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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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Interpolation schemes in the control of systems with unknown dynamics

Time-delay control for systems with unknown dynamics involves estimations. In its present form, these estimations include not only the interpolation of a time-varying function but also its derivative between data points. Presently, the control law is reformulated, taking into account the computation delay. A window-shifting scheme is then devised to view n data points as they are sampled in order to perform the function estimation. At each new sampling time, the window shifts to include the new data point as well as the last n-1 points. Several interpolation methods are considered. These methods use data points from a sampled function to construct a polynomial estimate of the function. The control system performance was experimentally tested using a servosystem. The results show that a Newtonian interpolation provided best results when the computation time was 0.4 times the sampling period.

Youcef-Toumi, K.↗
NASA NTRS1992

Curvilinear-Interpolation Program

INTERP2 is interactive program solving interpolation problems quickly and accurately. Solves for unknown based on true relationship among given values, whether linear or nonlinear. Using Lagrange interpolating polynomial, INTERP2 "draws" curve through input data points and interpolates to obtain f(x) for known x expediently. Written in BASIC.

Coppi, Michael J.↗
NASA NTRS1992

Program For Logarithmic Interpolation Of Test Data

DATASPACE program establishes logarithmically increasing time interval in relaxation data. First takes logarithm of abscissa values, then uses cubic-spline interpolation routine to create evenly spaced array from log values. As result of interpolation, data increasingly spaced. Experimental data curve retained, and interpolated points reflect desired spacing. Applicable to any situation with need for increasingly spaced abscissa values in set of data. Written in FORTRAN 77.

Ledbetter, Frank E., II↗
NASA NTRS1993

Rounded Approximate Step Functions For Interpolation

Rounded approximate step functions of form x(Sup m)/(x(Sup n) + 1) and 1/(x(Sup n) + 1) useful in interpolating between local steep slopes or abrupt changes in tabulated data varying more smoothly elsewhere. Used instead of polynomial curve fits. Interpolation formulas based on these functions implemented quickly and easily on computers. Used in real-time control computations to interpolate between tabulated data governing control responses.

Nunes, Arthur C., Jr.↗
NASA NTRS1992

A method of smooth bivariate interpolation for data given on a generalized curvilinear grid

A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.

Zingg, David W.↗
NASA NTRS1993

A rational interpolation method to compute frequency response

A rational interpolation method for approximating a frequency response is presented. The method is based on a product formulation of finite differences, thereby avoiding the numerical problems incurred by near-equal-valued subtraction. Also, resonant pole and zero cancellation schemes are developed that increase the accuracy and efficiency of the interpolation method. Selection techniques of interpolation points are also discussed.

Kenney, Charles↗
NASA NTRS1995

The Atmospheric Data Acquisition And Interpolation Process For Center-TRACON Automation System

The Center-TRACON Automation System (CTAS), an advanced new air traffic automation program, requires knowledge of spatial and temporal atmospheric conditions such as the wind speed and direction, the temperature and the pressure in order to accurately predict aircraft trajectories. Real-time atmospheric data is available in a grid format so that CTAS must interpolate between the grid points to estimate the atmospheric parameter values. The atmospheric data grid is generally not in the same coordinate system as that used by CTAS so that coordinate conversions are required. Both the interpolation and coordinate conversion processes can introduce errors into the atmospheric data and reduce interpolation accuracy. More accurate algorithms may be computationally expensive or may require a prohibitively large amount of data storage capacity so that trade-offs must be made between accuracy and the available computational and data storage resources. The atmospheric data acquisition and processing employed by CTAS will be outlined in this report. The effects of atmospheric data processing on CTAS trajectory prediction will also be analyzed, and several examples of the trajectory prediction process will be given.

Jardin, M. R.↗
NASA NTRS2006

Development of a Boundary Layer Property Interpolation Tool in Support of Orbiter Return To Flight

A new tool was developed to predict the boundary layer quantities required by several physics-based predictive/analytic methods that assess damaged Orbiter tile. This new tool, the Boundary Layer Property Prediction (BLPROP) tool, supplies boundary layer values used in correlations that determine boundary layer transition onset and surface heating-rate augmentation/attenuation factors inside tile gouges (i.e. cavities). BLPROP interpolates through a database of computed solutions and provides boundary layer and wall data (delta, theta, Re(sub theta)/M(sub e), Re(sub theta)/M(sub e), Re(sub theta), P(sub w), and q(sub w)) based on user input surface location and free stream conditions. Surface locations are limited to the Orbiter s windward surface. Constructed using predictions from an inviscid w/boundary-layer method and benchmark viscous CFD, the computed database covers the hypersonic continuum flight regime based on two reference flight trajectories. First-order one-dimensional Lagrange interpolation accounts for Mach number and angle-of-attack variations, whereas non-dimensional normalization accounts for differences between the reference and input Reynolds number. Employing the same computational methods used to construct the database, solutions at other trajectory points taken from previous STS flights were computed: these results validate the BLPROP algorithm. Percentage differences between interpolated and computed values are presented and are used to establish the level of uncertainty of the new tool.

Greene, Francis A.↗
NASA NTRS2008

Interpolating Fields of Carbon Monoxide Data Using a Hybrid Statistical-Physical Model

Atmospheric Carbon Monoxide (CO) is a pollutant gas of which the US congress has mandated regular monitoring, and satellite sensors can be used to retrieve regional concentrations of CO over several vertical layers. However, CO at cloudy locations cannot be observed and have to be estimated from the observed data set, resulting in an interpolation problem. The current state-of-the-art solution is to combine prior information, computed by a deterministic physical model, with observations. However, the deterministic model may introduce uncertainties that do not derive from the data. While sharing certain features with the physical model, this paper presents a Bayesian hierarchical model for interpolating CO on a 3-dimensional spatial grid, across time. To our knowledge such a model has not been considered before. The model is applied to a hypothetical air-quality monitoring scenario, and is compared to existing interpolation methods. The results provide motivation for the use of the statistical model for regional to local applications.

