Search NASA⌕ Search

SEARCH · Search NASA

Results for “INDEPENDENT VARIABLE”

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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Numerical results for the thermal scattering functions

A recent formulation in radiative transfer defined the thermal scattering functions that characterize radiative transfer from a general plane-parallel finite medium driven solely by an internal distribution of thermal sources. Exiting diffuse intensities are expressed as space convolutions of the thermal scattering functions with any thermal source distribution. A parametric study is presented to obtain the basic structure of these scattering functions. The independent variables of these azimuthally independent functions are the direction cosine and source location, while the parameters are the single-scattering albedo, total optical depth, and the asymmetry factor in the Henyey-Greenstein phase function. The basic functional trends are discussed by using various parametric plots, and selected results are given to allow numerical checks. The computational method is invariant imbedding.

Cogley, A. C.↗
NASA NTRS1978

Interaction of a strong blast wave with a free surface

When a point source explosion is initiated at the ocean surface, the shock propagated into the water is reflected at the surface as a centered expansion wave. The solution in the neighborhood of the interaction point is obtained by writing the equations of motion in the appropriate similarity variables and then changing the independent variables to polar coordinates based at the interaction point. From the zero-order solution of the resulting equations the slopes of boundaries at the interaction point are obtained. A first-order perturbation of this solution provides more accurate representation of the flow variables and the curvature of the shock surface near the interaction point.

Falade, A.↗
NASA NTRS1984

Generic Karman-Rostovstev plate equations in an affine space

The Karman-Rostovstev plate equations are affinely transformed into equations that depend on the generic plate constants generalized rigidity, generalized extensional rigidity, and generalized Poisson ratio associated with the well-known linearized orthotropic plate/slab equations. Furthermore, since the generalized extensional rigidity is a function of generalized rigidity and generalized Poisson ratio only, with generalized Poisson ratio being a weak parameter, the only fundamental constant is generalized rigidity. This means that regardless of what analysis technique is used, the results can be cast in terms of only one strong material parameter (whose range is from zero to one). The affine stretching is performed on the dependent variables as well as the independent variables, so that the dependence of all quantities of interest on generalized rigidity and generalized Poisson ratio are easily calculated (e.g., even auxiliary quantities such as stress, strain, all weighted stress resultants, etc.). Some typical results (static side load response, collapse load limited by rib buckling) are presented by modifying an approximate technique due to Donnell (1976).

Brunelle, E. J.↗
NASA NTRS1989

Guidance and Control strategies for aerospace vehicles

A neighboring optimal guidance scheme was devised for a nonlinear dynamic system with stochastic inputs and perfect measurements as applicable to fuel optimal control of an aeroassisted orbital transfer vehicle. For the deterministic nonlinear dynamic system describing the atmospheric maneuver, a nominal trajectory was determined. Then, a neighboring, optimal guidance scheme was obtained for open loop and closed loop control configurations. Taking modelling uncertainties into account, a linear, stochastic, neighboring optimal guidance scheme was devised. Finally, the optimal trajectory was approximated as the sum of the deterministic nominal trajectory and the stochastic neighboring optimal solution. Numerical results are presented for a typical vehicle. A fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is also addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in reference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions.

Hibey, J. L.↗
NASA NTRS1991

Neighboring optimal guidance for aeroassisted noncoplanar orbital transfer

The fuel-optimal control problem in aeroassisted noncoplanar orbital transfer is addressed. The equations of motion for the atmospheric maneuver are nonlinear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighboring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in preference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditions. The results are presented to a typical aeroassisted noncoplanar orbital transfer problem.

Naidu, D. S.↗
NASA NTRS1951

On the particular integrals of the Prandtl-Busemann iteration equations for the flow of a compressible fluid

The particular integrals of the second-order and third-order Prandtl-Busemann iteration equations for the flow of a compressible fluid are obtained by means of the method in which the complex conjugate variables are utilized as the independent variables of the analysis. The assumption is made that the Prandtl-Glauert solution of the linearized or first-order iteration equation for the two-dimensional flow of a compressible fluid is known. The forms of the particular integrals, derived for subsonic flow, are readily adapted to supersonic flows with only a change in sign of one of the parameters of the problem.

