Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Probability distribution”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Cosmological density fluctuations and large-scale structure From N-point correlation functions to the probability distribution

Knowledge of N-point correlation functions for all N allows one to invert and obtain the probability distribution of mass fluctuations in a fixed volume. The hierarchical sequence of higher order is applied to correlations with dimensionless amplitudes suggested by the BBGKY equations. The resulting distribution is significantly non-Gaussian, even for quite small mean square fluctuations. The qualitative and to some degree quantitative results are to a large degree independent of the exact sequence of amplitudes. An ensemble of such models compared with N-body simulations fails in detail to account for the low-density frequency distribution.

Fry, J. N.↗
DOE OSTI2021

A consistent, Bayesian, approach to the cross section probability distribution in the unresolved resonance region

The cross sections of neutron-induced reactions can be divided into three energy ranges: the resolved resonance region (RRR), the unresolved resonance region (URR), and the fast region. In general, the cross sections in the URR show significant fluctuations that cannot be predicted and cannot be experimentally resolved, thus, it is commonly assumed that the cross section at a specific energy is given by a probability distribution function (PDF) over a range of values that can span several orders of magnitude. The current methodology used to describe such behavior is to construct the PDF by stochastically generating resonance ladders and numerically measuring the PDF. The resonance ladders are sampled using known resonance statistical properties and average resonance widths and spacings extrapolated from the RRR. Although this is a standard and widely used technique, it is computationally very expensive, therefore, an alternative, analytical, approach would be preferable due to the considerable speed up of the computational time in real life applications. Moreover, the current methodology does not take into account existing experimental data, such for total and capture cross sections, that are available for many nuclei. Finally, this approach was developed to be used in reactor-scale applications and it is not suited for use in single-event applications. In this work we will rethink the entire approach to the PDF construction using a Bayesian mindset. This will allow us to provide a different definition of the PDF that allows a much faster calculation of the higher-temperature PDFs and a proper combination of theoretical and experimental PDFs following the probability theory. We will also show that our definition is well suited for single-event applications and we will make an explicit connection between our method and the standard approach. We do this by showing that the central limit theorem applies and our method leads to the same PDF obtained with the standard methodology, for a large number of events per history.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1988

Learning a Probability Distribution Efficiently and Reliably

A new algorithm, called the CDF-Inversion Algorithm, is described. Using it, one can efficiently learn a probability distribution over a finite set to a specified accuracy and confidence. The algorithm can be extended to learn joint distributions over a vector space. Some implementation results are described.

Laird, Philip↗
NASA NTRS1971

Opacity probability distribution functions for electronic systems of CN and C2 molecules including their stellar isotopic forms.

The basis and techniques are presented for generating opacity probability distribution functions for the CN molecule (red and violet systems) and the C2 molecule (Swan, Phillips, Ballik-Ramsay systems), two of the more important diatomic molecules in the spectra of carbon stars, with a view to including these distribution functions in equilibrium model atmosphere calculations. Comparisons to the CO molecule are also shown. T he computation of the monochromatic absorption coefficient uses the most recent molecular data with revision of the oscillator strengths for some of the band systems. The total molecular stellar mass absorption coefficient is established through fifteen equations of molecular dissociation equilibrium to relate the distribution functions to each other on a per gram of stellar material basis.

Querci, F.↗
NASA NTRS1979

The probability distribution of the predicted CFM-induced ozone depletion

It is argued from the central limit theorem that the uncertainty in model predicted changes of the ozone column density is best represented by a normal probability density distribution. This conclusion is validated by comparison with a probability distribution generated by a Monte Carlo technique. In the case of the CFM-induced ozone depletion, and based on the estimated uncertainties in the reaction rate coefficients alone the relative mean standard deviation of this normal distribution is estimated to be 0.29.

