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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Nonstationary envelope process and first excursion probability

A definition of the envelope of nonstationary random processes is proposed. The establishment of the envelope definition makes it possible to simulate the nonstationary random envelope directly. Envelope statistics, such as the density function, joint density function, moment function, and level crossing rate, which are relevent to analyses of catastrophic failure, fatigue, and crack propagation in structures, are derived. Applications of the envelope statistics to the prediction of structural reliability under random loadings are discussed in detail.

Yang, J.↗
NASA NTRS1990

Gaussian windows: A tool for exploring multivariate data

Presented here is a method for interactively exploring a large set of quantitative multivariate data, in order to estimate the shape of the underlying density function. It is assumed that the density function is more or less smooth, but no other specific assumptions are made concerning its structure. The local structure of the data in a given region may be examined by viewing the data through a Gaussian window, whose location and shape are chosen by the user. A Gaussian window is defined by giving each data point a weight based on a multivariate Gaussian function. The weighted sample mean and sample covariance matrix are then computed, using the weights attached to the data points. These quantities are used to compute an estimate of the shape of the density function in the window region. The local structure of the data is described by a method similar to the method of principal components. By taking many such local views of the data, we can form an idea of the structure of the data set. The method is applicable in any number of dimensions. The method can be used to find and describe simple structural features such as peaks, valleys, and saddle points in the density function, and also extended structures in higher dimensions. With some practice, we can apply our geometrical intuition to these structural features in any number of dimensions, so that we can think about and describe the structure of the data. Since the computations involved are relatively simple, the method can easily be implemented on a small computer.

Jaeckel, Louis A.↗
NASA NTRS1972

Nonstationary envelope process and first excursion probability.

The definition of stationary random envelope proposed by Cramer and Leadbetter, is extended to the envelope of nonstationary random process possessing evolutionary power spectral densities. The density function, the joint density function, the moment function, and the crossing rate of a level of the nonstationary envelope process are derived. Based on the envelope statistics, approximate solutions to the first excursion probability of nonstationary random processes are obtained. In particular, applications of the first excursion probability to the earthquake engineering problems are demonstrated in detail.

Yang, J.-N.↗
NASA NTRS1998

Probabilistic Modeling of High-Temperature Material Properties of a 5-Harness 0/90 Sylramic Fiber/ CVI-SiC/ MI-SiC Woven Composite

An integrated probabilistic approach has been developed to assess composites for high temperature applications. This approach was used to determine thermal and mechanical properties and their probabilistic distributions of a 5-harness 0/90 Sylramic fiber/CVI-SiC/Mi-SiC woven Ceramic Matrix Composite (CMC) at high temperatures. The purpose of developing this approach was to generate quantitative probabilistic information on this CMC to help complete the evaluation for its potential application for HSCT combustor liner. This approach quantified the influences of uncertainties inherent in constituent properties called primitive variables on selected key response variables of the CMC at 2200 F. The quantitative information is presented in the form of Cumulative Density Functions (CDFs). Probability Density Functions (PDFS) and primitive variable sensitivities on response. Results indicate that the scatters in response variables were reduced by 30-50% when the uncertainties in the primitive variables, which showed the most influence, were reduced by 50%.

Nagpal, Vinod K.↗
NASA NTRS2012

Accuracy Assessment of Aqua-MODIS Aerosol Optical Depth Over Coastal Regions: Importance of Quality Flag and Sea Surface Wind Speed

