Search NASA⌕ Search

SEARCH · Search NASA

Results for “interpolating methods”

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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Constraints on the finite volume two-nucleon spectrum at 𝑚𝜋 ≈806 MeV

The low-energy, finite-volume spectrum of the two-nucleon system at a quark mass corresponding to a pion mass of 𝑚𝜋≈806 MeV is studied with lattice quantum chromodynamics (LQCD) using variational methods. The interpolating-operator sets used in [Variational study of two-nucleon systems with lattice QCD, Phys. Rev. D 107, 094508 (2023).] are extended by including a complete basis of local hexaquark operators, as well as plane-wave dibaryon operators built from products of both positive- and negative-parity nucleon operators. Results are presented for the isosinglet and isotriplet two-nucleon channels. In both channels, noticeably weaker variational bounds on the lowest few energy eigenvalues are obtained from operator sets which contain only hexaquark operators or operators constructed from the product of two negative-parity nucleons, while other operator sets produce low-energy variational bounds which are consistent within statistical uncertainties. The consequences of these studies for the LQCD understanding of the two-nucleon spectrum are investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Machine Learning Approach for Spatiotemporal Multivariate Optimization of Environmental Monitoring Sensor Locations

Abstract Long-term environmental monitoring is critical for managing the soil and groundwater at contaminated sites. Recent improvements in state-of-the-art sensor technology, communication networks, and artificial intelligence have created opportunities to modernize this monitoring activity for automated, fast, robust, and predictive monitoring. In such modernization, it is required that sensor locations be optimized to capture the spatiotemporal dynamics of all monitoring variables as well as to make it cost-effective. The legacy monitoring datasets of the target area are important to perform this optimization. In this study, we have developed a machine-learning approach to optimize sensor locations for soil and groundwater monitoring based on ensemble supervised learning and majority voting. For spatial optimization, Gaussian process regression (GPR) is used for spatial interpolation, while the majority voting is applied to accommodate the multivariate temporal dimension. Results show that the algorithms significantly outperform the random selection of the sensor locations for predictive spatiotemporal interpolation. While the method has been applied to a four-dimensional dataset (with two-dimensional space, time, and multiple contaminants), we anticipate that it can be generalizable to higher-dimensional datasets for environmental monitoring sensor location optimization.

Siddiquee, Masudur R.↗
NASA NTRS1971

Estimation of total ozone from satellite measurements of backscattered ultraviolet earth radiance.

Total ozone is estimated from Nimbus IV satellite measurements of the attenuation of backscattered radiances at wavelengths between 3100 and 3400 A. A measurement of the backscattered radiance at 3800 A, outside the ozone absorption band, is used to determine an equivalent Lambert albedo for the cloud-ground-haze surface viewed by the instrument. The measured relative attenuation at two wavelengths is compared with such values precomputed for a series of standard ozone profiles and corrected for the equivalent Lambert albedo. Total ozone is obtained by interpolation. Two alternative methods are used to assign an equivalent Lambert albedo at the absorbing wavelengths. Total ozone values estimated by these methods are compared with the Dobson (ground-truth) data by linear regression. The available evidence suggests that the true standard error of the satellite data may be 0.015 atm-cm or less for solar zenith angles smaller than 60 deg.

Mateer, C. L.↗
NASA NTRS1986

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗
NASA NTRS1986

Retrieval of aerosol size distribution moments from multiwavelength particulate extinction data

An iterative method for deriving the particle size distribution from multiwavelength satellite remote sensing data is presented and its use illustrated with an application to SAGE II data. The compression size distribution method (CSD) features interpolation and look-up features for relating the coefficients of a least-squares fit as a function of wavelength to parameters of the compression function that have been obtained by Mie calculations. Results are reported of comparisons between particulate radii predicted for the El Chichon volcano aerosol based on SAGE II data and 14 radii measured with NASA flights through the aerosol with aircraft carrying wire impactors.

