Approximating Density Probability Distribution Functions Across Cosmologies
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Huanqing Chen↗
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.
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Probability Distribution Functions of the Number of Scattering Collisions in Electron Slowing Down.
Abstract not provided.
Franke, Brian C.↗
Develop a Tolerance System for the CODE V Monte Carlo Tolerancing Module that Uses Manufacturing Data as Input for the Required Probability Distribution Functions
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97 MATHEMATICS AND COMPUTING↗
Mapping variations of redshift distributions with probability integral transforms
We present a method for mapping variations between probability distribution functions and apply this method within the context of measuring galaxy redshift distributions from imaging survey data. This method, which we name PITPZ for the probability integral transformations it relies on, uses a difference in curves between distribution functions in an ensemble as a transformation to apply to another distribution function, thus transferring the variation in the ensemble to the latter distribution function. This procedure is broadly applicable to the problem of uncertainty propagation. In the context of redshift distributions, for example, the uncertainty contribution due to certain effects can be studied effectively only in simulations, thus necessitating a transfer of variation measured in simulations to the redshift distributions measured from data. We illustrate the use of PITPZ by using the method to propagate photometric calibration uncertainty to redshift distributions of the Dark Energy Survey Year 3 weak lensing source galaxies. For this test case, we find that PITPZ yields a lensing amplitude uncertainty estimate due to photometric calibration error within 1 per cent of the truth, compared to as much as a 30 per cent underestimate when using traditional methods.
79 ASTRONOMY AND ASTROPHYSICS↗
Study of nonparametric techniques for estimating reliability and other life quality parameters Final report
Nonparametric techniques for probability distribution, probability density, and hazard function estimates for life quality
Murthy, V. K.↗
Bounds on galaxy stochasticity from halo occupation distribution modeling
The joint probability distribution of matter overdensity and galaxy counts in cells is a powerful probe of cosmology, and the extent to which variance in galaxy counts at fixed matter density deviates from Poisson shot noise is not fully understood. The lack of informed bounds on this stochasticity is currently the limiting factor in constraining cosmology with the galaxy–matter probability distribution function (PDF). We investigate stochasticity in the conditional distribution of galaxy counts along lines of sight with fixed matter density, and we present a halo occupation distribution (HOD)-based approach for obtaining plausible ranges for stochasticity parameters. To probe the high-dimensional space of possible galaxy–matter connections, we derive a set of HODs that conserve the galaxies’ linear bias and number density to produce RED M A G I C-like galaxy catalogs within the A BACUS S UMMIT suite of N -body simulations. We study the impact of individual HOD parameters and cosmology on stochasticity and perform a Monte Carlo search in HOD parameter space subject to the constraints on bias and density. In mock catalogs generated by the selected HODs, shot noise in galaxy counts spans both sub-Poisson and super-Poisson values, ranging from 80% to 133% of Poisson variance for cells with mean matter density. Nearly all of the derived HODs show a positive relationship between local matter density and stochasticity. For galaxy catalogs with higher stochasticity, modeling galaxy bias to second order is required for an accurate description of the conditional PDF of galaxy counts at fixed matter density. The presence of galaxy assembly bias also substantially extends the range of stochasticity in the super-Poisson direction. This HOD-based approach leverages degrees of freedom in the galaxy–halo connection to obtain informed bounds on nuisance model parameters and can be adapted to study other parametrizations of shot noise in galaxy counts, in particular to motivate prior ranges on stochasticity for cosmological analyses.
Britt, Dylan (ORCID:000000019905601X)↗
Mesh objective stochastic simulations of quasibrittle fracture
Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. Here this issue has been addressed for deterministic analysis through the development of localization limiters. Here this study proposes a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The interest is placed on the analysis of large-size structures, where the mesh size is conveniently chosen to be larger than the width of the fracture process zone as well as the correlation length of the random fields of constitutive properties. The present model is formulated within the framework of continuum damage mechanics. Two localization parameters are introduced to describe the evolution of the damage pattern of each finite element. These parameters are used to guide the energy regularization of the constitutive law, as well as to formulate the mesh-dependent probability distributions of constitutive properties. Depending on the prevailing damage pattern, different energy regularization schemes and mesh dependence of the probability distribution functions are used in the constitutive law. The model is applied to simulate the stochastic failure behavior of quasibrittle structures of different geometries featuring different failure processes including damage initiation, localization, and propagation. It is shown that using fixed probability distribution functions of constitutive properties could lead to strong mesh dependence of the prediction of the mean and variance of the structural load capacity. The probability distribution functions of constitutive properties must be linked to the damage pattern, which may evolve during the failure process. Such a mechanism-based modeling of the probability distributions of constitutive properties is essential for mitigating the spurious mesh sensitivity in stochastic FE analysis of quasibrittle fracture.
