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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 NTRS1984

Exact differential equation for the density and ionization energy of a many-particle system

The present investigation is concerned with relations studied by Hohenberg and Kohn (1964) and Kohn and Sham (1965). The properties of a ground-state many-electron system are determined by the electron density. The correct differential equation for the density, as dictated by density-functional theory, is presented. It is found that the ground-state density n of a many-electron system obeys a Schroedinger-like differential equation which may be solved by standard Kohn-Sham programs. Results are connected to the traditional exact Kohn-Sham theory. It is pointed out that the results of the current investigations are readily extended to spin-density functional theory.

Levy, M.↗

NASA NTRS1975

LFSPMC: Linear feature selection program using the probability of misclassification

The computational procedure and associated computer program for a linear feature selection technique are presented. The technique assumes that: a finite number, m, of classes exists; each class is described by an n-dimensional multivariate normal density function of its measurement vectors; the mean vector and covariance matrix for each density function are known (or can be estimated); and the a priori probability for each class is known. The technique produces a single linear combination of the original measurements which minimizes the one-dimensional probability of misclassification defined by the transformed densities.

Guseman, L. F., Jr.↗

NASA NTRS1991

Numerical simulation of the emission and motion of neutral and charged dust from P/Halley

The present numerical model for neutral or charged dust-particle distribution prediction in P/Halley encompasses the spatial and temporal variations of the plasma parameters and magnetic field. A significant difference is noted between results for neutral dust trajectories and the trajectories of charged dust particles with radii smaller than 0.1 micron. While most of the model and in situ mass spectra were in good agreement, there is a shortage of the lowest-mass model particles, as well as an offset of the total counting rate for two outbound mass spectra. A combination of two Lorentzian particle mass-density functions with a 100:1 ratio for the number of particles with the lower and higher density functions yielded the best agreement.

Ellis, Tracy A.↗

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 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.↗

NASA NTRS1973

Statistical properties of two sine waves in Gaussian noise.

A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).

Esposito, R.↗

NASA NTRS1977

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗

NASA NTRS1978

Optimal estimation for discrete time jump processes

Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are derived. The approach used is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. Thus a general representation is obtained for optimum estimates, and recursive equations are derived for minimum mean-squared error (MMSE) estimates. In general, MMSE estimates are nonlinear functions of the observations. The problem is considered of estimating the rate of a DTJP when the rate is a random variable with a beta probability density function and the jump amplitudes are binomially distributed. It is shown that the MMSE estimates are linear. The class of beta density functions is rather rich and explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.

Vaca, M. V.↗

NASA NTRS2010

Bonding and Microstructural Stability in Ni55Ti45 Studied by Experimental and Theoretical Methods

Spiral orbit tribometry friction tests performed on Ni-rich Ni55Ti45 titanium ball bearings indicate that this alloy is a promising candidate for future aerospace bearing applications. Microstructural characterization of the bearing specimens was performed using transmission electron microscopy and energy dispersive spectroscopy, with NiTi, Ni4Ti3, Ni3Ti, and Ni2Ti4Ox phases identified within the microstructure of the alloy. Density functional theory was applied to predict the electronic structure of the NixTiy phases, including the band structure and site projected density of states. Ultraviolet photoemission spectroscopy was used to verify the density of states results from the density functional theory calculations, with good agreement observed between experiment and theory.

Stott, Amanda C.↗

NASA NTRS1984

Non-Gaussian statistical models of surface wave fields for remote sensing applications

Based on the complete Stokes wave model with the bias term and using a simple mapping approach and an iteration solution method, we established a formula for the joint probability density function of the surface slope elevation of a nonlinear random wave field. The formula requires three parameters to define the whole density function: the rms surface elevation and slope values and the significant slope. This model represents the dynamics of the wave in a more direct way than the Gram-Charlier approximation. Based on this new statistical model and laboratory experiments, formula and numerical values of EM bias and dynamics bias are derived. The results indicate that various biases should be considered seriously if accuracy of the altimeter measurement is required in centimeter range.

