Search NASA⌕ Search

SEARCH · Search NASA

Results for “Gradient”

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 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS2021

Multi-Pass Sequential Mini-Batch Stochastic Gradient Descent Algorithms for Noise Covariance Estimation in Adaptive Kalman Filtering

Estimation of unknown noise covariances in a Kalman filter is a problem of significant practical interest in a wide array of applications. Although this problem has a long history, reliable algorithms for their estimation were scant, and necessary and sufficient conditions for identifiability of the covariances were in dispute until recently. Necessary and sufficient conditions for covariance estimation and a batch estimation algorithm were presented in our previous study. This paper presents stochastic gradient descent algorithms for noise covariance estimation in adaptive Kalman filters that are an order of magnitude faster than the batch method for similar or better root mean square error. More significantly, these algorithms are applicable to non-stationary systems where the noise covariances can occasionally jump up or down by an unknown magnitude. The computational efficiency of the new algorithms stems from adaptive thresholds for convergence, recursive fading memory estimation of the sample cross-correlations of the innovations, and accelerated stochastic gradient descent algorithms. The comparative evaluation of the proposed methods on a number of test cases demonstrates their computational efficiency and accuracy.

Adaptive Kalman filtering↗
NASA NTRS1972

Calculation of turbulent boundary layers with heat transfer and pressure gradient utilizing a compressibility transformation. Part 3: Computer program manual

A computer program is described capable of determining the properties of a compressible turbulent boundary layer with pressure gradient and heat transfer. The program treats the two-dimensional problem assuming perfect gas and Crocco integral energy solution. A compressibility transformation is applied to the equation for the conservation of mass and momentum, which relates this flow to a low speed constant property flow with simultaneous mass transfer and pressure gradient. The resulting system of describing equations consists of eight ordinary differential equations which are solved numerically. For Part 1, see N72-12226; for Part 2, see N72-15264.

Schneider, J.↗
NASA NTRS1972

Vertical gradients in the theory of radio aurora.

Study of vertical density gradients as a potential source of irregularities responsible for radio aurorae and as a possible cause that might modify the aspect sensitivity of radio-auroral reflections coming from two-stream instability irregularities. Both of these effects are examined in a single calculation which incorporates vertical gradients into the two-stream instability theory of Farley (1963).

Moorcroft, D. R.↗
NASA NTRS1972

Compressible boundary layer with normal pressure gradients: Quasi-similarity equations - Their properties at the wall and at sharp and blunt leading edges.

The failure of most viscous-inviscid interaction methods at strong interactions is attributed to the presence of a normal pressure gradient. A new theory is proposed for supersonic laminar boundary layers that can generate normal pressure gradients. The Navier-Stokes equations are reexamined by an order of magnitude analysis and all first and second order terms are retained. The approximation is found to be dependent not only on the boundary layer thickness but also on the ratio of the dimensionless viscosity and density. The equations are transformed into two quasi-similar, nonlinear, third order, ordinary integro-differential equations for the velocity and pressure as functions of a single transverse variable. The properties of the equations at the boundaries are discussed.

Seginer, A.↗
NASA NTRS1972

Turbulent boundary layer in an adverse pressure gradient without effect of wall curvature

The hypersonic compressible turbulent boundary layer in an adverse pressure gradient along a cylindrical axisymmetric body was studied. The tests were conducted in a Mach 6 contoured axisymmetric nozzle. An external compression cowl was used to produce the gradual adverse pressure gradient and a maximum pressure rise of 7 times the freestream static pressure was achieved in a test region of 23 cm. Boundary layer profiles of static pressure, total pressure, and total temperature, as well as wall transient heat transfer rates were measured. Comparisons of the velocity total temperature profiles to linear and quadratic relations were made. Measured heat transfer data were in good agreement with the prediction from the flat-plate reference enthalpy method. Integral parameters were also in good agreement with results of numerical solutions for compressible turbulent boundary layer equations.

Zakkay, V.↗
NASA NTRS1973

A mesh gradient technique for numerical optimization

A class of successive-improvement optimization methods in which directions of descent are defined in the state space along each trial trajectory are considered. The given problem is first decomposed into two discrete levels by imposing mesh points. Level 1 consists of running optimal subarcs between each successive pair of mesh points. For normal systems, these optimal two-point boundary value problems can be solved by following a routine prescription if the mesh spacing is sufficiently close. A spacing criterion is given. Under appropriate conditions, the criterion value depends only on the coordinates of the mesh points, and its gradient with respect to those coordinates may be defined by interpreting the adjoint variables as partial derivatives of the criterion value function. In level 2, the gradient data is used to generate improvement steps or search directions in the state space which satisfy the boundary values and constraints of the given problem.