Livingston, J. M.↗
NASA NTRS1994

Automatic computation of Euler-marching and subsonic grids for wing-fuselage configurations

Algebraic procedures are described for the automatic generation of structured, single-block flow computation grids for relatively simple configurations (wing, fuselage, and fin). For supersonic flows, a quasi two-dimensional grid for Euler-marching codes is developed, and some sample results in graphical form are included. A type of grid for subsonic flow calculation is also described. The techniques are algebraic and are based on a generalization of the method of transfinite interpolation.

Barger, Raymond L.↗
NASA NTRS1998

A Conceptual Approach to Assimilating Remote Sensing Data to Improve Soil Moisture Profile Estimates in a Surface Flux/Hydrology Model: Disaggregation - 3

This is a followup on the preceding presentation by Crosson and Schamschula. The grid size for remote microwave measurements is much coarser than the hydrological model computational grids. To validate the hydrological models with measurements we propose mechanisms to disaggregate the microwave measurements to allow comparison with outputs from the hydrological models. Weighted interpolation and Bayesian methods are proposed to facilitate the comparison. While remote measurements occur at a large scale, they reflect underlying small-scale features. We can give continuing estimates of the small scale features by correcting the simple 0th-order, starting with each small-scale model with each large-scale measurement using a straightforward method based on Kalman filtering.

Caulfield, John↗
NASA NTRS2019

Improvements in the Uncertainty Model in the Goddard Institute for Space Studies Surface Temperature (GISTEMP) Analysis

We outline a new and improved uncertainty analysis for the Goddard Institute of Space Studies (GISS) Surface Temperature product version 4 (GISTEMP v4). Historical spatial variations in surface temperature anomalies are derived from historical weather station data and ocean data from ships, buoys and other sensors. Uncertainties arise from measurement uncertainty, changes in spatial coverage of the station record, and systematic biases due to technology shifts and land cover changes. Previously published uncertainty estimates for GISTEMP included only the effect of incomplete station coverage. Here, we update this term using currently available spatial distributions of source data, state‐of‐the‐art reanalyses and incorporate independently derived estimates for ocean data processing, station homogenization and other structural biases. The resulting 95% uncertainties are near 0.05° C in the global annual mean for the last 50 years, and increase going back further in time reaching 0.15° C in 1880. In addition, we quantify the benefits and inherent uncertainty due to the GISTEMP interpolation and averaging method. We use the total uncertainties to estimate the probability for each record year in the GISTEMP to actually be the true record year (to that date), and conclude with 86% likelihood that 2016 was indeed the hottest year of the instrumental period (so far).

Nathan J L Lenssen↗
NASA NTRS2004

High Order And High Resolution Methods For a Model CAA Problem

The initial value problem for the first order linear wave equation in one space dimension is treated for two cases with specified initial data and grid, and data from solutions at t = 400 and t = 800 are presented, as prescribed for Problem 1 in Category 1. Results are shown from computations with a sequence of recently developed high order and high resolution methods which combine Hermite interpolation, Cauchy-Kowaleskya recursion for time derivatives, and Taylor series time advancement. These methods have the same order of accuracy in time as in space. Results are shown from methods that range from third to nineteenth order. The stated problems with the prescribed coarse grid can be simulated with errors that are at the level of machine accuracy if the method is sufficiently high order. In addition, the growth of the maximum absolute error out to t = 100,000 is given for simulations with the stated problem data.

Goodrich, John W.↗
NASA NTRS1975

Resolution enhancement of ERTS imagery

A method is described for combined interpolation and enhancement of ERTS multispectral scanner data sets. Previous research has shown that good enhancement is most easily achieved when there are a large number of data points contained within the radius of gyration of the system point spread function. This requirement can be met using ERTS data by interpolating the data before enhancement. By varying the interpolation scale factor the data set can be empirically matched to a precalculated optimum restoration filter. Once the proper match of data and filter has been found the enhancement can be carried out directly or the enhancement and interpolation operations can be combined into a single filter thereby greatly reducing the processing time. Experimental results of applying this technique are shown along with more conventional methods of image interpolation and enlargement.