Kaplan, Carl↗
NASA NTRS1998

Global Nonlinear Parametric Modeling with Application to F-16 Aerodynamics

A global nonlinear parametric modeling technique is described and demonstrated. The technique uses multivariate orthogonal modeling functions generated from the data to determine nonlinear model structure, then expands each retained modeling function into an ordinary multivariate polynomial. The final model form is a finite multivariate power series expansion for the dependent variable in terms of the independent variables. Partial derivatives of the identified models can be used to assemble globally valid linear parameter varying models. The technique is demonstrated by identifying global nonlinear parametric models for nondimensional aerodynamic force and moment coefficients from a subsonic wind tunnel database for the F-16 fighter aircraft. Results show less than 10% difference between wind tunnel aerodynamic data and the nonlinear parameterized model for a simulated doublet maneuver at moderate angle of attack. Analysis indicated that the global nonlinear parametric models adequately captured the multivariate nonlinear aerodynamic functional dependence.

Morelli, Eugene A.↗
NASA NTRS1998

Predicting Ecologically Important Vegetation Variables from Remotely Sensed Optical/Radar Data Using Neural Networks

A number of satellite sensor systems will collect large data sets of the Earth's surface during NASA's Earth Observing System (EOS) era. Efforts are being made to develop efficient algorithms that can incorporate a wide variety of spectral data and ancillary data in order to extract vegetation variables required for global and regional studies of ecosystem processes, biosphere-atmosphere interactions, and carbon dynamics. These variables are, for the most part, continuous (e.g. biomass, leaf area index, fraction of vegetation cover, vegetation height, vegetation age, spectral albedo, absorbed photosynthetic active radiation, photosynthetic efficiency, etc.) and estimates may be made using remotely sensed data (e.g. nadir and directional optical wavelengths, multifrequency radar backscatter) and any other readily available ancillary data (e.g., topography, sun angle, ground data, etc.). Using these types of data, neural networks can: 1) provide accurate initial models for extracting vegetation variables when an adequate amount of data is available; 2) provide a performance standard for evaluating existing physically-based models; 3) invert multivariate, physically based models; 4) in a variable selection process, identify those independent variables which best infer the vegetation variable(s) of interest; and 5) incorporate new data sources that would be difficult or impossible to use with conventional techniques. In addition, neural networks employ a more powerful and adaptive nonlinear equation form as compared to traditional linear, index transformations, and simple nonlinear analyses. These neural networks attributes are discussed in the context of the authors' investigations of extracting vegetation variables of ecological interest.

Kimes, Daniel S.↗
NASA NTRS1997

Global Nonlinear Parametric Modeling with Application to F-16 Aerodynamics

A global nonlinear parametric modeling technique is described and demonstrated. The technique uses multivariate orthogonal modeling functions generated from the data to determine nonlinear model structure, then expands each retained modeling function into an ordinary multivariate polynomial. The final model form is a finite multivariate power series expansion for the dependent variable in terms of the independent variables. Partial derivatives of the identified models can be used to assemble globally valid linear parameter varying models. The technique is demonstrated by identifying global nonlinear parametric models for nondimensional aerodynamic force and moment coefficients from a subsonic wind tunnel database for the F-16 fighter aircraft. Results show less than 10% difference between wind tunnel aerodynamic data and the nonlinear parameterized model for a simulated doublet maneuver at moderate angle of attack. Analysis indicated that the global nonlinear parametric models adequately captured the multivariate nonlinear aerodynamic functional dependence.

Morelli, Eugene A.↗
NASA NTRS2005

Global Positioning System (GPS) Precipitable Water in Forecasting Lightning at Spaceport Canaveral