Willis, E. A., Jr.↗
NASA NTRS1973

Proposed gravity-gradient dynamics experiments in lunar orbit using the RAE-B spacecraft

A series of seven gravity-gradient dynamics experiments is proposed utilizing the Radio Astronomy Explorer (RAE-B) spacecraft in lunar orbit. It is believed that none of the experiments will impair the spacecraft structure or adversely affect the continuation of the scientific mission of the satellite. The first experiment is designed to investigate the spacecraft dynamical behavior in the absence of libration damper action and inertia. It requires stable gravity-gradient capture of the spacecraft in lunar orbit with small amplitude attitude librations as a prerequisite. Four subsequent experiments involve partial retraction, ultimately followed by full redeployment, of one or two of the 230-meter booms forming the lunar-directed Vee-antenna. These boom length change operations will induce moderate amplitude angular librations of the spacecraft.

Blanchard, D. L.↗
NASA NTRS1973

Pioneer-10 measurements of the differential and integral cosmic-ray gradient between 1 and 3 AU

The cosmic-ray experiment on Pioneer has provided measurements of the differential radial gradient of cosmic-ray helium nuclei between 1 and 3 AU. Upper limits are quoted between 10 and 500 MeV/nuc which are everywhere 25%/AU and in some cases substantially smaller. The integral proton gradient ( 56 MeV) was also measured and found to have the following values: 2.4 + or - 0.3%/AU (1-2 AU), 7.6 + or - 0.7%/AU (2-3 AU).

Teegarden, B. J.↗
NASA NTRS1973

Preliminary Pioneer-10 intensity gradients of galactic cosmic rays.

Selected data from the University of Chicago charged-particle telescope on the Pioneer-10 spacecraft bound for Jupiter have been examined and compared with data from the University of Chicago charged-particle telescopes on the Earth satellites IMP-5 and IMP-6 at 1 AU to derive a preliminary integral intensity gradient for relativistic galactic protons and helium nuclei. The preliminary value obtained is (4.5 plus or minus 1.0) percent per AU over the radial range 1-2.8 AU. Preliminary differential gradients also have been obtained for the energy range 29-67 MeV per nucleon.

Mckibben, R. B.↗
NASA NTRS1973

The development of an elastic reverse gradient garment to be used as a countermeasure for cardiovascular deconditioning

Using a new Nomex-Lycra elastic fabric and individualized garment engineering techniques, reverse gradient garments (RGG's) were designed, constructed, and tested for effectiveness as a countermeasure against cardiovascular deconditioning. By combining torso-compensated positive pressure breathing with a distally diminishing gradient of counterpressure supplied by the elastic fabric on the limbs, the RGG acts to pool blood in the extremities of recumbent persons much as though they were standing erect in 1 g. It was theorized that through the use of a dynamic pressurization scheme, the RGG would stress the vasculature in a fashion similar to that experienced by the noramlly active man, hence preventing or limiting the development of post-weightlessness orthostatic intolerance and related conditions. Four male, college-age subjects received daily treatments with the RGG during a 15-day bedrest study. Four additional subjects also underwent the bedrest, but received no treatments; they served as controls. The design and construction of the garments are described, and results of the treatment related measurements are given.

Annis, J. F.↗
NASA NTRS1974

Parameter estimation for terrain modeling from gradient data

A method is developed for modeling terrain surfaces for use on an unmanned Martian roving vehicle. The modeling procedure employs a two-step process which uses gradient as well as height data in order to improve the accuracy of the model's gradient. Least square approximation is used in order to stochastically determine the parameters which describe the modeled surface. A complete error analysis of the modeling procedure is included which determines the effect of instrumental measurement errors on the model's accuracy. Computer simulation is used as a means of testing the entire modeling process which includes the acquisition of data points, the two-step modeling process and the error analysis. Finally, to illustrate the procedure, a numerical example is included.

Dangelo, K. R.↗
NASA NTRS1974

Calculation of a realistic gradient as a function of radial distance from the sun

Numerical calculations of radial gradients of galactic cosmic ray protons have been performed for a model of the interplanetary cavity which includes processes of diffusion along the spiral interplanetary magnetic field lines, convection, and adiabatic energy change. The increasing spiral nature of the field lines with increasing distance from the sun results in the bulk of the modulation region being beyond the earth. The radial gradients for this model are found to be small near the earth and out to a few AU, increasing as one approaches the boundary.