Mcgillem, C. D.↗
NASA NTRS2008

Uplink Array Concept Demonstration with the EPOXI Spacecraft

Uplink array technology is currently being developed for NASA's Deep Space Network (DSN) to provide greater range and data throughput for future NASA missions, including manned missions to Mars and exploratory missions to the outer planets, the Kuiper belt, and beyond. Here we describe a novel technique for generating the frequency predicts that are used to compensate for relative Doppler, derived from interpolated earth position and spacecraft ephemerides. The method described here guarantees velocity and range estimates that are consistent with each other, hence one can always be recovered from the other. Experimental results have recently proven that these frequency predicts are accurate enough to maintain the phase of a three element array at the EPOXI spacecraft for three hours. Previous methods derive frequency predicts directly from interpolated relative velocities. However, these velocities were found to be inconsistent with the corresponding spacecraft range, meaning that range could not always be recovered accurately from the velocity predicts, and vice versa. Nevertheless, velocity-based predicts are also capable of maintaining uplink array phase calibration for extended periods, as demonstrated with the EPOXI spacecraft, however with these predicts important range and phase information may be lost. A comparison of the steering-vector method with velocity-based techniques for generating precise frequency predicts specifically for uplink array applications is provided in the following sections.

spacecraft uplink commands↗
NASA NTRS2008

Pointing-Vector and Velocity Based Frequency Predicts for Deep-Space Uplink Array Applications

Uplink array technology is currently being developed for NASA's Deep Space Network (DSN) to provide greater range and data throughput for future NASA missions, including manned missions to Mars and exploratory missions to the outer planets, the Kuiper belt, and beyond. Here we describe a novel technique for generating the frequency predicts that are used to compensate for relative Doppler, derived from interpolated earth position and spacecraft ephemerides. The method described here guarantees velocity and range estimates that are consistent with each other, hence one can always be recovered from the other. Experimental results have recently proven that these frequency predicts are accurate enough to maintain the phase of a three element array at the EPOXI spacecraft for three hours. Previous methods derive frequency predicts directly from interpolated relative velocities. However, these velocities were found to be inconsistent with the corresponding spacecraft range, meaning that range could not always be recovered accurately from the velocity predicts, and vice versa. Nevertheless, velocity-based predicts are also capable of maintaining uplink array phase calibration for extended periods, as demonstrated with the EPOXI spacecraft, however with these predicts important range and phase information may be lost. A comparison of the steering-vector method with velocity-based techniques for generating precise frequency predicts specifically for uplink array applications is provided in the following sections.

uplink arraying↗
NASA NTRS1983

Three-dimensional algebraic grid generation

One of the major approaches to numerical grid generation is the explicit algebraic expression of a physical grid as a function of a uniform grid in a rectangular computational coordinate system. The algebraic methods are based on mathematical interpolation, and the primary advantages are speed and directness. The relation between interpolation and grid generation is described. For three-dimensional grid generation, transfinite interpolation using the coordinate control processes developed in the multisurface method and two-boundary technique are advocated. Grid singularities encountered in three dimensions are discussed, and the exploration of multiple overlapping grids is proposed. Some aspects of interactive algebraic grid computation in three dimensions are discussed.

Smith, R. E.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parametrized surfaces

An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.