Ehhalt, D. H.↗
NASA NTRS2004

Probability Distribution Estimated From the Minimum, Maximum, and Most Likely Values: Applied to Turbine Inlet Temperature Uncertainty

Modern engineering design practices are tending more toward the treatment of design parameters as random variables as opposed to fixed, or deterministic, values. The probabilistic design approach attempts to account for the uncertainty in design parameters by representing them as a distribution of values rather than as a single value. The motivations for this effort include preventing excessive overdesign as well as assessing and assuring reliability, both of which are important for aerospace applications. However, the determination of the probability distribution is a fundamental problem in reliability analysis. A random variable is often defined by the parameters of the theoretical distribution function that gives the best fit to experimental data. In many cases the distribution must be assumed from very limited information or data. Often the types of information that are available or reasonably estimated are the minimum, maximum, and most likely values of the design parameter. For these situations the beta distribution model is very convenient because the parameters that define the distribution can be easily determined from these three pieces of information. Widely used in the field of operations research, the beta model is very flexible and is also useful for estimating the mean and standard deviation of a random variable given only the aforementioned three values. However, an assumption is required to determine the four parameters of the beta distribution from only these three pieces of information (some of the more common distributions, like the normal, lognormal, gamma, and Weibull distributions, have two or three parameters). The conventional method assumes that the standard deviation is a certain fraction of the range. The beta parameters are then determined by solving a set of equations simultaneously. A new method developed in-house at the NASA Glenn Research Center assumes a value for one of the beta shape parameters based on an analogy with the normal distribution (ref.1). This new approach allows for a very simple and direct algebraic solution without restricting the standard deviation. The beta parameters obtained by the new method are comparable to the conventional method (and identical when the distribution is symmetrical). However, the proposed method generally produces a less peaked distribution with a slightly larger standard deviation (up to 7 percent) than the conventional method in cases where the distribution is asymmetric or skewed. The beta distribution model has now been implemented into the Fast Probability Integration (FPI) module used in the NESSUS computer code for probabilistic analyses of structures (ref. 2).

Holland, Frederic A., Jr.↗
NASA NTRS1979

Higher-order skewness and excess coefficients of some probability distributions applicable to optical propagation phenomena

Expressions are derived for higher-order skewness and excess coefficients using central moments and cumulants up to 8th order. These coefficients are then calculated for three probability distributions: (1) Log-normal, (2) Rice-Nakagami, and (3) Gamma distributions. Curves are given to shown the variation of skewness with excess coefficients for these distributions. These curves are independent of the particular distribution parameters. This method is useful for studying fluctuating phenomena, which obey non-Gaussian statistics.

Majumdar, A. K.↗
DOE OSTI2024

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Astronomy & Astrophysics↗
NASA NTRS1992

Caustic-induced features in microlensing magnification probability distributions

Numerical simulations have uncovered a previously unrecognized 'bump' in the macroimage magnification probabilities produced by a planar distribution of point masses. The result could be relevant to cases of microlensing by star fields in single galaxies, for which this lensing geometry is an excellent approximation. The bump is produced by bright pairs of microimages formed by sources lying near the caustics of the lens. The numerically calculated probabilities for the magnifications in the range between 3 and 30 are significantly higher than those given by the asymptotic relation derived by Schneider. The bump present in the two-dimensional lenses appears not to exist in the magnification probability distribution produced by a fully three-dimensional lens.

Rauch, Kevin P.↗
DOE OSTI2025

The Forward Master Equation for the Joint Neutron-Photon Number Probability Distribution

The model is similar to the Binary Fission Model (BFM) in chapter three of the Stochastic Neutronics Primer Volume I, however, we add photons as a product of induced fission events (IFEs). We will find that tracking the population of an additional particle adds an additional layer of complexity because we are now looking for a joint probability distribution.

42 ENGINEERING↗
NASA NTRSDate not supplied

Hopping with an Adaptive Hop Probability Distribution

Monotonic Basin Hopping (MBH) is a stochastic global search technique that may be used to design complex interplanetary trajectories. Previous research on MBH empirically demonstrated that a bi-polar Pareto distribution is an effective way to generate search “hops.” However, no analytical foundation exists to explain this performance. In this work we provide the beginning of that analytical foundation and also introduce a new variant of MBH that uses an adaptive probability distribution to generate the hops. The technique is demonstrated on historical interplanetary trajectory design problems.

A C Englander↗
NASA NTRS1973

Bistatic-radar estimation of surface-slope probability distributions with applications to the moon.

A method for extracting surface-slope frequency distributions from bistatic-radar data has been developed and applied to the lunar surface. Telemetry transmissions from orbiting Apollo spacecraft were received on the earth after reflection from the lunar surface. The echo-frequency spectrum was related analytically to the probability distribution of lunar slopes. Standard regression techniques were used to solve the inverse problem of finding slope distributions from observed echo-frequency spectra. Data taken simultaneously at two wavelengths, 13 and 116 cm, have yielded diverse slope statistics.

