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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

An improved exceedance theory for combined random stresses

An extension is presented of Rice's classic solution for the exceedances of a constant level by a single random process to its counterpart for an n-dimensional vector process. An interaction boundary, analogous to the constant level considered by Rice for the one-dimensional case, is assumed in the form of a hypersurface. The theory for the numbers of boundary exceedances is developed by using a joint statistical approach which fully accounts for all cross-correlation effects. An exact expression is derived for the n-dimensional exceedance density function, which is valid for an arbitrary interaction boundary. For application to biaxial states of combined random stress, the general theory is reduced to the two-dimensional case. An elliptical stress interaction boundary is assumed and the exact expression for the density function is presented. The equations are expressed in a format which facilitates calculating the exceedances by numerically evaluating a line integral. The behavior of the density function for the two-dimensional case is briefly discussed.

Lester, H. C.↗
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 NTRS1981

Estimation of proportions in mixed pixels through their region characterization

A region of mixed pixels can be characterized through the probability density function of proportions of classes in the pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability density functions of proportions. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonalizes the covariance matrices of the two classes. If the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estmates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.

Chittineni, C. B.↗
NASA NTRS2018

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

Corbetta, M.↗
NASA NTRS2019

A Fast Monte Carlo Method for Model-Based Prognostics Based on Stochastic Calculus

This work proposes a fast Monte Carlo method to solve differential equations utilized in model-based prognostics. The methodology is derived from the theory of stochastic calculus, and the goal of such a method is to speed up the estimation of the probability density functions describing the independent variable evolution over time. In the prognostic scenarios presented in this paper, the stochastic differential equations describe variables directly or indirectly related to the degradation of a monitored system. The method allows the estimation of the probability density functions by solving the deterministic equation and approximating the stochastic integrals using samples of the model noise. By so doing, the prognostic problem is solved without the Monte Carlo simulation based on Euler's forward method, which is typically the most time consuming task of the prediction stage. Three different prognostic scenarios are presented as proof of concept: (i) life prediction of electrolytic capacitors, (ii) remaining time to discharge of Lithium-ion batteries, and (iii) prognostic of cracked structures under fatigue loading. The paper shows how the method produces probability density functions that are statistically indistinguishable from the distributions estimated with Euler's forward Monte Carlo simulation. However, the proposed solution is orders of magnitude faster when computing the time-to-failure distribution of the monitored system. The approach may enable complex real-time prognostics and health management solutions with limited computing power.

stochastic calculus↗
NASA NTRS1983

Spline Classification Methods

The use of spline functions in the development of classification algorithms is discussed. A method is formulated for producing spline approximations to univariate density functions when each density function is described by a histogram of measurements. The resulting approximations are then incorporated into a Bayesian classification procedure for which the probability of misclassification can be readily computed. Some preliminary numerical results are presented to illustrate the method.

Guseman, L. F., Jr.↗
NASA NTRS1984

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.↗
NASA NTRS1977

Characterization of nonGaussian atmospheric turbulence for prediction of aircraft response statistics

Mathematical expressions were derived for the exceedance rates and probability density functions of aircraft response variables using a turbulence model that consists of a low frequency component plus a variance modulated Gaussian turbulence component. The functional form of experimentally observed concave exceedance curves was predicted theoretically, the strength of the concave contribution being governed by the coefficient of variation of the time fluctuating variance of the turbulence. Differences in the functional forms of response exceedance curves and probability densities also were shown to depend primarily on this same coefficient of variation. Criteria were established for the validity of the local stationary assumption that is required in the derivations of the exceedance curves and probability density functions. These criteria are shown to depend on the relative time scale of the fluctuations in the variance, the fluctuations in the turbulence itself, and on the nominal duration of the relevant aircraft impulse response function. Metrics that can be generated from turbulence recordings for testing the validity of the local stationary assumption were developed.

Mark, W. D.↗
NASA NTRS2012

A Discussion on Uncertainty Representation and Interpretation in Model-Based Prognostics Algorithms based on Kalman Filter Estimation Applied to Prognostics of Electronics Components

This article discusses several aspects of uncertainty representation and management for model-based prognostics methodologies based on our experience with Kalman Filters when applied to prognostics for electronics components. In particular, it explores the implications of modeling remaining useful life prediction as a stochastic process and how it relates to uncertainty representation, management, and the role of prognostics in decision-making. A distinction between the interpretations of estimated remaining useful life probability density function and the true remaining useful life probability density function is explained and a cautionary argument is provided against mixing interpretations for the two while considering prognostics in making critical decisions.