Spekreijse, S. P.↗
NASA NTRS2005

Generic Sensor Modeling Using Pulse Method

Recent development of high spatial resolution satellites such as IKONOS, Quickbird and Orbview enable observation of the Earth's surface with sub-meter resolution. Compared to the 30 meter resolution of Landsat 5 TM, the amount of information in the output image was dramatically increased. In this era of high spatial resolution, the estimation of spatial quality of images is gaining attention. Historically, the Modulation Transfer Function (MTF) concept has been used to estimate an imaging system's spatial quality. Sometimes classified by target shapes, various methods were developed in laboratory environment utilizing sinusoidal inputs, periodic bar patterns and narrow slits. On-orbit sensor MTF estimation was performed on 30-meter GSD Landsat4 Thematic Mapper (TM) data from the bridge pulse target as a pulse input . Because of a high resolution sensor s small Ground Sampling Distance (GSD), reasonably sized man-made edge, pulse, and impulse targets can be deployed on a uniform grassy area with accurate control of ground targets using tarps and convex mirrors. All the previous work cited calculated MTF without testing the MTF estimator's performance. In previous report, a numerical generic sensor model had been developed to simulate and improve the performance of on-orbit MTF estimating techniques. Results from the previous sensor modeling report that have been incorporated into standard MTF estimation work include Fermi edge detection and the newly developed 4th order modified Savitzky-Golay (MSG) interpolation technique. Noise sensitivity had been studied by performing simulations on known noise sources and a sensor model. Extensive investigation was done to characterize multi-resolution ground noise. Finally, angle simulation was tested by using synthetic pulse targets with angles from 2 to 15 degrees, several brightness levels, and different noise levels from both ground targets and imaging system. As a continuing research activity using the developed sensor model, this report was dedicated to MTF estimation via pulse input method characterization using the Fermi edge detection and 4th order MSG interpolation method. The relationship between pulse width and MTF value at Nyquist was studied including error detection and correction schemes. Pulse target angle sensitivity was studied by using synthetic targets angled from 2 to 12 degrees. In this report, from the ground and system noise simulation, a minimum SNR value was suggested for a stable MTF value at Nyquist for the pulse method. Target width error detection and adjustment technique based on a smooth transition of MTF profile is presented, which is specifically applicable only to the pulse method with 3 pixel wide targets.

Helder, Dennis L.↗
NASA NTRS2007

Semianalytical Propagation of Satellite Orbits about an Arbitrary Central Body

Precision mean element (PME) satellite theories play a key role in orbit dynamics analyses. These theories employ: nonsingular orbital elements comprehensive force models Generalized Method of Averaging Numerical interpolation concepts The Draper Semianalytical Satellite Theory (DSST) (Refs. 1 - 6), whose development was led by the author, and the independently-developed Universal Semianalytical Method (USM) (Ref. 7) are examples of such theories. These theories provide the capability to tailor the force modeling to meet the desired computational speed vs. accuracy trade-off. The flexibility of such theories is demonstrated by their ability to include complicated atmosphere density models and spacecraft models in the perturbation theory context. The value of high speed satellite theories, in this era of computational plenty, is that they allow new ways of looking at astrodynamical problems such as orbit design (Refs. 8, 9) and atmosphere density updating (Refs. 10, 11). In the mid to late-1980 s, the geodynamics community led the development of very precise geopotential models such as GEM T2 and GEM T3 (Ref. 12), and with the subsequent analysis of the TOPEX flight data, JGM-2 and JGM-3 (Ref. 13). These were high degree and order geopotentials, at least 50 x 50. In 1993, the DSST implementation in the GTDS program was extended to include the 50 x 50 geopotential models (Ref. 14). The 50 x 50 geopotential, J2000 integration coordinate system, and solid Earth tide capabilities were integrated in GTDS by Scott Carter (Ref. 15). This capability demonstrated 1 m accuracy versus the TOPEX Precise Orbit Ephemerides. Subsequently the DSST Standalone program was also extended to include high degree and order geopotential models (Ref. 5). More recently GTDS has been hosted in the Linux PC environment. However, all of these efforts have been limited to modeling the motion of an artificial Earth satellite. They did not consider the additional complexities associated with lunar, planetary, or other natural satellite orbiters. Such complexities include: additional coordinate systems (associated with the direction of the north pole of rotation and the prime meridian of the new central bodies) (Ref. 16) normalized gravity model coefficients (desirable for high degree and order fields) (Ref. 17) indirect oblateness

Cefola, Paul J.↗
NASA NTRS1982

Fitting surfaces to scattered data

A variety of numerical methods for fitting a function to data given at a set of points scattered throughout a domain in the plane are surveyed. Four classes of methods are discussed: (1) global interpolation; (2) local interpolation; (3) global approximation; and (4) local approximation. Also, two-stage methods and contouring are discussed. The surfaces constructed include polynomials, spline functions, and rational functions, among others.

Schumaker, L. L.↗
NASA NTRS1995

Elliptic surface grid generation on minimal and parmetrized surfaces

An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.

Spekreijse, S. P.↗