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NASA NTRS1994

Data Analysis with Graphical Models: Software Tools

Probabilistic graphical models (directed and undirected Markov fields, and combined in chain graphs) are used widely in expert systems, image processing and other areas as a framework for representing and reasoning with probabilities. They come with corresponding algorithms for performing probabilistic inference. This paper discusses an extension to these models by Spiegelhalter and Gilks, plates, used to graphically model the notion of a sample. This offers a graphical specification language for representing data analysis problems. When combined with general methods for statistical inference, this also offers a unifying framework for prototyping and/or generating data analysis algorithms from graphical specifications. This paper outlines the framework and then presents some basic tools for the task: a graphical version of the Pitman-Koopman Theorem for the exponential family, problem decomposition, and the calculation of exact Bayes factors. Other tools already developed, such as automatic differentiation, Gibbs sampling, and use of the EM algorithm, make this a broad basis for the generation of data analysis software.

Buntine, Wray L.↗
NASA NTRS2000

Theoretical Study of Indium Compounds of Interest for Organometallic Chemical Vapor Deposition

The structural. electronic and therinochemical properties of indium compounds which are of interest in halide transport and organometallic chemical vapor deposition processes have been studied by ab initio and statistical mechanics methods. The compounds reported include: indium halides and hydrides (InF, InCl, InCl3, InH, InH2, InH3); indium clusters (In2, In3); methylindium, dimethylindium, and their hydrogen derivatives [In(CH3), In(CH3)H, In(CH3)H2, In(CH3)2, In(CH3)2H]; dimethyl-indium dimer [In2(CH3)4], trimethyl-indium [In(CH3)3]; dehydrogenated methyl, dimethyl and trimethylindium [In(CH3)2CH2, In(CH3)CH2, In(CH2)], trimethylindium adducts with ammonia, trimethylamine and hydrazine [(CH3)3In:NH3, (CH3)3In:N(CH3)3, (CH3)3In:N(H2)N(H2)]; dimethylamino-indium and methylimino-indium [In(CH3)2(NH2), In(CH3)(NH)]; indium nitride and indium nitride dimer (InN, In2N2), indium phosphide, arsenide and antimonide ([InP, InAs, InSb). The predicted electronic properties are based on density functional theory calculations; the calculated thermodynamic properties are reported following the format of the JANAF (Joint Army, Navy, NASA, Air Force) Tables. Equilibrium compositions at two temperatures (298 and 1000 K) have been analyzed for groups of competing simultaneous reactions.

Cardelino, B. H.↗
NASA NTRS2002

Effect of Random Geometric Uncertainty on the Computational Design of a 3-D Flexible Wing

The effect of geometric uncertainty due to statistically independent, random, normally distributed shape parameters is demonstrated in the computational design of a 3-D flexible wing. A first-order second-moment statistical approximation method is used to propagate the assumed input uncertainty through coupled Euler CFD aerodynamic / finite element structural codes for both analysis and sensitivity analysis. First-order sensitivity derivatives obtained by automatic differentiation are used in the input uncertainty propagation. These propagated uncertainties are then used to perform a robust design of a simple 3-D flexible wing at supercritical flow conditions. The effect of the random input uncertainties is shown by comparison with conventional deterministic design results. Sample results are shown for wing planform, airfoil section, and structural sizing variables.

Gumbert, C. R.↗
NASA NTRS1957

Study of the Micro-Nonuniformity of the Plastic Deformation of Steel

The plastic flow during deformation of real polycrystalline metals has specific characteristics which distinguish the plastic deformation of metals from the deformation of ordinary isotropic bodies. One of these characteristics is the marked micro-nonuniformity of the plastic deformation of metals. P.O. Pashkov demonstrated the presence of a considerable micro-nonuniformity of the plastic deformation of coarse-grained steel wit medium or low carbon content. Analogous results in the case of tension of coarse-grained aluminum were obtained by W. Boas, who paid particular attention to the role of the grain boundaries in plastic flow. The nonuniformit of the plastic deformation in microvolumes was also recorded by T.N. Gudkova and others, on the alloy KhN80T. N.F. Lashko pointed out the nonuniformity of the plastic deformation for a series of pure polycrystalline metals and one-phase alloys. In his later reports, P.O. Pashkov arrives at he conclusion that the nonuniformity of the distribution of the deformation along the individual grains has a significant effect on the strength and plastic characteristics of polycrystalline metals in the process of plastic flow. However, until now there has not existed any systematic investigation of the general rules of the microscopic nonuniformit of plastic deformation even though the real polycrystalline metals are extremely simple with regard to structure. In the present report, an attempt is made to study the micrononuniformity of the flow of polycrystalline metals by the method of statistical analysis of the variation of the frequency diagrams of the nonuniformity of the grains in the process of plastic deformation.

