Search NASA⌕ Search

SEARCH · Search NASA

Results for “function 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

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↗

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.↗

Thermal exchange-correlation functionals: Capturing quantum electron behavior in warm, dense plasmas

We summarize and give perspective upon recent progress in developing non-empirical constraint-based thermal (i.e., free energy) exchange-correlation (XC) density functionals essential for accurate description of the quantum behavior of electrons in warm, dense plasmas. After delineating the critical role of ground-state functionals for zero-temperature, time-dependent DFT, we outline the underpinnings of local density approximation, generalized gradient approximation (GGA), and meta-GGA XC free-energy functionals. Two basic thermalization principles for upgrading ground-state XC functionals to successful thermal ones are emphasized. Then, we turn to a long-standing challenge, assessment of the accuracy of well-founded functionals. Unlike the ground state, there are a few exact results for large T and P. An exception is path integral Monte Carlo (PIMC) data for dense H/D and He plasmas. For those, we did ab initio molecular dynamics simulations under selected thermodynamic conditions employing five thermal XC functionals: two approximate thermal GGAs, fully thermal GGA, an approximate meta-GGA, and fully thermal meta-GGA. Comparisons with the PIMC data show that functionals thermalized by augmenting a non-thermal functional with a lower-level thermal contribution are inferior to functionals with thermal XC and spatial inhomogeneity effects taken into account at the same level of refinement. We believe this and similar evidence should be convincing to the high-energy density physics community of the necessity of use of proper thermal XC functionals in simulation studies of finite-temperature quantum effects in warm, dense plasmas.

Ab-initio molecular dynamics↗

Time domain unsteady incompressible cascade airfoil theory for helicopter rotors in hover

A detailed derivation of a finite-time arbitrary-motion incompressible cascade theory is presented for both Laplace and frequency domains. The generalized cascade lift deficiency function is shown to be consistent with the generalized Theodorsen's lift deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity; it also yields a correct value for the zero reduced frequency limit. Efficient numerical procedures are presented for the evaluation of the cascade lift deficiency function. Numerical examples comparing the cascade lift deficiency function with Loewy's (1957) rotary-wing lift deficiency function in frequency domain are presented. Pade approximants of the cascade lift deficiency function are constructed using a Bode plot approach that allows for complex poles. A general-purpose optimization program is used to determine the coefficients of the approximant.

Dinyavari, M. A. H.↗

Rational approximations from power series of vector-valued meromorphic functions

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Sidi, Avram↗

Long Focal Length Large Mirror Fabrication System

The goals of this ambitious program are (1) to develop systems to make large superpolished optical mirrors, (2) to develop low scatter polishing techniques using centrifugal elutriation, (3) to develop a means of measuring scatter at any point on the mirror, (4) to polish a Hindle sphere to measure the optical figure of a one meter diameter convex mandrel, and (5) to fabricate low scatter, large adaptive optic graphite filled, cyanate ester replica transfer mirrors using these mandrels. Deliverables are a 30 cm diameter superpolished composite AO mirror. We fabricated a 1/3rd meter superpolished zerodur flat mandrel and with the support of our major subcontractor, Composite Mirror Applications Inc (CMA) we have demonstrated a 30 cm lightweight cyanate ester mirror with an rms microroughness between 0.6 and 0.8 nm and 8 faceplate influence function of 5 cm. The influence function was chosen to be comparable to the atmospheric correlation coefficient r(sub 0) which is about 5 cm at sea level. There was no print-thru of the graphite fibers in the cyanate ester surface (the bane of many previous efforts to use cyanate ester mirrors). Our subcontractor has devised a means for developing a 30-50 nm thick layer of graphite free pure ester resin on the surface of the mirrors. This graphite fiber filled material has a thermal expansion coefficient in the 10(exp -8) centimeter per Kelvin range (the same range of expansion coefficient as Zerodur and ULE glasses) and does not take up water and swell, so it is a nearly ideal mirror material in these areas. Unfortunately for these 0.8mm thick faceplates, the number of plies is not enough to result in isometric coverage. Isolated figure irregularities can appear, making it necessary to go to thicker faceplates. The influence function will then only approximate the length of r(sub 0), at higher altitudes or longer wavelengths. The influence function goes as the cube of the thickness, so we are now making a faceplate optimized for an infrared wavelength, possibly that used for the AO system of the Keck telescope, instead of 0.63 microns. We have polished a 55 cm diameter mandrel to better than 1/20th wave optical figure in the visible using centrifugal elutriation. CMA has just told us that it needs to retool to get optimum mirror faceplate quality in this size, so implementing the 55 cm AO mirror may be delayed somewhat. We expect to complete our 1/3 rd meter AO mirror on time using novel piezoelectric actuators with a throw of one micrometer per volt, as compared to 0.005 micrometers per volt for conventional piezoelectric actuators. We will then demonstrate its AO performance interferometrically.

Bennett, H. E.↗

High-energy heavy-ion scattering and the optical phase shift function

Within the framework of the Glauber approximation, an exact expression for the optical phase shift function is derived which takes into account the center-of-mass correlation function. We calculate total and differential cross sections using the first-order term for the shift function and compare them with the usual (first-order) optical limit results and, for the lighter nuclei, with the exact Glauber results. The nucleus-nucleus elastic scattering amplitude does not exhibit the large-q divergence which characterizes the usual optical limit. The obtained results improve the calculated total and differential cross sections dramatically for light nuclei, and significantly for medium and heavy nuclei.

Franco, V.↗