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At least 163 records · Page 9

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NASA NTRS2018

A Simple, Velocity Dependent, Collision Probability Algorithm for Small Combined Hard Body Radii Close Approach Events

Over the last few years progress has been made in the velocity dependent collision probability problem. Recent progress in this problem has been approached via integration of the probability flux into the surface of the combined hard body object. The algorithm presented uses the surface flux approach and is designed to compute the collision probability rate between two objects given their time dependent states and state error covariance matrices. With regards to the computation of the collision probability (Pc) rate, two major differences exist between the development of this algorithm and the usual Pc algorithm. First, the shape of the at-risk volume is assumed to be a cube rather than a sphere. The size of the cube is chosen so that it circumscribes the usual hard body sphere chosen for the spherical Pc problem. This will result in half the length of a side of the cube being equal to the hard body radius (HBR) of the sphere. Second, it is assumed that the HBR of the cube is much smaller than the smallest combined position uncertainty (σ(sub min) > 5*HBR) at each time point of evaluation. This is necessary as the actual collision probability calculation is based on a first order, small variable expansion in the position components of the Gaussian probability density function. This leads to the collision probability rate being to second order in the combined HBR. The collision probability rate is in a concise, closed form containing exponential and error functions.

Frisbee, Joe↗

NASA NTRS1989

Probabilities and statistics for backscatter estimates obtained by a scatterometer

Methods for the recovery of winds near the surface of the ocean from measurements of the normalized radar backscattering cross section must recognize and make use of the statistics (i.e., the sampling variability) of the backscatter measurements. Radar backscatter values from a scatterometer are random variables with expected values given by a model. A model relates backscatter to properties of the waves on the ocean, which are in turn generated by the winds in the atmospheric marine boundary layer. The effective wind speed and direction at a known height for a neutrally stratified atmosphere are the values to be recovered from the model. The probability density function for the backscatter values is a normal probability distribution with the notable feature that the variance is a known function of the expected value. The sources of signal variability, the effects of this variability on the wind speed estimation, and criteria for the acceptance or rejection of models are discussed. A modified maximum likelihood method for estimating wind vectors is described. Ways to make corrections for the kinds of errors found for the Seasat SASS model function are described, and applications to a new scatterometer are given.

Pierson, Willard J., Jr.↗

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.↗

DOE OSTI2024

Size resolved particle volatility for 30, 60, and 90 nm particles collected at the EPCAPE Mount Soledad site from 04/23/2023 to 06/15/2023

VTDMA GF-PDF: Growth factor probability density functions from the Gysel inversion are located here, where probability is out of 200. The instrument measured three different diameters 30 nm, 60nm and 90nm each diameter was selected for an hour. During that hour three different temperatures where scanned (40°C, 80°C, 160°C) in between each temperature a bypass scan was taken at room temperature. Each scan took 10-minutes and scanned growth factors from 0.2-1.2. Calibrations of the instrument with NaCl were performed on 4/26/2023 from 11:20 to 14:20, on 5/16/2023 from 11:40 to 16:00, and on 5/30/2023 from 10:20 to 14:20. Calibrations with (NH4)2SO4 were performed on 5/8/2023 from 11:45 to 14:40, on 5/23/2023 from 11:20 to 3:00, and on 6/14/2023 from 13:00 to 16:00. Time is recorded in seconds since 1/1/1904. GF_Vol_avg: Growth factor volume average calculated by the Gysel inversion. The instrument measured three different diameters 30 nm, 60nm and 90nm each diameter was selected for an hour. During that hour three different temperatures where scanned (40°C, 80°C, 160°C) in between each temperature a bypass scan was taken at room temperature. Each scan took 10-minutes and scanned growth factors from 0.2-1.2. Calibrations of the instrument with NaCl were performed on 4/26/2023 from 11:20 to 14:20, on 5/16/2023 from 11:40 to 16:00, and on 5/30/2023 from 10:20 to 14:20. Calibrations with (NH4)2SO4 were performed on 5/8/2023 from 11:45 to 14:40, on 5/23/2023 from 11:20 to 3:00, and on 6/14/2023 from 13:00 to 16:00. Time is recorded in seconds since 1/1/1904.

30nm growth factor volume average at 160C (GF_vol_↗

NASA NTRS1973

Remote optical measurement of wind speed spectra

The paper presents some new analytical and experimental results on the cross-correlation function and power spectrum for the flow speed by the passive optical crossed-beam correlation technique. Cross-correlation functions of crossed-beam measurements for both intersecting beams and separated beams have been reviewed for the case of varying wind speeds. The corresponding spectral density functions were derived and expressed in terms of the probability density of wind speed variations and the correlation of atmospheric turbulent eddies. The associated spectral density for a special approximate model was derived by assuming a Gaussian distribution of transit times. The theoretical predictions were then compared with actual field test data, and a reasonably good agreement in the valid frequency range was observed.

