numerical techniques of utilizing the BIE method are presented. The boundary unknowns are represented by parabolas over each interval which are integrated in closed form. These integrals are listed for easy use. For problems involving crack tip singularities, these singularities are included in the boundary integrals so that the stress intensity factor becomes just one more unknown in the set of boundary unknowns thus avoiding the uncertainties of plotting and extrapolating techniques. The method is applied to the problems of a notched beam in tension and bending, with excellent results.

Mendelson, A.↗

NASA NTRS1977

The use of parabolic variations and the direct determination of stress intensity factors using the BIE method

Mendelson, A.↗

DOE OSTI2020

Prediction of Structures and Atomization Energies of Coinage Metals, (M)n, n < 20: Extrapolation of Normalized Clustering Energies to Predict the Cohesive Energy

The geometries of the group 11 coinage metals (n = 2-20) were optimized to determine the lowest energy isomers for each cluster size, singlets for even numbers and doublets for odd numbers. For copper and silver, 2-D (planar) geometries were favored up to n = 6. For gold, 2D (planar) geometries were favored up to n = 13. Normalized clustering energies were plotted as a function of cluster size (n-1/3, for n = 4-20) with various DFT functionals and the CCSD(T)-F12b method and were extrapolated to predict the bulk cohesive energy. In the case of copper and silver, there is excellent agreement between the cohesive energies predicted at the CCSD(T)-F12b level of theory and the experimental values. For gold, the CCSD(T)-F12b values needed to be corrected for spin-orbit relativistic effects to obtain good agreement with experiment. Electronic properties including the HOMO-LUMO gaps for the even clusters and the spin densities for the odd clusters were calculated. The lowest gap is predicted to occur for n = 16 where the HOMO and LUMO are very similar in shape.

Persuad, Rudradatt R.↗

DOE OSTI2026

Computing the Critical Temperature of the Affine-Transformed $D=3$ Ising Model Using Masked Autoregressive Flow

The simple Ising model provides a rich environment to build and study lattice field theories. As part of an ongoing project to construct a conformal field theory (CFT) on an arbitrarily curved manifold, in this work we develop methods to measure the critical temperature $β_c$ of the affine-transformed Ising model on the face-centered cubic (FCC) lattice. The main challenge in this endeavor is finding a computationally efficient and accurate method of interpolating and extrapolating Monte Carlo observables with respect to coupling coefficients and temperature. Herein, we compare two such methods. A traditional statistical approach uses the multiple histogram (MH) method, while a newer machine learning approach uses a masked autoregressive flow (MAF) to estimate the underlying probability density function of a set of observables. While the MH method is specifically designed to interpolate and extrapolate Monte Carlo observables, we find that MAF is a viable alternative for measuring $β_c$ with a computational cost that scales more favorably. Furthermore, we comment on additional advantages of MAF relevant to our work, such as extrapolating in system volume.

Svenson, Kai [Texas U.]↗

NASA NTRS2012

A Low Cost Weather Balloon Borne Solar Cell Calibration Payload

Calibration of standard sets of solar cell sub-cells is an important step to laboratory verification of on-orbit performance of new solar cell technologies. This paper, looks at the potential capabilities of a lightweight weather balloon payload for solar cell calibration. A 1500 gr latex weather balloon can lift a 2.7 kg payload to over 100,000 ft altitude, above 99% of the atmosphere. Data taken between atmospheric pressures of about 30 to 15 mbar may be extrapolated via the Langley Plot method to 0 mbar, i.e. AMO. This extrapolation, in principle, can have better than 0.1 % error. The launch costs of such a payload arc significantly less than the much larger, higher altitude balloons, or the manned flight facility. The low cost enables a risk tolerant approach to payload development. Demonstration of 1% standard deviation flight-to-flight variation is the goal of this project. This paper describes the initial concept of solar cell calibration payload, and reports initial test flight results. .

