Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability density function”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Radiative transfer theory for active remote sensing of a layer of small ellipsoidal scatterers

The radiative transfer theory is applied within the Rayleigh approximation to calculate the backscattering cross section of a layer of randomly positioned and oriented small ellipsoids. The orientation of the ellipsoids is characterized by a probability density function of the Eulerian angles of rotation. The radiative transfer equations are solved by an iterative approach to first order in albedo. In the half space limit the results are identical to those obtained via the approach of Foldy's and distorted Born approximation. Numerical results of the theory are illustrated using parameters encountered in active remote sensing of vegetation layers. A distinctive characteristic is the strong depolarization shown by vertically aligned leaves.

Tsang, L.↗
NASA NTRS1981

Remote sensing of sea state by laser altimeters

The reflection of short laser pulses from the ocean surface was analyzed based on the specular point theory of scattering. The expressions for the averaged received signal, shot noise and speckle induced noise were derived for a direct detection system. It is found that the reflected laser pulses have an average shape closely related to the probability density function associated with the surface profile. This result is applied to estimate the mean sea level and significant wave height from the receiver output of the laser altimeter.

Tsai, B.↗
NASA NTRS1982

A comprehensive model to determine the effects of temperature and species fluctuations on reaction rates in turbulent reacting flows

A principal element to be derived from modeling turbulent reacting flows is an expression for the reaction rates of the various species involved in any particular combustion process under consideration. A temperature-derived most-likely probability density function (pdf) was used to describe the effects of temperature fluctuations on the Arrhenius reaction rate constant. A most-likely bivariate pdf described the effects of temperature and species concentrations fluctuations on the reaction rate. A criterion is developed for the use of an "appropriate" temperature pdf. The formulation of models to calculate the mean turbulent Arrhenius reaction rate constant and the mean turbulent reaction rate is considered and the results of calculations using these models are presented.

Foy, E.↗
NASA NTRS1981

Mass and Momentum Turbulent Transport Experiments with Confined Coaxial Jets

Downstream mixing of coaxial jets discharging in an expanded duct was studied to obtain data for the evaluation and improvement of turbulent transport models currently used in a variety of computational procedures throughout the propulsion community for combustor flow modeling. Flow visualization studies showed four major shear regions occurring; a wake region immediately downstream of the inlet jet inlet duct; a shear region further downstream between the inner and annular jets; a recirculation zone; and a reattachment zone. A combination of turbulent momentum transport rate and two velocity component data were obtained from simultaneous measurements with a two color laser velocimeter (LV) system. Axial, radial and azimuthal velocities and turbulent momentum transport rate measurements in the r-z and r-theta planes were used to determine the mean value, second central moment (or rms fluctuation from mean), skewness and kurtosis for each data set probability density function (p.d.f.). A combination of turbulent mass transport rate, concentration and velocity data were obtained system. Velocity and mass transport in all three directions as well as concentration distributions were used to obtain the mean, second central moments, skewness and kurtosis for each p.d.f. These LV/LIF measurements also exposed the existence of a large region of countergradient turbulent axial mass transport in the region where the annular jet fluid was accelerating the inner jet fluid.

Johnson, B. V.↗
NASA NTRS1982

A comprehensive model to determine the effects of temperature and species fluctuations on reaction rates in turbulent reacting flows

The use of probability theory to determine the effects of turbulent fluctuations on reaction rates in turbulent combustion systems is briefly reviewed. Results are presented for the effect of species fluctuations in particular. It is found that turbulent fluctuations of species act to reduce the reaction rates, in contrast with the temperature fluctuations previously determined to increase Arrhenius reaction rate constants. For the temperature fluctuations, a criterion is set forth for determining if, in a given region of a turbulent flow field, the temperature can be expected to exhibit ramp like fluctuations. Using the above results, along with results previously obtained, a model is described for testing the effects of turbulent fluctuations of temperature and species on reaction rates in computer programs dealing with turbulent reacting flows. An alternative model which employs three variable probability density functions (temperature and two species) and is currently being formulated is discussed as well.