Su, M.-Y.↗

NASA NTRS1974

Optimal design of an unsupervised adaptive classifier with unknown priors

An adaptive detection scheme for M hypotheses was analyzed. It was assumed that the probability density function under each hypothesis was known, and that the prior probabilities of the M hypotheses were unknown and sequentially estimated. Each observation vector was classified using the current estimate of the prior probabilities. Using a set of nonlinear transformations, and applying stochastic approximation theory, an optimally converging adaptive detection and estimation scheme was designed. The optimality of the scheme lies in the fact that convergence to the true prior probabilities is ensured, and that the asymptotic error variance is minimum, for the class of nonlinear transformations considered. An expression for the asymptotic mean square error variance of the scheme was also obtained.

Kazakos, D.↗

NASA NTRS2003

A Novel Strategy for Numerical Simulation of High-speed Turbulent Reacting Flows

The objective of this research is to improve and implement the filtered mass density function (FDF) methodology for large eddy simulation (LES) of high-speed reacting turbulent flows. We have just completed Year 1 of this research. This is the Final Report on our activities during the period: January 1, 2003 to December 31, 2003. 2002. In the efforts during the past year, LES is conducted of the Sandia Flame D, which is a turbulent piloted nonpremixed methane jet flame. The subgrid scale (SGS) closure is based on the scalar filtered mass density function (SFMDF) methodology. The SFMDF is basically the mass weighted probability density function (PDF) of the SGS scalar quantities. For this flame (which exhibits little local extinction), a simple flamelet model is used to relate the instantaneous composition to the mixture fraction. The modelled SFMDF transport equation is solved by a hybrid finite-difference/Monte Carlo scheme.

Sheikhi, M. R. H.↗

NASA NTRS1993

Microjansky source counts and spectral indices at 8.44 GHz

Deep images were made with 10 arcsec resolution at 8.44 GHz with microjansky sensitivity of two regions previously imaged at several lower frequencies. The differential microjansky source count fits a power-law distribution with slope 2.3 +/- 0.2. This slope is roughly constant between 1.41 and 8.44 GHz and between S(v) = about 4 and X(v) = 1000 microJy. Unless the majority of radio sources at microJy levels are local, their average luminosity and/or space density probably has evolved with cosmic epoch in order to sustain the steep and nearly Euclidean value of the slope over such a large range in flux density. The 8.44 GHz counts probably converge at less than the 1 microjansky level if the evolutionary properties of these weak sources are similar to those of luminous gE radio galaxies and quasars. The median angular size of sources detected at 8.44 GHz at microjansky levels is 2.6 +/- 1.4 arcsec, and 40 percent of the source are larger than 5 arcsec.

Windhorst, Rogier 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 NTRS1976

Aircraft motion and passenger comfort data from scheduled commercial airline flights

Data concerning the ride quality of aircraft taken on board commercial airline flights was presented. Five types of data are included: (1) root mean square (RMS) values of linear acceleration, angular acceleration or angular velocities, along with passenger subjective evaluations, (2) power spectra for the motion in each of six degrees of freedom, (3) scattergrams showing the probability density of the rms accelerations in the vertical and transverse directions, (4) probability distributions of the motion, and (5) on board noise levels during takeoff, climb, cruise, and descent.

Gruesbeck, M. G.↗

NASA NTRS1982

Review of some results in bivariate density estimation

Results are reviewed for choosing smoothing parameters for some bivariate density estimators. Experience gained in comparing the effects of smoothing parameters on probability density estimators for univariate and bivariate data is summarized.

Scott, D. W.↗

NASA NTRS2011

Safe Onboard Guidance and Control Under Probabilistic Uncertainty

An algorithm was developed that determines the fuel-optimal spacecraft guidance trajectory that takes into account uncertainty, in order to guarantee that mission safety constraints are satisfied with the required probability. The algorithm uses convex optimization to solve for the optimal trajectory. Convex optimization is amenable to onboard solution due to its excellent convergence properties. The algorithm is novel because, unlike prior approaches, it does not require time-consuming evaluation of multivariate probability densities. Instead, it uses a new mathematical bounding approach to ensure that probability constraints are satisfied, and it is shown that the resulting optimization is convex. Empirical results show that the approach is many orders of magnitude less conservative than existing set conversion techniques, for a small penalty in computation time.