Using meteorology data, focusing on precipitable water (PW), obtained during the 2000-2003 thunderstorm seasons in Central Florida, this paper will, one, assess the skill and accuracy measurements of the current Mazany forecasting tool and, two, provide additional forecasting tools that can be used in predicting lightning. Kennedy Space Center (KSC) and Cape Canaveral Air Force Station (CCAFS) are located in east Central Florida. KSC and CCAFS process and launch manned (NASA Space Shuttle) and unmanned (NASA and Air Force Expendable Launch Vehicles) space vehicles. One of the biggest cost impacts is unplanned launch scrubs due to inclement weather conditions such as thunderstorms. Each launch delay/scrub costs over a quarter million dollars, and the need to land the Shuttle at another landing site and return to KSC costs approximately $ 1M. Given the amount of time lost and costs incurred, the ability to accurately forecast (predict) when lightning will occur can result in significant cost and time savings. All lightning prediction models were developed using binary logistic regression. Lightning is the dependent variable and is binary. The independent variables are the Precipitable Water (PW) value for a given time of the day, the change in PW up to 12 hours, the electric field mill value, and the K-index value. In comparing the Mazany model results for the 1999 period B against actual observations for the 2000-2003 thunderstorm seasons, differences were found in the False Alarm Rate (FAR), Probability of Detection (POD) and Hit Rate (H). On average, the False Alarm Rate (FAR) increased by 58%, the Probability of Detection (POD) decreased by 31% and the Hit Rate decreased by 20%. In comparing the performance of the 6 hour forecast period to the performance of the 1.5 hour forecast period for the Mazany model, the FAR was lower by 15% and the Hit Rate was higher by 7%. However, the POD for the 6 hour forecast period was lower by 16% as compared to the POD of the 1.5 hour forecast period. Neither forecast period performed at the accuracy measures expected. A 2-Hr Forecasting Tool was developed to support a Phase I Lightning Advisory, which requires a 30-minute lead time for predicting lightning.

Kehrer, Kristen↗
NASA NTRSDate not supplied

Silicon Partitioning Between Iron-Rich Metal and Silicate Melt: New Constraints From Aerodynamic Laser Levitation Furnace Experiments

The partitioning of light elements (e.g., Si, C, H, etc.) between silicate melts and iron metal alloys as a function of pressure and temperature is a critical constraint in defining the compositional evolution of planetary interiors. While there are a significant number of experimental studies in the literature that examine the various influences of oxygen fugacity, temperature, pressure, and composition on the metal-melt partitioning of silicon, it is difficult to disentangle the effects of each variable due to the nominally independent parameters (e.g., pressure, temperature, composition) being collinear. To better test for the independent effects of pressure, temperature, and melt composition on the partitioning of silicon between iron alloy and silicate melt, new high temperature (1800°–2500°C), rapid quench (~700°C/s) aerodynamic levitation laser-heating experiments in the Fe-Si-Mg-O (En65-Fa5-Si3-Fe27) system were conducted. This high temperature, low pressure method is ideal for these experiments because it eliminates the metal container as a sink for elements of interest to partition into, and it has a rapid quench rate that minimizes potential exsolution of silicon from the metal phase during quench cooling. Given the short run times of the levitation experiments (30–60 seconds), a time series at a lower temperature (1700°C) in a vertical gas-mixing muffle tube furnace was also conducted to assess equilibrium times of the bulk composition. All successful runs were imaged using back-scatter electron imaging and analyzed for phase composition using a JEOL 8530F field emission microprobe. These new data were added to a comprehensive and internally consistent data set created from published experiments, and subsequently modeled using parameters designed to minimize collinearity (e.g., optical basicity is used as a proxy for melt composition). High collinearity is found in the data set however between temperature and oxygen fugacity, precluding any model that contains both as nominally independent variables. The resulting model demonstrates a statistically significant effect of pressure, temperature, and melt composition on the partitioning of silicon in Fe-rich metal, which has implications for the formation of planetary cores in rocky planets and provides important constraints on potential bulk core compositions.

Metal↗
NASA NTRS2001

Multivariate Analysis of Solar Spectral Irradiance Measurements

Principal component analysis is used to characterize approximately 7000 downwelling solar irradiance spectra retrieved at the Southern Great Plains site during an Atmospheric Radiation Measurement (ARM) shortwave intensive operating period. This analysis technique has proven to be very effective in reducing a large set of variables into a much smaller set of independent variables while retaining the information content. It is used to determine the minimum number of parameters necessary to characterize atmospheric spectral irradiance or the dimensionality of atmospheric variability. It was found that well over 99% of the spectral information was contained in the first six mutually orthogonal linear combinations of the observed variables (flux at various wavelengths). Rotation of the principal components was effective in separating various components by their independent physical influences. The majority of the variability in the downwelling solar irradiance (380-1000 nm) was explained by the following fundamental atmospheric parameters (in order of their importance): cloud scattering, water vapor absorption, molecular scattering, and ozone absorption. In contrast to what has been proposed as a resolution to a clear-sky absorption anomaly, no unexpected gaseous absorption signature was found in any of the significant components.