Chinitz, W.↗
NASA NTRS1981

The effect of temperature fluctuations of reaction rate constants in turbulent reacting flows

Current models of turbulent reacting flows frequently use Arrhenius reaction rate constants obtained from static or laminar flow theory and/or experiments, or from best fits of static, laminar, and turbulent data. By treating the reaction rate constant as a continuous random variable which is temperature-dependent, the present study assesses the effect of turbulent temperature fluctuations on the reaction rate constant. This model requires that a probability density function (PDF) describing the nature of the fluctuations be specified. Three PDFs are examined: the clipped Gaussian, the beta PDF, and the ramp model. All the models indicate that the reaction rate constant is greater in a turbulent flow field than in an equivalent laminar flow. In addition, an amplification ratio, which is the ratio of the turbulent rate constant to the laminar rate constant, is defined and its behavior as a function of the mean temperature fluctuations is described

Chinitz, W.↗
NASA NTRS1982

A bootstrap approach to bump hunting

An important question in cluster analysis and pattern recognition is the determination of the number of clusters into which a given population should be divided. Frequently, particularly when certain specific clustering methods are being used, the number of clusters is taken to be equal to the number of modes, or local maxima, in the probability density function underlying the given data set. The use of kernal density estimates in mode estimation is discussed. The test statistic to be used is defined and a bootstrap technique for assessing significance is given. An illustrative application is followed by an examination of the asymptotic behavior of the test statistic.

Silverman, B. W.↗
NASA NTRS1983

A comprehensive model to determine the effects of temperature and species fluctuations on reaction rates in turbulent reacting flows

Reaction rates in turbulent, reacting flows are reviewed. Assumed probability density functions (pdf) modeling of reaction rates is being investigated in relation to a three variable pdf employing a 'most likely pdf' model. Chemical kinetic mechanisms treating hydrogen air combustion is studied. Perfectly stirred reactor modeling of flame stabilizing recirculation regions was used to investigate the stable flame regions for silane, hydrogen, methane, and propane, and for certain mixtures thereof. It is concluded that in general, silane can be counted upon to stabilize flames only when the overall fuel air ratio is close to or greater than unity. For lean flames, silane may tend to destabilize the flame. Other factors favoring stable flames are high initial reactant temperatures and system pressure.

Goldstein, D.↗
NASA NTRS1983

Monte Carlo Modeling in Elliptic Flows

A Monte Carlo method capable of predicting scalar (e.g., concentration) probability density functions (pdf's) in nonreacting and reacting elliptic flows was developed. A research combustor specifically designed to provide measurements of concentration and temperature pdf's in nonreacting and reacting flows is emphasized.

Radhakrishnan, K.↗
NASA NTRS1983

A mathematical characterization of vegetation effect on microwave remote sensing from the Earth

In passive microwave remote sensing of the earth, a theoretical model that utilizes the radiative transfer equations was developed to account for the volume scattering effects of the vegetation canopy. Vegetation canopies such as alfalfa, sorghum, and corn are simulated by a layer of ellipsoidal scatterers and cylindrical structures. The ellipsoidal scatterers represent the leaves of vegetation and are randomly positioned and oriented. The orientation of ellipsoids is characterized by a probability density function of Eulerian angles of rotation. The cylindrical structures represent the stalks of vegetation and their radii are assumed to be much smaller than their lengths. The underlying soil is represented by a half-space medium with a homogeneous permittivity and uniform temperature profile. The radiative transfer quations are solved by a numerical method using a Gaussian quadrature formula to compute both the vertical and horizontal polarized brightness temperature as a function of observation angle. The theory was applied to the interpretation of experimental data obtained from sorghum covered fields near College Station, Texas.

Choe, Y.↗
NASA NTRS1983

B-57B gust gradient program

Analysis of data obtained from the Joint Airport Weather Studies Flights 6 and 7 is underway. Data from Flight 7 indicate that the B-57B encountered the upper portion of an outflow feature (microburst) at an altitude of 400 meters above ground level. Horizontal wind vector plots along the flight path have provided clues concerning the meteorological setting of the flights. In addition to suspected outflow features, wavelike variations of the horizontal wind vectors were observed. Statistical studies of gust gradients were undertaken with the goal of fitting probability density functions to the data. As expected, the density functions were highly non-Gaussian. Spectral analyses are proceeding and several spectral models for the gust gradient data are being investigated.

Campbell, W.↗
NASA NTRS1982

Solution to the backward-Kolmogorov equation for a nonstationary oscillation problem

The transition probability density function of a Markovian approximation of the response amplitude of an oscillator under nonstationary excitation is determined in an analytical form. A solution is presented for the associated backward-Kolmogorov equation by transforming the equation into a form amenable to solution by the method of the separation of variables. This procedure results in a boundary value problem which is then solved by using an infinite series of Laguerre polynomials. It is found that the infinite series solution is equivalent to a closed-form solution involving a Bessel function.