Parker, M. N.↗
NASA NTRS2004

Use of Probability Distribution Functions for Discriminating Between Cloud and Aerosol in Lidar Backscatter Data

In this paper we describe the algorithm hat will be used during the upcoming Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) mission for discriminating between clouds and aerosols detected in two wavelength backscatter lidar profiles. We first analyze single-test and multiple-test classification approaches based on one-dimensional and multiple-dimensional probability density functions (PDFs) in the context of a two-class feature identification scheme. From these studies we derive an operational algorithm based on a set of 3-dimensional probability distribution functions characteristic of clouds and aerosols. A dataset acquired by the Cloud Physics Lidar (CPL) is used to test the algorithm. Comparisons are conducted between the CALIPSO algorithm results and the CPL data product. The results obtained show generally good agreement between the two methods. However, of a total of 228,264 layers analyzed, approximately 5.7% are classified as different types by the CALIPSO and CPL algorithm. This disparity is shown to be due largely to the misclassification of clouds as aerosols by the CPL algorithm. The use of 3-dimensional PDFs in the CALIPSO algorithm is found to significantly reduce this type of error. Dust presents a special case. Because the intrinsic scattering properties of dust layers can be very similar to those of clouds, additional algorithm testing was performed using an optically dense layer of Saharan dust measured during the Lidar In-space Technology Experiment (LITE). In general, the method is shown to distinguish reliably between dust layers and clouds. The relatively few erroneous classifications occurred most often in the LITE data, in those regions of the Saharan dust layer where the optical thickness was the highest.

Liu, Zhaoyan↗
NASA NTRS1993

Development and application of an empirical probability distribution for the prediction error of re-entry body maximum dynamic pressure

The relationship between actual and predicted re-entry maximum dynamic pressure is characterized using a probability density function and a cumulative distribution function derived from sounding rocket flight data. This paper explores the properties of this distribution and demonstrates applications of this data with observed sounding rocket re-entry body damage characteristics to assess probabilities of sustaining various levels of heating damage. The results from this paper effectively bridge the gap existing in sounding rocket reentry analysis between the known damage level/flight environment relationships and the predicted flight environment.

Lanzi, R. James↗
NASA NTRS1980

An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Laboratory experiments were performed to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data along with some limited field data were compared. The statistical properties of the surface elevation were processed for comparison with the results derived from the Longuet-Higgins (1963) theory. It is found that, even for the highly non-Gaussian cases, the distribution function proposed by Longuet-Higgins still gives good approximations.

Huang, N. E.↗
DOE OSTI2021

Examination of probability distribution of mixture fraction in LES/FDF modelling of a turbulent partially premixed jet flame

An accurate prediction of the probability density function (PDF) of the mixture fraction is crucial to the prediction of combustion since mixing plays an important role in turbulent non-premixed and partially premixed flames. This work provides an assessment of the large-eddy simulation (LES)/filtered density function (FDF) method for the prediction of the PDF of the mixture fraction. The advantage of the LES/FDF method is that it provides the full predictions of the statistical distribution of scalars including the mixture fraction. The predictive accuracy of the method for the PDF is yet to be fully validated. Assessing the prediction of the PDF of the mixture fraction, a conserved scalar, is an important starting point. The Sydney/Sandia inhomogeneous inlet jet flame is used as a test case. A quick comparison shows that the LES/FDF predicted PDF shapes of the mixture fraction deviate significantly from the commonly presumed Beta-PDF as well as from the experimental data in the flame. Here, to examine the source of the discrepancy, we clarify the different PDF definitions used in the comparison among the predictions, measurements, and the presumed shape PDFs. The discrepancy observed from the comparison is largely reconciled by clarifying the difference between the PDFs that are examined. The PDF of the resolved mixture fraction is shown to be close to the Beta-PDF in both the measurements and predictions, while the PDF directly deduced from the LES/FDF particles deviates significantly from the Beta-PDF. A multimodal PDF analysis and a pseudo convergence analysis are conducted to provide plausible evidence to support the predicted multimodal PDF shapes. The sub-filter scale FDF is shown to be close to the Beta-PDF too through the construction of a synthesized PDF, which supports the common presumed Beta-PDF assumption used in the presumed PDF methods when combined with LES.

42 ENGINEERING↗