Arellano, A. A.↗
NASA NTRS2011

Tropospheric Correction for InSAR Using Interpolated ECMWF Data and GPS Zenith Total Delay

To mitigate atmospheric errors caused by the troposphere, which is a limiting error source for spaceborne interferometric synthetic aperture radar (InSAR) imaging, a tropospheric correction method has been developed using data from the European Centre for Medium- Range Weather Forecasts (ECMWF) and the Global Positioning System (GPS). The ECMWF data was interpolated using a Stretched Boundary Layer Model (SBLM), and ground-based GPS estimates of the tropospheric delay from the Southern California Integrated GPS Network were interpolated using modified Gaussian and inverse distance weighted interpolations. The resulting Zenith Total Delay (ZTD) correction maps have been evaluated, both separately and using a combination of the two data sets, for three short-interval InSAR pairs from Envisat during 2006 on an area stretching from northeast from the Los Angeles basin towards Death Valley. Results show that the root mean square (rms) in the InSAR images was greatly reduced, meaning a significant reduction in the atmospheric noise of up to 32 percent. However, for some of the images, the rms increased and large errors remained after applying the tropospheric correction. The residuals showed a constant gradient over the area, suggesting that a remaining orbit error from Envisat was present. The orbit reprocessing in ROI_pac and the plane fitting both require that the only remaining error in the InSAR image be the orbit error. If this is not fulfilled, the correction can be made anyway, but it will be done using all remaining errors assuming them to be orbit errors. By correcting for tropospheric noise, the biggest error source is removed, and the orbit error becomes apparent and can be corrected for

Webb, Frank H.↗
NASA NTRS2012

Spatiotemporal Interpolation of Elevation Changes Derived from Satellite Altimetry for Jakobshavn Isbrae, Greenland

Estimation of ice sheet mass balance from satellite altimetry requires interpolation of point-scale elevation change (dHdt) data over the area of interest. The largest dHdt values occur over narrow, fast-flowing outlet glaciers, where data coverage of current satellite altimetry is poorest. In those areas, straightforward interpolation of data is unlikely to reflect the true patterns of dHdt. Here, four interpolation methods are compared and evaluated over Jakobshavn Isbr, an outlet glacier for which widespread airborne validation data are available from NASAs Airborne Topographic Mapper (ATM). The four methods are ordinary kriging (OK), kriging with external drift (KED), where the spatial pattern of surface velocity is used as a proxy for that of dHdt, and their spatiotemporal equivalents (ST-OK and ST-KED).

Jakobshavn Isbrae↗
DOE OSTI2019

Areal interpolation of population in the USA using a combination of national parcel data and a national building outline layer

We build on the recent literature on the use of parcel data in areal interpolation of population by incorporating high resolution building outline data. Our results show that models that constrain the operating footprint of the areal interpolation not just to parcel boundaries but the outlines of the buildings themselves have the potential to further reduce the areal interpolation error beyond what has already been demonstrated in previous literature. We also demonstrate that these principles apply not just to residential populations but to worker populations as well.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2017

High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps

This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.

58 GEOSCIENCES↗
DOE OSTI2017

Scientific data interpolation with low dimensional manifold model

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Interpolation of computed gamma-ray detector response functions

Gamma-ray spectra measured by traditional detectors contain features that result from a combination of the effects of detector materials/geometry, the incident gamma-ray energy, and the angle of entry. The features, such as the full-energy photopeak, Compton continuum, annihilation peak, and escape peaks, are governed by simple relationships depending on incident energy and have been known for a long time. Monte Carlo computer simulations of gamma rays interacting with a detector will show these features, and with a resolution function applied, the results should look similar to real measurements. The traditional approach to creating a detector response function requires many separate simulations of monoenergetic gamma rays striking the detector. This paper presents a new approach to developing computed detector response functions. The new approach involves a much smaller number of monoenergetic gamma-ray simulations and uses interpolation to quickly generate the responses of gamma rays that were not simulated. During the interpolation process, the underlying physics equations are used to accurately compute the response of a given energy gamma ray from the small set of simulations. Such work enables accelerated generation of synthetic radiation detector data.

Detector response↗
DOE OSTI2015

Construction of exchange-correlation functionals through interpolation between the non-interacting and the strong-correlation limit

Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

An adaptive interpolation scheme for molecular potential energy surfaces

The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

CONORBIT: constrained optimization by radial basis function interpolation in trust regions

Here, this paper presents CONORBIT (CONstrained Optimization by Radial Basis function Interpolation in Trust regions), a derivative-free algorithm for constrained black-box optimization where the objective and constraint functions are computationally expensive. CONORBIT employs a trust-region framework that uses interpolating radial basis function (RBF) models for the objective and constraint functions, and is an extension of the ORBIT algorithm. It uses a small margin for the RBF constraint models to facilitate the generation of feasible iterates, and extensive numerical tests confirm that such a margin is helpful in improving performance. CONORBIT is compared with other algorithms on 27 test problems, a chemical process optimization problem, and an automotive application. Numerical results show that CONORBIT performs better than COBYLA, a sequential penalty derivative-free method, an augmented Lagrangian method, a direct search method, and another RBF-based algorithm on the test problems and on the automotive application.

97 MATHEMATICS AND COMPUTING↗