Solomos, G. P.↗
NASA NTRS1983

Classification by thresholding

A procedure is given which substantially reduces the processing time needed to perform maximum likelihood classification on large data sets. The given method uses a set of fixed thresholds which, if exceeded by one probability density function, makes it unnecessary to evaluate a competing density function. Proofs are given of the existence and optimality of these thresholds for the class of continuous, unimodal, and quasi-concave density functions (which includes the multivariable normal), and a method for computing the thresholds is provided for the specific case of multivariate normal densities. An example with remote sensing data consisting of some 20,000 observations of four-dimensional data from nine ground-cover classes shows that by using thresholds, one could cut the processing time almost in half.

Feiveson, A. H.↗
NASA NTRS1983

Prediction of an axisymmetric combusting flow

A numerical model for turbulent, recirculating combusting flow is developed and applied to a research combustor. The model is based on the time-averaged Navier-Stokes equations with k-epsilon turbulence closure and the compositional fluctuations at each point are given probabilistically in terms of the mixture fraction. The probability density function is derived from transport equations for its first two moments along with an assumption regarding its shape. The resulting equations are solved using a standard line relaxation algorithm. It is found that the predictions of the model are in good agreement with data from an axisymmetric, bluff-body stabilized research combustor, while the major discrepancies are similar to those found in isothermal flow comparisons. The peculiar features of this flow which contribute to the errors are examined. The agreement between the theory and data deteriorates as the central jet velocity is increased which indicates an enhanced role for unsteady effects.

Correa, S. M.↗
NASA NTRS1983

An analysis of spanwise gust gradient data

Plots of winds encountered during flight are presented for severe turbulence cases from flights 6 and 7 of the Joint Airport Weather Studies (JAWS) Project (McCarthy et al., 1982). During run 10 of flight 7, analyzed here in considerable detail, the B-57B Cambera aircraft showed a sharp increase in airspeed of 15 m/sec over a distance of about 130 m and then a more gradual decrease of 20 to 25 m/sec over a distance of about 2 km. This suspected outflow feature was associated with a downdraft exceeding 10 m/sec. The horizontal wind direction changed nearly 180 deg during the pass through the feature. Unexpectedly, the intensity of the velocity differences decreased for all three components within the downdraft. Calculated probability density functions for u, v, and w show a jagged character, whereas delta-u, delta-v, and delta-w show a much smoother, unimodal behavior. The distributions for delta-u, delta-v, and delta-w are distinctly non-Gaussian.

Campbell, W.↗
NASA NTRS1982

A statistical model for radar images of agricultural scenes

The presently derived and validated statistical model for radar images containing many different homogeneous fields predicts the probability density functions of radar images of entire agricultural scenes, thereby allowing histograms of large scenes composed of a variety of crops to be described. Seasat-A SAR images of agricultural scenes are accurately predicted by the model on the basis of three assumptions: each field has the same SNR, all target classes cover approximately the same area, and the true reflectivity characterizing each individual target class is a uniformly distributed random variable. The model is expected to be useful in the design of data processing algorithms and for scene analysis using radar images.

Frost, V. S.↗
NASA NTRS1984

A stochastic model for photon noise induced by charged particles in multiplier phototubes of the space telescope fine guidance sensors

The Space Telescope (ST) is subjected to charged particle strikes in its space environment. ST's onboard fine guidance sensors utilize multiplier phototubes (PMT) for attitude determination. These tubes, when subjected to charged particle strikes, generate spurious photons in the form of Cerenkov radiation and fluorescence which give rise to unwanted disturbances in the pointing of the telescope. A stochastic model for the number of these spurious photons which strike the photocathode of the multiplier phototube which in turn produce the unwanted photon noise are presented. The model is applicable to both galactic cosmic rays and charged particles trapped in the Earth's radiation belts. The model which was programmed allows for easy adaption to a wide range of particles and different parameters for the phototube of the multiplier. The probability density functions for photons noise caused by protons, alpha particles, and carbon nuclei were using thousands of simulated strikes. These distributions are used as part of an overall ST dynamics simulation. The sensitivity of the density function to changes in the window parameters was also investigated.

Howell, L. W.↗