Snyder, David B.↗

DOE OSTI2026

PISCES two-detector covariance matrix fit for the NOvA Experiment

NOvA is a long-baseline neutrino oscillation experiment with two functionally identical detectors: a Near Detector (ND) at Fermilab, placed 1 km from the neutrino source, and a Far Detector (FD) located 810 km away from the ND in Minnesota. NOvA's primary physics goals are the precise measurements of neutrino oscillation parameters $\theta_{23}$ and $\Delta m^2_{32}$ , determine the neutrino mass ordering, and constrain the value of $\delta_{CP}$, via the study of muon neutrino to electron neutrino oscillation. In the standard NOvA three-flavor analysis, oscillation parameters are extracted using an extrapolation technique in which the ND data constrain the FD prediction through a ratio method. While this allows for systematic uncertainties sharing the same effects in both detectors to cancel, it remains an FD-only fit and does not fully leverage the constraining power of the high-statistics ND. This analysis proposes a simultaneous ND+FD fit using the PISCES method. PISCES (Parameter Inference with Systematic Covariance and Exact Statistics) is a framework designed to support complex configurations such as a joint ND+FD fit. This allows PISCES to take full advantage of the ND data to directly constrain systematic uncertainties across all samples. In PISCES, systematic uncertainties are encoded in a fractional covariance matrix, and statistical uncertainties are handled with a Poisson likelihood, making the approach well suited for low-statistics samples. For interpretability, we further use a Newton–Raphson + PCA method to recover per-systematic pulls from the covariance formulation. This poster presents the full PISCES joint ND+FD fit for the NOvA three-flavor analysis, describes its implementation and evaluates its performance through extensive robustness tests and fake data studies. It also provides a comparison between the PISCES joint ND+FD results and the standard NOvA extrapolation method.

Rajaoalisoa, Miriama [Cincinnati U.] (ORCID:000000↗

DOE OSTI2024

Efficient continuous Energy-Multigroup hybrid depletion scheme using the Shift Monte Carlo code. Part I: Energy condensation sensitivity analysis

Monte Carlo (MC) codes coupled to depletion solvers are increasingly used to provide high fidelity fuel cycle modeling capabilities. Here, these coupled depletion-MC tools produce accurate results in general but can experience nonphysical spatial oscillations when time steps are large or when a system’s dominance ratio approaches unity. Two substepping techniques have been developed previously to remedy and dampen these spatial oscillations without needing to reduce step sizes. The first approach relied on higher-order techniques to account for spectral changes within steps (extrapolation and interpolation techniques). The second approach used the first order perturbation (FOP) theory to account for the change in the one-group spatial flux distribution within steps. This paper develops a hybrid depletion methodology which, in a way, combines how the flux is handled in both substepping techniques. Specifically, the multigroup (MG) MC Shift code is used to update the flux distribution within steps rather than a one-group FOP solver. A fully reflected pincell is investigated, which is not spatially dependent in the MG representation. Thus, the analysis in this paper is an initial demonstration of hybrid depletion. An upcoming companion paper will focus on how the hybrid depletion dampens spatial oscillations. The hybrid depletion approach is verified to be consistent with previous constant extrapolation depletion (CED) methods. This paper finds that the hybrid CED exhibits some error in the eigenvalue and one group constants within macro steps. To address this discrepancy, a simple interpolation scheme (CELI) is investigated. This work found that CELI sufficiently addresses the discrepancy in spectrum for macro steps up to 100 days. Overall, this work demonstrates that the hybrid depletion method can significantly reduce the number of high fidelity MC executions in a MC-coupled depletion with an acceptable eigenvalue error.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Rapid assessment of the creep rupture life of metals: A model enabling experimental design

Prediction of the creep rupture life of engineering metals is critical for qualification and design of new materials. The use of long-term creep tests and the need to quantify the performance variability in a priori similar systems hinder the rapid creep assessment of a given material. Therefore, it is essential to develop methods that can extrapolate the long-term performance of alloys and the associated variability from short-term experiments. To this end, this study introduces a new model which enables the estimation of the rupture life of a material for a given stress and temperature. This model relies on two components. First, a new relation for the minimum creep rate (MCR) of materials is introduced. It includes a stress dependent stress exponent allowing the model to capture the variation of MCR across a wide range of temperatures and stresses. Second, employing the Monkman-Grant (MG) law, we establish a relation between stress, temperature and creep rupture life. Together, these two elements yield a new closed-form mathematical expression for the Larson Miller parameter as a function of stress and temperature. This expression captures the creep rupture time for many metals (Gr91, Copper, Gr122 and 347H) and compares favorably with alternate empirical approaches. The model is then used to assess the minimum duration of creep rates necessary to qualify the material up to 100000h. Furthermore, it is found that depending on the material system, creep tests as few as five limited to 5000 h for steels (Gr91, Gr122, 347H) and 100 h for copper are sufficient to model creep lifetimes. Finally, using a Bayesian inference-based approach to calibrate the model, we demonstrate that variability in rupture life can be captured via the quantification of the uncertainty in the model parameters and extrapolated from a limited number of short to moderately short creep tests; thereby paving the way for accelerated creep testing.

36 MATERIALS SCIENCE↗