Coastal regions around the globe are a major source for anthropogenic aerosols in the atmosphere, but the underlying surface characteristics are not favorable for the Moderate Resolution Imaging Spectroradiometer (MODIS) algorithms designed for retrieval of aerosols over dark land or open-ocean surfaces. Using data collected from 62 coastal stations worldwide from the Aerosol Robotic Network (AERONET) from approximately 2002-2010, accuracy assessments are made for coastal aerosol optical depth (AOD) retrieved from MODIS aboard Aqua satellite. It is found that coastal AODs (at 550 nm) characterized respectively by the MODIS Dark Land (hereafter Land) surface algorithm, the Open-Ocean (hereafter Ocean) algorithm, and AERONET all exhibit a log-normal distribution. After filtering by quality flags, the MODIS AODs respectively retrieved from the Land and Ocean algorithms are highly correlated with AERONET (with R(sup 2) is approximately equal to 0.8), but only the Land algorithm AODs fall within the expected error envelope greater than 66% of the time. Furthermore, the MODIS AODs from the Land algorithm, Ocean algorithm, and combined Land and Ocean product show statistically significant discrepancies from their respective counterparts from AERONET in terms of mean, probability density function, and cumulative density function, which suggest a need for future improvement in retrieval algorithms. Without filtering with quality flag, the MODIS Land and Ocean AOD dataset can be degraded by 30-50% in terms of mean bias. Overall, the MODIS Ocean algorithm overestimates the AERONET coastal AOD by 0.021 for AOD less than 0.25 and underestimates it by 0.029 for AOD greater than 0.25. This dichotomy is shown to be related to the ocean surface wind speed and cloud contamination effects on the satellite aerosol retrieval. The Modern Era Retrospective-Analysis for Research and Applications (MERRA) reveals that wind speeds over the global coastal region 25 (with a mean and median value of 2.94 meters per second and 2.66 meters per second, respectively) are often slower than 6 meters per second assumed in the MODIS Ocean algorithm. As a result of high correlation (R(sup 2) greater than 0.98) between the bias in binned MODIS AOD and the corresponding binned wind speed over the coastal sea surface, an empirical scheme for correcting the bias of AOD retrieved from the MODIS Ocean algorithm is formulated and is shown to be effective over the majority of the coastal AERONET stations, and hence can be used in future analysis of AOD trend and MODIS AOD data assimilation.

Anderson, J. C.↗
NASA NTRS2015

Simulations of Turbulent Momentum and Scalar Transport in Non-Reacting Confined Swirling Coaxial Jets

This paper presents the numerical simulations of confined three-dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code (NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS); both without and with invoking the APDF or DWFDF equation. When the APDF (ensemble averaged probability density function) or DWFDF (density weighted filtered density function) equation is invoked, the simulations are of a hybrid nature, i.e., the transport equations of energy and species are replaced by the APDF or DWFDF equation. Results of simulations are compared with the available experimental data. Some positive impacts of the nonlinear turbulence models and the Eulerian scalar APDF and DWFDF approach are observed.

combustors↗
NASA NTRS1998

Dynamic Density: An Air Traffic Management Metric

The definition of a metric of air traffic controller workload based on air traffic characteristics is essential to the development of both air traffic management automation and air traffic procedures. Dynamic density is a proposed concept for a metric that includes both traffic density (a count of aircraft in a volume of airspace) and traffic complexity (a measure of the complexity of the air traffic in a volume of airspace). It was hypothesized that a metric that includes terms that capture air traffic complexity will be a better measure of air traffic controller workload than current measures based only on traffic density. A weighted linear dynamic density function was developed and validated operationally. The proposed dynamic density function includes a traffic density term and eight traffic complexity terms. A unit-weighted dynamic density function was able to account for an average of 22% of the variance in observed controller activity not accounted for by traffic density alone. A comparative analysis of unit weights, subjective weights, and regression weights for the terms in the dynamic density equation was conducted. The best predictor of controller activity was the dynamic density equation with regression-weighted complexity terms.

Laudeman, I. V.↗
NASA NTRS1978

Simplified model of statistically stationary spacecraft rotation and associated induced gravity environments

A stochastic model of spacecraft motion was developed based on the assumption that the net torque vector due to crew activity and rocket thruster firings is a statistically stationary Gaussian vector process. The process had zero ensemble mean value, and the components of the torque vector were mutually stochastically independent. The linearized rigid-body equations of motion were used to derive the autospectral density functions of the components of the spacecraft rotation vector. The cross-spectral density functions of the components of the rotation vector vanish for all frequencies so that the components of rotation were mutually stochastically independent. The autospectral and cross-spectral density functions of the induced gravity environment imparted to scientific apparatus rigidly attached to the spacecraft were calculated from the rotation rate spectral density functions via linearized inertial frame to body-fixed principal axis frame transformation formulae. The induced gravity process was a Gaussian one with zero mean value. Transformation formulae were used to rotate the principal axis body-fixed frame to which the rotation rate and induced gravity vector were referred to a body-fixed frame in which the components of the induced gravity vector were stochastically independent. Rice's theory of exceedances was used to calculate expected exceedance rates of the components of the rotation and induced gravity vector processes.

