Search NASA⌕ Search

SEARCH · Search NASA

Results for “functional approximation”

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 541 records · Page 30

A Point Spread Function for the EPOXI Mission

The Extrasolar Planet Observation Characterization and the Deep Impact Extended Investigation missions (EPOXI) are currently observing the transits of exoplanets, two comet nuclei at short range, and the Earth and Mars using the High Resolution Instrument (HRI) - a 0.3 m f/35 telescope on the Deep Impact probe. The HRI is in a permanently defocused state with the instrument pOint of focus about 0.6 cm before the focal plane due to the use of a reference flat mirror that took a power during ground thermal-vacuum testing. Consequently, the point spread function (PSF) covers approximately nine pixels FWHM and is characterized by a patch with three-fold symmetry due to the three-point support structures of the primary and secondary mirrors. The PSF is also strongly color dependent varying in shape and size with change in filtration and target color. While defocus is highly desirable for exoplanet transit observations to limit sensitivity to intra-pixel variation, it is suboptimal for observations of spatially resolved targets. Consequently, all images used in our analysis of such objects were deconvolved with an instrument PSF. The instrument PSF is also being used to optimize transit analysis. We discuss development and usage of an instrument PSF for these observations.

Barry, Richard K.↗

Mini AERCam for In-Space Inspection

The NASA Johnson Space Center Engineering Directorate has developed the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam) as a free-flying, robotic inspection vehicle intended for future external inspection and remote viewing of human spacecraft. The Mini AERCam technology demonstration unit has been successfully integrated into the approximate form and function of a nanosatellite flight system by leveraging the success of AERCam Sprint flight system and related free-flyer technology development. The Mini AERCam free flyer can be operated via remote piloting from a control station supporting teleoperation and supervised autonomous commanding, with functions such as automatic stationkeeping, point-to-point maneuvering, and automatic docking. Free-flyer testing has been conducted on an air-bearing table and in a six degree-of-freedom closed-loop orbital simulation, and enhancements have been made to provide additional capabilities for future space-based inspection. This presentation will provide a technical overview of the Mini AERCam development, including strategies for spacecraft integration.

Fredrickson, Steven E.↗

Symbolic Execution Enhanced System Testing

We describe a testing technique that uses information computed by symbolic execution of a program unit to guide the generation of inputs to the system containing the unit, in such a way that the unit's, and hence the system's, coverage is increased. The symbolic execution computes unit constraints at run-time, along program paths obtained by system simulations. We use machine learning techniques treatment learning and function fitting to approximate the system input constraints that will lead to the satisfaction of the unit constraints. Execution of system input predictions either uncovers new code regions in the unit under analysis or provides information that can be used to improve the approximation. We have implemented the technique and we have demonstrated its effectiveness on several examples, including one from the aerospace domain.

Davies, Misty D.↗

Design, Development and Testing of the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam) Guidance, Navigation and Control System

Engineers at NASA Johnson Space Center have designed, developed, and tested a nanosatellite-class free-flyer intended for future external inspection and remote viewing of human spaceflight activities. The technology demonstration system, known as the Miniature Autonomous Extravehicular Robotic Camera (Mini AERCam), has been integrated into the approximate form and function of a flight system. The primary focus has been to develop a system capable of providing external views of the International Space Station. The Mini AERCam system is spherical-shaped and less than eight inches in diameter. It has a full suite of guidance, navigation, and control hardware and software, and is equipped with two digital video cameras and a high resolution still image camera. The vehicle is designed for either remotely piloted operations or supervised autonomous operations. Tests have been performed in both a six degree-of-freedom closed-loop orbital simulation and on an air-bearing table. The Mini AERCam system can also be used as a test platform for evaluating algorithms and relative navigation for autonomous proximity operations and docking around the Space Shuttle Orbiter or the ISS.

Wagenknecht, J.↗

Challenges of Debris-Impact Risk Assessment for Robotic Spacecraft

This paper describes an orbital debris impact risk assessment performed on the command and data subsystem electronics box of QuikSCAT, a functioning spacecraft with approximately 18 years on orbit. Several aspects of the analysis are paid particular attention. First is the modeling of a thermal blanket at a small stand-off distance from the box chassis. The properties of the blanket are such that under some assumptions, it may be treated as an effective bumper shield, and under other assumptions, it may not. The assumptions and their effects on the results of the analysis are explored. Similarly, the configuration of the electronic components inside the chassis are such that several definitions of failure criteria appear plausible. The results of each treatment are presented together and compared with the status of the actual electronics box. The failure predictions vary widely between treatments, and the more conservative assumption sets predict incredulously high probabilities of failure. This is problematic because the conservative assumptions are the ones typically used in analyses for flight projects.