42 ENGINEERING↗
An efficient method to estimate the probability density of seismic Green's functions
We present a computationally efficient method to approximate the probability distribution of seismic Green's functions given the uncertainty of an Earth model. The method is based on the Karhunen-Loève (KL) theorem and an approximation of the Green's function (or seismogram) covariance. Using Monte Carlo (MC) simulations as a control case, we demonstrate that our KL-based method can accurately reproduce a probability distribution of seismograms that results from an uncertain Earth model for a MC-derived seismogram covariance. We then describe a method to estimate the covariance of the seismograms resulting from those Earth models that is not based on MC simulations. We use the estimated Green's function covariance in conjunction with our KL-based method to produce a Green's function probability distribution, and compare that distribution to a Green's function probability distribution produced using a MC finite difference method. We find that the Green's function probability distribution approximated using our KL-based method generally mimics that produced using the MC simulations, especially for direct-arriving body waves. However the accuracy of the KL-based method generally decreases for later times in the simulated Green's function distribution.
58 GEOSCIENCES↗
Statistical analysis of mesoscale rainfall: Dependence of a random cascade generator on large-scale forcing
Under the theory of independent and identically distributed random cascades, the probability distribution of the cascade generator determines the spatial and the ensemble properties of spatial rainfall. Three sets of radar-derived rainfall data in space and time are analyzed to estimate the probability distribution of the generator. A detailed comparison between instantaneous scans of spatial rainfall and simulated cascades using the scaling properties of the marginal moments is carried out. This comparison highlights important similarities and differences between the data and the random cascade theory. Differences are quantified and measured for the three datasets. Evidence is presented to show that the scaling properties of the rainfall can be captured to the first order by a random cascade with a single parameter. The dependence of this parameter on forcing by the large-scale meteorological conditions, as measured by the large-scale spatial average rain rate, is investigated for these three datasets. The data show that this dependence can be captured by a one-to-one function. Since the large-scale average rain rate can be diagnosed from the large-scale dynamics, this relationship demonstrates an important linkage between the large-scale atmospheric dynamics and the statistical cascade theory of mesoscale rainfall. Potential application of this research to parameterization of runoff from the land surface and regional flood frequency analysis is briefly discussed, and open problems for further research are presented.
Over, Thomas, M.↗
Summary report of the Turbulence Committee
The effects of atmospheric turbulence are discussed. Aircraft design and aircraft operations are reviewed. Turbulence in terms of intensity and scale in design considerations was examined. Turbulence models were used in the form of discrete gusts, spectral distributions, and probability distributions. Various aspects of the design and operations problems, simulation and training factors of pilots, and weather services and forecasts are reported.
Elderkin, C. E.↗
A non-homogeneous Markov model for phased-mission reliability analysis
Three assumptions of Markov modeling for reliability of phased-mission systems that limit flexibility of representation are identified. The proposed generalization has the ability to represent state-dependent behavior, handle phases of random duration using globally time-dependent distributions of phase change time, and model globally time-dependent failure and repair rates. The approach is based on a single nonhomogeneous Markov model in which the concept of state transition is extended to include globally time-dependent phase changes. Phase change times are specified using nonoverlapping distributions with probability distribution functions that are zero outside assigned time intervals; the time intervals are ordered according to the phases. A comparison between a numerical solution of the model and simulation demonstrates that the numerical solution can be several times faster than simulation.