Huang, N. E.↗

NASA NTRS2005

Surveillance system and method having an adaptive sequential probability fault detection test

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Herzog, James P.↗

NASA NTRS2006

Surveillance system and method having an adaptive sequential probability fault detection test

Bickford, Randall L.↗

NASA NTRS2008

Surveillance System and Method having an Adaptive Sequential Probability Fault Detection Test

Bickford, Randall L.↗

NASA NTRS2026

Diffusion Quantum Monte Carlo Calculation of the Austenite and Martensite Phases of NiTi

NiTi is a promising material for smart and active technologies due to its exhibition of the shape memory effect, superelasticity, and biocompatibility. The shape memory effect is tied to the reversible transition between the austenite and martensite phases. A major research direction is to alloy NiTi with Zr, Hf, Pd, Pt, etc., in order to tune the martensitic transition temperature (MTT). Modeling the MTT from first principles is challenging because the lattice dynamics is complicated by anharmonicity and various low-energy structures. Using density functional theory, the energy difference between the austenite and martensite phases of NiTi varies by up to 100 meV/atom depending on the choice of density functional, which is of the same order of the energy difference itself. Consequently, free energy calculations with different functionals can result in estimates of the MTT that vary by several hundred K. Using diffusion quantum Monte Carlo, we calculated the energy difference between the B2 and B19' structures of NiTi to be 70.9 +- 2.5 meV/atom.

Kevin K Ly↗

NASA NTRS1977

Radar backscattering from a sea having an anisotropic large-scale surface, part 2

A two scale scattering model was derived that combines specular reflections from sea waves and Bragg scattering in a manner consistent with energy conservation. The effect of the tilting of the small scale roughness by the large scale roughness was included, which accounted for the reduction of reflected power. The special case of backscattering for which the transmitted polarization equaled the received polarization was considered. An anisotropic large scale surface was used to specify the probability density function of the large scale surface normal. In order to isolate the azimuthal variation of the normalized radar cross section produced by the anisotropic probability density function, an isotropical small scale spectrum was assumed.

Wentz, F. J.↗

NASA NTRS1973

On minimizing the probability of misclassification for linear feature selection

The use of techniques for feature selection permits treatment of classification problems in spaces of reduced dimensions. A method is considered of linear feature selection for n-dimensional observation vectors which belong to one of two populations, where each population is described by a known multivariate normal density function. More specifically, the problem of finding a 1xn transformation matrix B for which the probability of misclassification with respect to the one-dimensional transformed density functions was minimized was considered. Theoretical results are presented which give rise to a numerically tractable expression for the variation in the probability of misclassification with respect to B. Using this expression a computational procedure is discussed for obtaining a B which minimizes the probability of misclassification. Preliminary numerical results are discussed.

Guseman, L. F., Jr.↗

NASA NTRS2002

Optimization of Systems with Uncertainty: Initial Developments for Performance, Robustness and Reliability Based Designs

This paper presents a study on the optimization of systems with structured uncertainties, whose inputs and outputs can be exhaustively described in the probabilistic sense. By propagating the uncertainty from the input to the output in the space of the probability density functions and the moments, optimization problems that pursue performance, robustness and reliability based designs are studied. Be specifying the desired outputs in terms of desired probability density functions and then in terms of meaningful probabilistic indices, we settle a computationally viable framework for solving practical optimization problems. Applications to static optimization and stability control are used to illustrate the relevance of incorporating uncertainty in the early stages of the design. Several examples that admit a full probabilistic description of the output in terms of the design variables and the uncertain inputs are used to elucidate the main features of the generic problem and its solution. Extensions to problems that do not admit closed form solutions are also evaluated. Concrete evidence of the importance of using a consistent probabilistic formulation of the optimization problem and a meaningful probabilistic description of its solution is provided in the examples. In the stability control problem the analysis shows that standard deterministic approaches lead to designs with high probability of running into instability. The implementation of such designs can indeed have catastrophic consequences.

Crespo, Luis G.↗