Blackmore, Lars James↗

NASA NTRS1990

An analytical approach to gravitational lensing by an ensemble of axisymmetric lenses

The problem of gravitational lensing by an ensemble of identical axisymmetric lenses randomly distributed on a single lens plane is considered and a formal expression is derived for the joint probability density of finding shear and convergence at a random point on the plane. The amplification probability for a source can be accurately estimated from the distribution in shear and convergence. This method is applied to two cases: lensing by an ensemble of point masses and by an ensemble of objects with Gaussian surface mass density. There is no convergence for point masses whereas shear is negligible for wide Gaussian lenses.

Lee, Man Hoi↗

NASA NTRS2010

Turbulence and the Stabilization Principle

Further results of research, reported in several previous NASA Tech Briefs articles, were obtained on a mathematical formalism for postinstability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence). To recapitulate: Fictitious control forces are introduced to couple the dynamical equations with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in ordinary perceived three-dimensional space is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. Con sequently, the postinstability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable. The previously reported findings are analyzed from the perspective of the authors Stabilization Principle, according to which (1) stability is recognized as an attribute of mathematical formalism rather than of underlying physics and (2) a dynamical system that appears unstable when modeled by differentiable functions only can be rendered stable by modifying the dynamical equations to incorporate intrinsic stochasticity.

Zak, Michail↗

NASA NTRS2009

Extending Newtonian Dynamics to Include Stochastic Processes

A paper presents further results of continuing research reported in several previous NASA Tech Briefs articles, the two most recent being Stochastic Representations of Chaos Using Terminal Attractors (NPO-41519), [Vol. 30, No. 5 (May 2006), page 57] and Physical Principle for Generation of Randomness (NPO-43822) [Vol. 33, No. 5 (May 2009), page 56]. This research focuses upon a mathematical formalism for describing post-instability motions of a dynamical system characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism involves fictitious control forces that couple the equations of motion of the system with a Liouville equation that describes the evolution of the probability density of errors in initial conditions. These stabilizing forces create a powerful terminal attractor in probability space that corresponds to occurrence of a target trajectory with probability one. The effect in configuration space (ordinary three-dimensional space as commonly perceived) is to suppress exponential divergences of neighboring trajectories without affecting the target trajectory. As a result, the post-instability motion is represented by a set of functions describing the evolution of such statistical quantities as expectations and higher moments, and this representation is stable.

Zak, Michail↗

NASA NTRS1981

Statistics of some atmospheric turbulence records relevant to aircraft response calculations

Methods for characterizing atmospheric turbulence are described. The methods illustrated include maximum likelihood estimation of the integral scale and intensity of records obeying the von Karman transverse power spectral form, constrained least-squares estimation of the parameters of a parametric representation of autocorrelation functions, estimation of the power spectra density of the instantaneous variance of a record with temporally fluctuating variance, and estimation of the probability density functions of various turbulence components. Descriptions of the computer programs used in the computations are given, and a full listing of these programs is included.

Mark, W. D.↗

NASA NTRS1978

Error probability performance of unbalanced QPSK receivers

A simple technique for calculating the error probability performance and associated noisy reference loss of practical unbalanced QPSK receivers is presented. The approach is based on expanding the error probability conditioned on the loop phase error in a power series in the loop phase error and then, keeping only the first few terms of this series, averaging this conditional error probability over the probability density function of the loop phase error. Doing so results in an expression for the average error probability which is in the form of a leading term representing the ideal (perfect synchronization references) performance plus a term proportional to the mean-squared crosstalk. Thus, the additional error probability due to noisy synchronization references occurs as an additive term proportional to the mean-squared phase jitter directly associated with the receiver's tracking loop. Similar arguments are advanced to give closed-form results for the noisy reference loss itself.

Simon, M. K.↗

NASA NTRS1989

Probabilities for gravitational lensing by point masses in a locally inhomogeneous universe

Probability functions for gravitational lensing by point masses that incorporate Poisson statistics and flux conservation are formulated in the Dyer-Roeder construction. Optical depths to lensing for distant sources are calculated using both the method of Press and Gunn (1973) which counts lenses in an otherwise empty cone, and the method of Ehlers and Schneider (1986) which projects lensing cross sections onto the source sphere. These are then used as parameters of the probability density for lensing in the case of a critical (q0 = 1/2) Friedmann universe. A comparison of the probability functions indicates that the effects of angle-averaging can be well approximated by adjusting the average magnification along a random line of sight so as to conserve flux.

Isaacson, Jeffrey A.↗