Fichtl, G. H.↗
NASA NTRS1979

The correlation function for density perturbations in an expanding universe. IV - The evolution of the correlation function

The evolution of the two-point correlation function for the large-scale distribution of galaxies in an expanding universe is studied on the assumption that the perturbation densities lie in a Gaussian distribution centered on any given mass scale. The perturbations are evolved according to the Friedmann equation, and the correlation function for the resulting distribution of perturbations at the present epoch is calculated. It is found that: (1) the computed correlation function gives a satisfactory fit to the observed function in cosmological models with a density parameter (Omega) of approximately unity, provided that a certain free parameter is suitably adjusted; (2) the power-law slope in the nonlinear regime reflects the initial fluctuation spectrum, provided that the density profile of individual perturbations declines more rapidly than the -2.4 power of distance; and (3) both positive and negative contributions to the correlation function are predicted for cosmological models with Omega less than unity.

Mcclelland, J.↗
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 NTRS1966

On the statistics of correlator outputs

Characteristic function, probability density function, and probability distribution function computations for correlation detector output, and correlator output statistics

Wintz, P. A.↗
NASA NTRS1974

Classification by means of B-spline potential functions with applications to remote sensing

A method is presented for using B-splines as potential functions in the estimation of likelihood functions (probability density functions conditioned on pattern classes), or the resulting discriminant functions. The consistency of this technique is discussed. Experimental results of using the likelihood functions in the classification of remotely sensed data are given.

Bennett, J. O.↗
NASA NTRS1975

A sequential nonparametric pattern classification algorithm based on the Wald SPRT

A sequential nonparametric pattern classification procedure is presented. The method presented is an estimated version of the Wald sequential probability ratio test (SPRT). This method utilizes density function estimates, and the density estimate used is discussed, including a proof of convergence in probability of the estimate to the true density function. The classification procedure proposed makes use of the theory of order statistics, and estimates of the probabilities of misclassification are given. The procedure was tested on discriminating between two classes of Gaussian samples and on discriminating between two kinds of electroencephalogram (EEG) responses.

Poage, J. L.↗
NASA NTRS1999

Multiple Point Dynamic Gas Density Measurements Using Molecular Rayleigh Scattering

A nonintrusive technique for measuring dynamic gas density properties is described. Molecular Rayleigh scattering is used to measure the time-history of gas density simultaneously at eight spatial locations at a 50 kHz sampling rate. The data are analyzed using the Welch method of modified periodograms to reduce measurement uncertainty. Cross-correlations, power spectral density functions, cross-spectral density functions, and coherence functions may be obtained from the data. The technique is demonstrated using low speed co-flowing jets with a heated inner jet.

Seasholtz, Richard↗
NASA NTRS1983

Atmospheric attenuation for correlated satellite communication ground sites

Link margin estimates are calculated for 30/20 GHz satellite communication systems employing closely-spaced (4 to 100 km) 'dual diversity' switched ground sites. The link margin estimates are based on a new analysis in which the bivariate rain attenuation density function for two correlated ground sites is modelled by an exponential density function. The results of the exponential density function analysis enable derivation of a direct relation between rain margin estimates and probability of exceedance (link availability). Margins typically in the range 2 to 12 dB are calculated for various ground site separations and summarized for seven city locations and five satellite orbit positions over the U.S. The results can be easily extended to other EHF satellite frequencies and other locations.

Christopher, P.↗
NASA NTRS1992

Derivation of phase statistics from the Mueller matrix

Experimental observations show a strong dependence of phase differences of scattering matrix elements on the physical parameters of random media. Here, the statistical behavior of the phase differences is studied for distributed targets. The pdfs of the phase differences are derived from the Mueller matrix of the target. In deriving the density functions, it is assumed that the real and imaginary parts of the copolarized and cross-polarized terms of the scattering matrix are jointly Gaussian and their covariance matrices are found in terms of the Mueller matrix elements. The functional forms of the copolarized and cross-polarized density functions are similar and are obtained independently. It is shown that the density function of the phase difference is completely determined in terms of only two parameters.

Sarabandi, K.↗
NASA NTRS1990

First-passage problems: A probabilistic dynamic analysis for degraded structures

Structures subjected to random excitations with uncertain system parameters degraded by surrounding environments (a random time history) are studied. Methods are developed to determine the statistics of dynamic responses, such as the time-varying mean, the standard deviation, the autocorrelation functions, and the joint probability density function of any response and its derivative. Moreover, the first-passage problems with deterministic and stationary/evolutionary random barriers are evaluated. The time-varying (joint) mean crossing rate and the probability density function of the first-passage time for various random barriers are derived.

Shiao, Michael C.↗