Ratliff, Martin↗

Midlatitude Lightning NOx Production Efficiency Inferred From OMI and WWLLN Data

Oxides of nitrogen are critical trace gases in the troposphere and are precursors for nitrate aerosol and ozone, which is an important pollutant and greenhouse gas. Lightning is the major source of NOx(NO + NO2) in the mid-to upper troposphere. We estimate the production efficiency (PE) of lightning NOx (LNOx) using satellite data from the Ozone Monitoring Instrument (OMI) and the ground-based WorldWide Lightning Location Network (WWLLN) in three northern midlatitude, primarily continental regions that include much of North America, Europe and East Asia. Data were obtained over 5 boreal summers, 2007 –2011 and comprise the largest number of midlatitude convective events to date for estimating the LNOx PE with satellite NO2and ground-based lightning measurements. In contrast to some previous studies, the algorithm assumes no minimum flash-rate threshold and estimates freshly produced LNOxby subtracting a background of aged NOx estimated from the OMI dataset itself. We infer an average value of 180 ± 100 moles LNOx produced per lightning flash. We also show evidence of a dependence of PE on lightning flash rate and find an approximate empirical power function relating moles LNOxto flashes. PE decreases by an order of magnitude for a 2-order of magnitude increase in flash rate. This phenomenon has not been reported in previous satellite LNOxstudies but is consistent with ground-based observations suggesting an inverse relationship between flash rate and size.

LNOx↗

Non-Causal Controller Approximation Methodology Augmented with Model Reference Control – Robust Design

This paper describes the development of a new control design methodology based on a non-causal controller structure and its approximation. The non-causal controller design is based on a loop shaping approach. Partial fraction decomposition is used, along with derivative approximations, to derive a proper transfer function design for a causal control structure. The premise for this non-causal control methodology is that the phase delay as a function of frequency ideally remains within approximately -90o, which tends to make the system robustly stable to uncertainties in the plant dynamics. To have a predictable control system response in lieu of the tolerance of this methodology to relatively large uncertainty in the plant dynamics, the approach is augmented with model reference control. The addition of model reference control can potentially further enhance the robustness of the design. A control system design example is presented in this paper, along with simulation results, to demonstrate the high degree of robustness of this non-causal methodology and its augmentation.

Control Systems↗

Automation of Geometric Accuracy Assessment Algorithm

When end-users are using multiple satellite images for a study the first step is often the assessment and rectification of geolocation offsets. We have developed an automated algorithm to calculate the geometric offsets between two satellite images. It splits both images into subset images (chips) and resamples them to a common resolution. Offsets are imposed on matching chips and the Pearson Cross Correlation (PCC) value calculated for each offset, where the best PCC gives the true offsets. With the true offsets corrected for, a quality of image registration is calculated, measurement uncertainty (MU). The MU threshold value is non-uniform across sensors because it depends on spectral characteristics of each sensor. Previously, the MU threshold was determined by manual inspection for each new sensor assessed. In this study, we automated MU threshold determination. 1/MU vs calculated offset approximates a Gaussian function in shape, see abstract image. A Gaussian function is fit to this dataset, and the root of the third derivative is calculated and applied as a quality threshold, removing the data of lower quality from the final assessment of image offsets. We apply this algorithm to commercial satellite data for proof of concept.

Alana Semple↗

Multivariate spline methods in surface fitting

The use of spline functions in the development of classification algorithms is examined. In particular, a method is formulated for producing spline approximations to bivariate density functions where the density function is decribed by a histogram of measurements. The resulting approximations are then incorporated into a Bayesiaan classification procedure for which the Bayes decision regions and the probability of misclassification is readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr.↗

Convolution of a Doppler line by a Gaussian instrument function

A simple and direct method is obtained for assessing the distortion of a Doppler line by a Gaussian instrument function. It is suggested that a close approximation to the width of a Gaussian instrument function, or an almost Gaussian function, may be obtained by measuring a line with a Doppler absorption coefficient. The method is applicable to diode laser measurements, and may be used whenever a Gaussian instrument function is a reasonable approximation to real conditions

Fridovich, B.↗

Properties of the Io plasma torus inferred from Voyager EUV data

A physical model for the Io plasma torus is constructed to explain the EUV radiative emission observed by the Voyager UV spectrometer. Electron impact excitation rate coefficients for electronic transitions of S III, S IV, O II and O III are calculated by the method of distorted waves (Davis, Kepple, and Blaha, 1976); these coefficients account for the asymmetric shape of the 686 A feature. It is concluded that the electron gas must have a distribution function with a non-Maxwellian tail. An approximate representation of the distribution function as two temperature components requires a cold component of 3.5-4 eV and density of 2000 per cu cm and a hot component of about 100 eV and density of 50-100 per cu cm to satisfy observational constraints.