Celaya, Jose R.↗
NASA NTRS1994

An evaluation with the Fourier Amplitude Sensitivity Test (FAST) of which land-surface parameters are of greatest importance in atmospheric modeling

Land-surface parameterizations based on a statistical-dynamical have been suggested recently to improve the representation of the surface forcing from heterogeneous land in atmospheric models. With this approach, land-surface characteristics are prescribed by probability density functions (PDFs) rather than single 'representative' values as in 'big-leaf' parameterizations. Yet the use of many PDFs results in an increased computational burden and requires the complex problem of representing covariances between PDFs to be addressed. In this study, a sensitivity analysis of a land-surface parameterization for atmospheric modeling was performed to evaluate the surface parameters most important to the variability of surface heat fluxes. The Fourier amplitude sensitivity test (FAST) used for this analysis determines the relative contribution of individual input parameters to the variance of energy fluxes resulting from a heterogeneous surface. By simultaneously varying all parameters according to their individual probability density functions, the number of computations needed is very much reduced by this technique. This analysis demonstrates that most of the variability of surface heat fluxes may be described by the distributions of relative stomatal conductance and surface roughness. Thus, the statistical-dynamical approach may be simplified by the use of only these two probability density functions.

Collins, Dan C.↗
NASA NTRS1978

The correlation function for density perturbations in an expanding universe. III The three-point and predictions of the four-point and higher order correlation functions

Higher-order correlation functions for the large-scale distribution of galaxies in space are investigated. It is demonstrated that the three-point correlation function observed by Peebles and Groth (1975) is not consistent with a distribution of perturbations that at present are randomly distributed in space. The two-point correlation function is shown to be independent of how the perturbations are distributed spatially, and a model of clustered perturbations is developed which incorporates a nonuniform perturbation distribution and which explains the three-point correlation function. A model with hierarchical perturbations incorporating the same nonuniform distribution is also constructed; it is found that this model also explains the three-point correlation function, but predicts different results for the four-point and higher-order correlation functions than does the model with clustered perturbations. It is suggested that the model of hierarchical perturbations might be explained by the single assumption of having density fluctuations or discrete objects all of the same mass randomly placed at some initial epoch.

Mcclelland, J.↗
NASA NTRS2003

Large Eddy Simulation Of Gravitational Effects In Transitional And Turbulent Gas-Jet Diffusion Flames

The influence of gravity on the spatial and the compositional structures of transitional and turbulent hydrocarbon diffusion flames are studies via large eddy simulation (LES) and direct numerical simulation (DNS) of round and planar jets. The subgrid-scale (SGS) closures in LES are based on the filtered mass density function (FMDF) methodology. The FMDF represents the joint probability density function (PDF) of the SGS scalars, and is obtained by solving its transport equation. The fundamental advantage of LES/FMDF is that it accounts for the effects of chemical reaction and buoyancy exactly. The methodology is employed for capturing some of the fundamental influences of gravity in equilibrium flames via realistic chemical kinetic schemes. Some preliminary investigation of the gravity effects in non-equilibrium flames is also conducted, but with idealized chemical kinetics models.

Jaberi, Farhad A.↗
NASA NTRS1978

An optimum PN code search technique for a given apriori signal location density

A method is presented for optimizing (minimizing) the acquisition time for a PN-type spread spectrum system when the a priori probability density function is not uniform. For an assumed a priori Gaussian density function, calculations show that the acquisition time, when the 0.5 probability acquisition time is used as a measure of acquisition time, is reduced by 40% for a cell detection probability of 0.25 and when three sweeps are used. For the same parameters and with four sweeps the acquisition time is reduced by 41%. When the acquisition time probability is set to 0.9 instead of 0.5, the reduction is 25% of the uniform sweep time.

Holmes, J. K.↗
NASA NTRS1977

The correlation function for density perturbations in an expanding universe. II - Nonlinear theory

A formalism is developed to find the two-point and higher-order correlation functions for a given distribution of sizes and shapes of perturbations which are randomly placed in three-dimensional space. The perturbations are described by two parameters such as central density and size, and the two-point correlation function is explicitly related to the luminosity function of groups and clusters of galaxies

Mcclelland, J.↗
NASA NTRS1978

The role of drop velocity in statistical spray description

The justification for describing a spray by treating drop velocity as a random variable on an equal statistical basis with drop size was studied experimentally. A double exposure technique using fluorescent drop photography was used to make size and velocity measurements at selected locations in a steady ethanol spray formed by a swirl atomizer. The size velocity data were categorized to construct bivariate spray density functions to describe the spray immediately after formation and during downstream propagation. Bimodal density functions were formed by environmental interaction during downstream propagation. Large differences were also found between spatial mass density and mass flux size distribution at the same location.

Groeneweg, J. F.↗
NASA NTRS1986

Estimation of vegetation cover at subpixel resolution using LANDSAT data

The present report summarizes the various approaches relevant to estimating canopy cover at subpixel resolution. The approaches are based on physical models of radiative transfer in non-homogeneous canopies and on empirical methods. The effects of vegetation shadows and topography are examined. Simple versions of the model are tested, using the Taos, New Mexico Study Area database. Emphasis has been placed on using relatively simple models requiring only one or two bands. Although most methods require some degree of ground truth, a two-band method is investigated whereby the percent cover can be estimated without ground truth by examining the limits of the data space. Future work is proposed which will incorporate additional surface parameters into the canopy cover algorithm, such as topography, leaf area, or shadows. The method involves deriving a probability density function for the percent canopy cover based on the joint probability density function of the observed radiances.

Jasinski, Michael F.↗