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.↗
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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)↗
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.↗
Probabilistic Modeling of the Renal Stone Formation Module
The Integrated Medical Model (IMM) is a probabilistic tool, used in mission planning decision making and medical systems risk assessments. The IMM project maintains a database of over 80 medical conditions that could occur during a spaceflight, documenting an incidence rate and end case scenarios for each. In some cases, where observational data are insufficient to adequately define the inflight medical risk, the IMM utilizes external probabilistic modules to model and estimate the event likelihoods. One such medical event of interest is an unpassed renal stone. Due to a high salt diet and high concentrations of calcium in the blood (due to bone depletion caused by unloading in the microgravity environment) astronauts are at a considerable elevated risk for developing renal calculi (nephrolithiasis) while in space. Lack of observed incidences of nephrolithiasis has led HRP to initiate the development of the Renal Stone Formation Module (RSFM) to create a probabilistic simulator capable of estimating the likelihood of symptomatic renal stone presentation in astronauts on exploration missions. The model consists of two major parts. The first is the probabilistic component, which utilizes probability distributions to assess the range of urine electrolyte parameters and a multivariate regression to transform estimated crystal density and size distributions to the likelihood of the presentation of nephrolithiasis symptoms. The second is a deterministic physical and chemical model of renal stone growth in the kidney developed by Kassemi et al. The probabilistic component of the renal stone model couples the input probability distributions describing the urine chemistry, astronaut physiology, and system parameters with the physical and chemical outputs and inputs to the deterministic stone growth model. These two parts of the model are necessary to capture the uncertainty in the likelihood estimate. The model will be driven by Monte Carlo simulations, continuously randomly sampling the probability distributions of the electrolyte concentrations and system parameters that are inputs into the deterministic model. The total urine chemistry concentrations are used to determine the urine chemistry activity using the Joint Expert Speciation System (JESS), a biochemistry model. Information used from JESS is then fed into the deterministic growth model. Outputs from JESS and the deterministic model are passed back to the probabilistic model where a multivariate regression is used to assess the likelihood of a stone forming and the likelihood of a stone requiring clinical intervention. The parameters used to determine to quantify these risks include: relative supersaturation (RS) of calcium oxalate, citrate/calcium ratio, crystal number density, total urine volume, pH, magnesium excretion, maximum stone width, and ureteral location. Methods and Validation: The RSFM is designed to perform a Monte Carlo simulation to generate probability distributions of clinically significant renal stones, as well as provide an associated uncertainty in the estimate. Initially, early versions will be used to test integration of the components and assess component validation and verification (V&V), with later versions used to address questions regarding design reference mission scenarios. Once integrated with the deterministic component, the credibility assessment of the integrated model will follow NASA STD 7009 requirements.
kidney stones↗
Pseudorandom noise for telemetry error rate measurement applications and limitations.
A pseudorandom noise (PRN) generator functional design has been developed which is superior to the commercially available instrument in usable bandwidth and in the closeness of fit to the gaussian probability distribution in the 'tails' of the curve. The principal disadvantage of PRN sources for bit error rate (BER) measurements is that the probability distribution is truncated in the tails. This truncation of the probability distribution results in a similar truncation of the BER curve - i.e., there is a minimum BER which can be measured, below which the only possible result is zero. The minimum nonzero BER actually computed with the PRN source developed was 0.00001 with a pseudorandom sequence of 131,071 bits. It is theoretically possible, with a longer sequence, to achieve a minimum BER of 0.000001 with the same design.
Hopkins, P. M.↗
Bivariate extreme value distributions
In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.
Elshamy, M.↗
Experimental probability density distributions for optical and infrared cross-beam units
A series of cross beam experiments for measuring meteorological parameters was conducted. Both optical and infrared sensors were tested for comparison. The test configuration and experiment identification are provided. A data report is presented for an approximate analysis of the probability density distributions of the signals from both the optical and the infared units. Two runs representing each of the two types of cross-beam units were selected for analysis. Probability density functions are also presented for the instantaneous product of the signals for each of the runs.
Huff, L. L.↗
Gravitational lensing, time delay, and gamma-ray bursts
The probability distributions of time delay in gravitational lensing by point masses and isolated galaxies (modeled as singular isothermal spheres) are studied. For point lenses (all with the same mass) the probability distribution is broad, and with a peak at delta(t) of about 50 S; for singular isothermal spheres, the probability distribution is a rapidly decreasing function with increasing time delay, with a median delta(t) equals about 1/h month, and its behavior depends sensitively on the luminosity function of galaxies. The present simplified calculation is particularly relevant to the gamma-ray bursts if they are of cosmological origin. The frequency of 'recurrent' bursts due to gravitational lensing by galaxies is probably between 0.05 and 0.4 percent. Gravitational lensing can be used as a test of the cosmological origin of gamma-ray bursts.
Mao, Shude↗
Measurements of the stochastic nature of atmospheric spectral amplitudes
The stochastic nature of the power spectral amplitudes of the neutral atmospheric boundary layer is examined. Probability density distributions and probability distributions of longitudinal and lateral power spectra amplitudes are computed from neutral atmospheric boundary layers. The statistical distributions are computed for frequencies of 0.006, 0.01, 0.03, 0.06, 0.1, and 0.5 Hz at each of the elevations of 18, 30, 60, 90, 120, and 150 m. When the probability density distributions are properly nondimensionalized, the data tend to collapse to a universal curve. An empirical curve fit to the universal nondimensionalized probability density distribution is also given. Probability distributions of individual frequency power spectral amplitudes are also presented for all elevations and frequencies. An interesting observation from the data is that greater than 10 percent of the time the power spectral amplitude at a given frequency will genrally be more than three times the temporal mean value computed by standard Fourier techniques. The standard power spectral density curves are also included in the report.
Cliff, W. C.↗