Strobel, D. F.↗

An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable

The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.

Demkowicz, L.↗

Parameter estimation techniques based on optimizing goodness-of-fit statistics for structural reliability

New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell's numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper's nonlinear regression algorithm.

Starlinger, Alois↗

Learning Functions Varying along a Central Subspace

Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of an s-Hölder function in $R^D$ which varies along a central subspace of dimension $d$ while $d \ll D$. A direct approximation of $f$ in $R^D$ with an accuracy $\varepsilon$ requires the number of samples in the order of $\varepsilon^{-(2s+D)/s}$. In this paper, we analyze the generalized contour regression (GCR) algorithm for the estimation of the central subspace and use piecewise polynomials for function approximation. GCR is among the best estimators for the central subspace, but its sample complexity is an open question. In this paper, we partially answer this questions by proving that if a variance quantity is exactly known, GCR leads to a mean squared estimation error of $O(n^{-1})$ for the central subspace. The estimation error of this variance quantity is also given in this paper. The mean squared regression error of $f$ is proved to be in the order of $(n/\log n)^{-\frac{2s}{2s+d}}$, where the exponent depends on the dimension of the central subspace instead of the ambient space . This result demonstrates that GCR is effective in learning the low-dimensional central subspace. We also propose a modified GCR with improved efficiency. Here, the convergence rate is validated through several numerical experiments.

97 MATHEMATICS AND COMPUTING↗

Polarization options in inclusive DIS off tensor polarized deuteron

In the near future, the Jefferson Lab b 1 experiment will provide the second measurement of tensor polarized asymmetries in inclusive DIS on the deuteron. In this asymmetry, 4 independent tensor polarized structure functions contribute. This necessitates systematic approximations in the extraction of the leading twist structure function b 1 from a single tensor asymmetry measurement. Contamination from higher twist structure functions and kinematic effects is discussed here. Using a deuteron convolution model, we quantify the systematic errors from these approximations for two different choices for the target polarization direction (momentum transfer, electron beam direction). For Jefferson Lab 12 GeV kinematics, the systematic error turns out to be comparable between the two polarization options, while at higher Q 2 values the momentum transfer direction is preferred.

Cosyn, Wim [Florida International University, Miam↗

Very low mass stars and white dwarfs in NGC 6397

Deep Wide Field/Planetary Camera 2 (WFPC2) images in wide bands centered at 606 and 802 nm were taken with the Hubble Space Telescope (HST) 4.6 min from the center of the galactic globular cluster NGC 6397. The images were used to accurately position approximately 2120 stars detected in the field on a color magnitude diagram down to a limiting magnitude m(sub 814) approximately = m(sub I) approximately = 26 determined reliably and solely by counting statistics. A white dwarf sequence and a rich, narrow cluster main sequence are detected for the first time, the latter stretching from m(sub 814) = 18.5 to m(sub 814) = 24.0 where it becomes indistinguishable from the field population. Two changes of slope of the main sequence at m(sub 814) approximately = 20 and m(sub 814) approximately = 22.5 are evident. The corresponding luminosity function increases slowly from M(sub 814) approximately = 6.5 to 8.5 are expected from ground-based observations but then drops sharply from there dwon to the measurement limit. The corresponding mass function obtained bu using the only presently available mass-luminosity function for the cluster's metallicity rises to a plateau between approximately 0.25 and approximately 0.15 solar mass, but drops toward the expected mass limit of the normal hydrogen burning main sequence at approximately 0.1 solar mass. This result is in clear contrast to that obtained from the ground and implies either a substantial modification of the cluster's initial mass function due to dynamical evolution in its lifetime, or that very low mass stars are not produced in any dynamically significant amount by clusters of this type. The white dwarf sequence is in reasonable agreement with a cooling sequence of models of mass 0.5 solar mass at the canonical distance of NGC 6397 with a scatter that is most likely due to photometric errors, but may also reflect real differences in mass or chemical composition. Contamination from unresolved galaxies, which cannot be reliably identified with our filters, makes it difficult to meaningfully compare the observed white dwarf luminosity function with its theoretical counterpart.

Paresce, Francesco↗

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, Jeffrey M.↗

An adaptive pseudospectral method for discontinuous problems

The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.

Augenbaum, J. M.↗