Lezniak, J. A.↗
NASA NTRS1974

Evolution of a moderately short turbulent boundary layer in a severe pressure gradient

The early and intermediate development of a highly accelerated (or decelerated) turbulent boundary layer is analyzed. For sufficiently large accelerations (or pressure gradients) and for total normal strains which are not excessive, the equation for the Reynolds shear stress simplifies to give a stress that remains approximately constant as it is convected along streamlines. The theoretical results for the evolution of the mean velocity in favourable and adverse pressure gradients agree well with experiment for the cases considered. A calculation which includes mass injection at the wall is also given.

Deissler, R. G.↗
NASA NTRS1974

The effect of temperature induced surface tension gradients on bubble mechanics

Experiments were conducted to examine in detail the influence of surface tension gradient induced flow, the Marangoni effect. One set of studies provided visual results that demonstrated the occurrence and magnitude of the Marangoni effect. Another portion of the work was directed to bubble force measurements. These studies used in deflection of a very fine cantilevered wire with an attached bubble as a means of measuring force with and without temperature gradients. The experimental force data were found to check existing theoretical predictions reasonably well except for the case where the test fluid had a sizeable vapor pressure. In this situation the thermophoretic force on the bubble was much higher than predicted.

Mcgrew, J. L.↗
NASA NTRS1974

A model for jet-noise analysis using pressure-gradient correlations on an imaginary cone

The technique for determining the near and far acoustic field of a jet through measurements of pressure-gradient correlations on an imaginary conical surface surrounding the jet is discussed. The necessary analytical developments are presented, and their feasibility is checked by using a point source as the sound generator. The distribution of the apparent sources on the cone, equivalent to the point source, is determined in terms of the pressure-gradient correlations.

Norum, T. D.↗
NASA NTRS1975

Pressure gradient effects on heat transfer to reusable surface insulation tile-array gaps

An experimental investigation was performed to determine the effect of pressure gradient on the heat transfer within space shuttle reusable surface insulation (RSI) tile-array gaps under thick, turbulent boundary-layer conditions. Heat-transfer and pressure measurements were obtained on a curved array of full-scale simulated RSI tiles in a tunnel-wall boundary layer at a nominal free-stream Mach number and free-stream Reynolds numbers. Transverse pressure gradients of varying degree were induced over the model surface by rotating the curved array with respect to the flow. Definition of the tunnel-wall boundary-layer flow was obtained by measurement of boundary-layer pitot pressure profiles, wall pressure, and heat transfer. Flat-plate heat-transfer data were correlated and a method was derived for prediction of heat transfer to a smooth curved surface in the highly three-dimensional tunnel-wall boundary-layer flow. Pressure on the floor of the RSI tile-array gap followed the trends of the external surface pressure. Heat transfer to the surface immediately downstream of a transverse gap is higher than that for a smooth surface at the same location. Heating to the wall of a transverse gap, and immediately downstream of it, at its intersection with a longitudinal gap is significantly greater than that for the simple transverse gap.

Throckmorton, D. A.↗
NASA NTRS1974

Evidence of a velocity gradient in the solar wind

Sector-boundary velocity data obtained by Mariner 5 near Venus and by Explorers 33, 34, and 35 near earth are analyzed to determine why higher velocities were measured at earth. Differences in the corresponding velocities are plotted as a function of the heliocentric latitude separation of Mariner and earth, and evidence of a significant latitude gradient in the solar wind is found. Several indirect arguments in support of a latitude gradient are presented, and it is concluded that if the solar wind velocity varies with latitude, latitudinal stresses may have a significant effect on the properties of the solar wind, such as the existence and character of the north-south component of the interplanetary magnetic field.

Smith, E. J.↗
NASA NTRS1974

The relationship between velocity gradients and magnetic turbulence in the solar wind

The correlations among the time derivative of the solar-wind velocity, the magnitude of the interplanetary magnetic field (IMF), and the IMF turbulence level are examined to test the idea that interaction between two colliding solar-wind streams can generate turbulence in the solar wind and the IMF. Data obtained by Explorer 33 on the solar wind and IMF are described, and the analysis techniques are outlined. The results indicate that the IMF turbulence level, as measured by the variance, is correlated with the existence of positive velocity gradients in the solar wind. It is noted that while the variance is an increasing function of the field magnitude, it is also independently correlated with the solar-wind velocity gradient.

Garrett, H. B.↗