Smotherman, Mark↗
Unit-Sphere Anisotropic Multiaxial Stochastic-Strength Model Probability Density Distribution for the Orientation of Critical Flaws
Models that predict the failure probability of monolithic glass and ceramic components under multiaxial loading have been developed by authors such as Batdorf, Evans, and Matsuo. These "unit-sphere" failure models assume that the strength-controlling flaws are randomly oriented, noninteracting planar microcracks of specified geometry but of variable size. This report develops a formulation to describe the probability density distribution of the orientation of critical strength-controlling flaws that results from an applied load. This distribution is a function of the multiaxial stress state, the shear sensitivity of the flaws, the Weibull modulus, and the strength anisotropy. Examples are provided showing the predicted response on the unit sphere for various stress states for isotropic and transversely isotropic (anisotropic) materials--including the most probable orientation of critical flaws for offset uniaxial loads with strength anisotropy. The author anticipates that this information could be used to determine anisotropic stiffness degradation or anisotropic damage evolution for individual brittle (or quasi-brittle) composite material constituents within finite element or micromechanics-based software
Nemeth, Noel↗
Probabilistic Reasoning for Robustness in Automated Planning
A general-purpose computer program for planning the actions of a spacecraft or other complex system has been augmented by incorporating a subprogram that reasons about uncertainties in such continuous variables as times taken to perform tasks and amounts of resources to be consumed. This subprogram computes parametric probability distributions for time and resource variables on the basis of user-supplied models of actions and resources that they consume. The current system accepts bounded Gaussian distributions over action duration and resource use. The distributions are then combined during planning to determine the net probability distribution of each resource at any time point. In addition to a full combinatoric approach, several approximations for arriving at these combined distributions are available, including maximum-likelihood and pessimistic algorithms. Each such probability distribution can then be integrated to obtain a probability that execution of the plan under consideration would violate any constraints on the resource. The key idea is to use these probabilities of conflict to score potential plans and drive a search toward planning low-risk actions. An output plan provides a balance between the user s specified averseness to risk and other measures of optimality.
Schaffer, Steven↗
Path-length distributions of photons diffusely reflected from a semi-infinite atmosphere.
Knowledge of the probability distribution of photon path lengths for diffuse reflection in the continuum from a planetary atmosphere greatly simplifies computation of the shape and strength of absorption lines formed under conditions of multiple scattering. Graphs of this probability distribution are presented for diffuse reflection from a semiinfinite conservative atmosphere for both isotropic and forward-directed scattering, and for several angles of incidence and reflection. Graphs showing distributions for the case of absorption in the continuum are also discussed. The distributions are obtained from an analytic expression for the path-length distribution for nth-order scattering and a tabulation of nth-order intensities. It is found that te shape of the probability distribution depends markedly on the degree of forward scattering due to the phase function. The results are compared with those obtained by a Monte Carlo computation of the sort which might be used if tabulated nth-order intensities were not available.
Appleby, J. F.↗
Notes on SAW Tag Interrogation Techniques
We consider the problem of interrogating a single SAW RFID tag with a known ID and known range in the presence of multiple interfering tags under the following assumptions: (1) The RF propagation environment is well approximated as a simple delay channel with geometric power-decay constant alpha >/= 2. (2) The interfering tag IDs are unknown but well approximated as independent, identically distributed random samples from a probability distribution of tag ID waveforms with known second-order properties, and the tag of interest is drawn independently from the same distribution. (3) The ranges of the interfering tags are unknown but well approximated as independent, identically distributed realizations of a random variable rho with a known probability distribution f(sub rho) , and the tag ranges are independent of the tag ID waveforms. In particular, we model the tag waveforms as random impulse responses from a wide-sense-stationary, uncorrelated-scattering (WSSUS) fading channel with known bandwidth and scattering function. A brief discussion of the properties of such channels and the notation used to describe them in this document is given in the Appendix. Under these assumptions, we derive the expression for the output signal-to-noise ratio (SNR) for an arbitrary combination of transmitted interrogation signal and linear receiver filter. Based on this expression, we derive the optimal interrogator configuration (i.e., transmitted signal/receiver filter combination) in the two extreme noise/interference regimes, i.e., noise-limited and interference-limited, under the additional assumption that the coherence bandwidth of the tags is much smaller than the total tag bandwidth. Finally, we evaluate the performance of both optimal interrogators over a broad range of operating scenarios using both numerical simulation based on the assumed model and Monte Carlo simulation based on a small sample of measured tag waveforms. The performance evaluation results not only provide guidelines for proper interrogator design, but also provide some insight on the validity of the assumed signal model. It should be noted that the assumption that the impulse response of the tag of interest is known precisely implies that the temperature and range of the tag are also known precisely, which is generally not the case in practice. However, analyzing interrogator performance under this simplifying assumption is much more straightforward and still provides a great deal of insight into the nature of the problem.
Barton, Richard J.↗
Distributed errors in orbit transfer.
Probability distribution errors effect in linear and planar impulse orbital transfers, considering angular orientation and impulsive velocity
IMPULSE ORBITAL TRANSFER↗
The application of structural reliability techniques to plume impingement loading of the Space Station Freedom Photovoltaic Array
A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design, during its 15 year life, is minute.
Yunis, Isam S.↗
The Application of Structural Reliability Techniques to Plume Impingement Loading of the Space Station Freedom Photovoltaic Array
A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design, during its 15 year life, is minute.
Yunis, Isam S.↗