Pilewskie, P.↗
NASA NTRS1977

Production of a water quality map of Saginaw Bay by computer processing of LANDSAT-2 data

Surface truth and LANDSAT measurements collected July 31, 1975, for Saginaw Bay were used to demonstrate a technique for producing a color coded water quality map. On this map, color was used as a code to quantify five discrete ranges in the following water quality parameters: (1) temperature, (2) Secchi depth, (3) chloride, (4) conductivity, (5) total Kjeldahl nitrogen, (6) total phosphorous, (7)chlorophyll a, (8) total solids and (9) suspended solids. The LANDSAT and water quality relationship was established through the use of a set of linear regression equations where the water quality parameters are the dependent variables and LANDSAT measurements are the independent variables. Although the procedure is scene and surface truth dependent, it provides both a basis for extrapolating water quality parameters from point samples to unsampled areas and a synoptic view of water mass boundaries over the 3000 sq. km bay area made from one day's ship data that is superior, in many ways, to the traditional machine contoured maps made from three day's ship data.

Mckeon, J. B.↗
NASA NTRS1989

Self-similar Lagrangian hydrodynamics of beam-heated solar flare atmospheres

The one-dimensional hydrodynamic problem in Lagrangian coordinates (Y, t) is considered for which the specific energy input Q has a power-law dependence on both Y and t, and the initial density distribution is rho(0) which is directly proportional to Y exp gamma. In regimes where the contributions of radiation, conduction, quiescent heating, and gravitational terms in the energy equation are negligible compared to those arising from Q, the problem has a self-similar solution, with the hydrodynamic variables depending only on a single independent variable which is a combination of Y, t, and the dimensional constants of the problem. It is then shown that the problem of solar flare chromospheric heating due to collisional interaction of a beam of electrons (or protons) with a power-law energy spectrum can be approximated by such forms of Q(Y, t) and rho(0)(Y), and that other terms are negligible compared to Q over a restricted regime early in the flare.

Brown, John C.↗
NASA NTRS2013

Classification of Dust Days by Satellite Remotely Sensed Aerosol Products

Considerable progress in satellite remote sensing (SRS) of dust particles has been seen in the last decade. From an environmental health perspective, such an event detection, after linking it to ground particulate matter (PM) concentrations, can proxy acute exposure to respirable particles of certain properties (i.e. size, composition, and toxicity). Being affected considerably by atmospheric dust, previous studies in the Eastern Mediterranean, and in Israel in particular, have focused on mechanistic and synoptic prediction, classification, and characterization of dust events. In particular, a scheme for identifying dust days (DD) in Israel based on ground PM10 (particulate matter of size smaller than 10 nm) measurements has been suggested, which has been validated by compositional analysis. This scheme requires information regarding ground PM10 levels, which is naturally limited in places with sparse ground-monitoring coverage. In such cases, SRS may be an efficient and cost-effective alternative to ground measurements. This work demonstrates a new model for identifying DD and non-DD (NDD) over Israel based on an integration of aerosol products from different satellite platforms (Moderate Resolution Imaging Spectroradiometer (MODIS) and Ozone Monitoring Instrument (OMI)). Analysis of ground-monitoring data from 2007 to 2008 in southern Israel revealed 67 DD, with more than 88 percent occurring during winter and spring. A Classification and Regression Tree (CART) model that was applied to a database containing ground monitoring (the dependent variable) and SRS aerosol product (the independent variables) records revealed an optimal set of binary variables for the identification of DD. These variables are combinations of the following primary variables: the calendar month, ground-level relative humidity (RH), the aerosol optical depth (AOD) from MODIS, and the aerosol absorbing index (AAI) from OMI. A logistic regression that uses these variables, coded as binary variables, demonstrated 93.2 percent correct classifications of DD and NDD. Evaluation of the combined CART-logistic regression scheme in an adjacent geographical region (Gush Dan) demonstrated good results. Using SRS aerosol products for DD and NDD, identification may enable us to distinguish between health, ecological, and environmental effects that result from exposure to these distinct particle populations.

satellite remote sensing↗
NASA NTRS1976

Pressure model of a four-way spool valve for simulating electrohydraulic control systems

An equation that relates the pressure flow characteristics of hydraulic spool valves was developed. The dependent variable is valve output pressure, and the independent variables are spool position and flow. This causal form of equation is preferred in applications that simulate the effects of hydraulic line dynamics. Results from this equation are compared with those from the conventional valve equation, whose dependent variable is flow. A computer program of the valve equations includes spool stops, leakage spool clearances, and dead-zone characteristics of overlap spools.

Gebben, V. D.↗