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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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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
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.↗
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 NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer with applications to new scatterometer design data

The values of the Normalized Radar Backscattering Cross Section (NRCS), sigma (o), obtained by a scatterometer are random variables whose variance is a known function of the expected value. The probability density function can be obtained from the normal distribution. Models for the expected value obtain it as a function of the properties of the waves on the ocean and the winds that generated the waves. Point estimates of the expected value were found from various statistics given the parameters that define the probability density function for each value. Random intervals were derived with a preassigned probability of containing that value. A statistical test to determine whether or not successive values of sigma (o) are truly independent was derived. The maximum likelihood estimates for wind speed and direction were found, given a model for backscatter as a function of the properties of the waves on the ocean. These estimates are biased as a result of the terms in the equation that involve natural logarithms, and calculations of the point estimates of the maximum likelihood values are used to show that the contributions of the logarithmic terms are negligible and that the terms can be omitted.

Pierson, Willard J., Jr.↗
NASA NTRS1972

Off-line data analysis and data reduction from digitally controlled random test systems.

This paper discusses the merits of employing the new computer-controlled random environment control systems for fast and efficient large-scale data analysis when they are not being used for test control. Hardware and software requirements are stated. Several of the more familiar frequency functions are defined from the Fourier coefficients, the main product of the Fourier processors used in these control systems. Another function, the probability density function, is defined and suggestions for its application are made. An analysis example is presented. Some programming tips are listed, and the accuracy and reliability of frequency analysis measurements are considered.

Chapman, C. P.↗
NASA NTRS1985

New results on mean time-to-first-slip for a first-order loop

Approximate results are derived from a new expression for the mean time-to-first-slip for a first-order loop with arbitrary periodic equivalent phase detector characteristic in the presence of frequency detuning. They are accurate for loop signal-to-noise ratios greater than 3 dB or less than 0 dB. The approximations found serve to provide insight into the mean first slip time dependence on the shape of the equivalent phase detector characteristic and the frequency detuning, and dependence on loop parameters. The new expression itself is also of theoretical interest, since it allows one to explicitly express the stationary phase error probability density function and probability current in terms of the mean first slip time. This sheds further light on the interconnections between the conventional modulo-2 pi approach and the renewal theory approach to the Fokker-Planck method. Extensions to nonperiodic equivalent phase detector characteristics are also considered.

Chie, C. M.↗
NASA NTRS1972

A comparative study of nonparametric methods for pattern recognition

The applied research discussed in this report determines and compares the correct classification percentage of the nonparametric sign test, Wilcoxon's signed rank test, and K-class classifier with the performance of the Bayes classifier. The performance is determined for data which have Gaussian, Laplacian and Rayleigh probability density functions. The correct classification percentage is shown graphically for differences in modes and/or means of the probability density functions for four, eight and sixteen samples. The K-class classifier performed very well with respect to the other classifiers used. Since the K-class classifier is a nonparametric technique, it usually performed better than the Bayes classifier which assumes the data to be Gaussian even though it may not be. The K-class classifier has the advantage over the Bayes in that it works well with non-Gaussian data without having to determine the probability density function of the data. It should be noted that the data in this experiment was always unimodal.

Hahn, S. F.↗
NASA NTRS1989

Probability function of breaking-limited surface elevation

The effect of wave breaking on the probability function of surface elevation is examined. The surface elevation limited by wave breaking zeta sub b(t) is first related to the original wave elevation zeta(t) and its second derivative. An approximate, second-order, nonlinear, non-Gaussian model for zeta(t) of arbitrary but moderate bandwidth is presented, and an expression for the probability density function zeta sub b(t) is derived. The results show clearly that the effect of wave breaking on the probability density function of surface elevation is to introduce a secondary hump on the positive side of the probability density function, a phenomenon also observed in wind wave tank experiments.

Tung, C. C.↗
NASA NTRS1987

Bragg-cell receiver study

Bragg-cell receivers are employed in specialized Electronic Warfare (EW) applications for the measurement of frequency. Bragg-cell receiver characteristics are fully characterized for simple RF emitter signals. This receiver is early in its development cycle when compared to the IFM receiver. Functional mathematical models are derived and presented in this report for the Bragg-cell receiver. Theoretical analysis is presented and digital computer signal processing results are presented for the Bragg-cell receiver. Probability density function analysis are performed for output frequency. Probability density function distributions are observed to depart from assumed distributions for wideband and complex RF signals. This analysis is significant for high resolution and fine grain EW Bragg-cell receiver systems.

Wilson, Lonnie A.↗
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.↗
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 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 NTRS1983

A non-Gaussian statistical model for surface elevation of nonlinear random wave fields

Probability density function of the surface elevation of a nonlinear random wave field is obtained. The wave model is based on the Stokes expansion carried to the third order for both deep water waves and waves in finite depth. The amplitude and phase of the first-order component of the Stokes wave are assumed to be Rayleigh and uniformly distributed and slowly varying, respectively. The probability density function for the deep water case was found to depend on two parameters: the root-mean-square surface elevation and the significant slope. For water of finite depth, an additional parameter, the nondimensional depth, is also required. An important difference between the present result and the Gram-Charlier representation is that the present probability density functions are always nonnegative. It is also found that the 'constant' term in the Stokes expansion, usually neglected in deterministic studies, plays an important role in determining the details of the density function. The results compare well with laboratory and field experiment data.

Huang, N. E.↗
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 NTRS1993

PDF approach for compressible turbulent reacting flows

The objective of the present work is to develop a probability density function (pdf) turbulence model for compressible reacting flows for use with a CFD flow solver. The probability density function of the species mass fraction and enthalpy are obtained by solving a pdf evolution equation using a Monte Carlo scheme. The pdf solution procedure is coupled with a compressible CFD flow solver which provides the velocity and pressure fields. A modeled pdf equation for compressible flows, capable of capturing shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed, and an averaging procedure is developed to provide smooth Monte-Carlo solutions to ensure convergence. Two supersonic diffusion flames are studied using the proposed pdf model and the results are compared with experimental data; marked improvements over CFD solutions without pdf are observed. Preliminary applications of pdf to 3D flows are also reported.

Hsu, A. T.↗