Chechulin, B. B.↗
NASA NTRS2004

Employing Sensitivity Derivatives for Robust Optimization under Uncertainty in CFD

A robust optimization is demonstrated on a two-dimensional inviscid airfoil problem in subsonic flow. Given uncertainties in statistically independent, random, normally distributed flow parameters (input variables), an approximate first-order statistical moment method is employed to represent the Computational Fluid Dynamics (CFD) code outputs as expected values with variances. These output quantities are used to form the objective function and constraints. The constraints are cast in probabilistic terms; that is, the probability that a constraint is satisfied is greater than or equal to some desired target probability. Gradient-based robust optimization of this stochastic problem is accomplished through use of both first and second-order sensitivity derivatives. For each robust optimization, the effect of increasing both input standard deviations and target probability of constraint satisfaction are demonstrated. This method provides a means for incorporating uncertainty when considering small deviations from input mean values.

Newman, Perry A.↗
NASA NTRS2006

Does The Nile Reflect Solar Variability?

Historical records of the Nile water level provide a unique opportunity to investigate the possibility that solar variability influences the Earth's climate. Particularly important are the annual records of the water level, which are uninterrupted for the years 622-1470 A.D. These records are non-stationary, so that standard spectral analyses cannot adequately characterize them. Here the Empirical Mode Decomposition technique, which is designed to deal with nonstationary, nonlinear time series, becomes useful. It allows the identification of two characteristic time scales in the water level data that can be linked to solar variability: the 88 year period and a time scale of about 200 years. These time scales are also present in the concurrent aurora data. Auroras are driven by coronal mass ejections and the rate of auroras is an excellent proxy for solar variability. Analysis of auroral data contemporaneous with the Nile data shows peaks at 88 years and about 200 years. This suggests a physical link between solar variability and the low frequency variations of the Nile water level. The link involves the influence of solar variability on the North Annual Mode of atmospheric variability and its North Atlantic and Indian Oceans patterns that affect rainfall over Eastern Equatorial Africa where the Nile originates.

statistical methods↗
NASA NTRS2007

SEM-EDS Analyses of Small Craters in Stardust Aluminum Foils: Implications for the Wild-2 Dust Distribution

Aluminium foils were used on Stardust to stabilize the aerogel specimens in the modular collector tray. Part of these foils were fully exposed to the flux of cometary grains emanating from Wild 2. Because the exposed part of these foils had to be harvested before extraction of the aerogel, numerous foil strips some 1.7 mm wide and 13 or 33 mm long were generated during Stardusts's Preliminary Examination (PE). These strips are readily accommodated in their entirety in the sample chambers of modern SEMs, thus providing the opportunity to characterize in situ the size distribution and residue composition - employing EDS methods - of statistically more significant numbers of cometary dust particles compared to aerogel, the latter mandating extensive sample preparation. We describe here the analysis of nearly 300 impact craters and their implications for Wild 2 dust.

Borg, J.↗
NASA NTRS2007

Applicability of a Conservative Margin Approach for Assessing NDE Flaw Detectability

Nondestructive Evaluation (NDE) procedures are required to detect flaws in structures with a high percentage detectability and high confidence. Conventional Probability of Detection (POD) methods are statistical in nature and require detection data from a relatively large number of flaw specimens. In many circumstances, due to the high cost and long lead time, it is impractical to build the large set of flaw specimens that is required by the conventional POD methodology. Therefore, in such situations it is desirable to have a flaw detectability estimation approach that allows for a reduced number of flaw specimens but provides a high degree of confidence in establishing the flaw detectability size. This paper presents an alternative approach called the conservative margin approach (CMA). To investigate the applicability of the CMA approach, flaw detectability sizes determined by the CMA and POD approaches have been compared on actual datasets. The results of these comparisons are presented and the applicability of the CMA approach is discussed.

Koshti, ajay M.↗
NASA NTRS2007

Automated Simulation Updates based on Flight Data

A statistically-based method for using flight data to update aerodynamic data tables used in flight simulators is explained and demonstrated. A simplified wind-tunnel aerodynamic database for the F/A-18 aircraft is used as a starting point. Flight data from the NASA F-18 High Alpha Research Vehicle (HARV) is then used to update the data tables so that the resulting aerodynamic model characterizes the aerodynamics of the F-18 HARV. Prediction cases are used to show the effectiveness of the automated method, which requires no ad hoc adjustments by the analyst.

Morelli, Eugene A.↗
NASA NTRS2005

Bayesian Analysis of the Power Spectrum of the Cosmic Microwave Background

There is a wealth of cosmological information encoded in the spatial power spectrum of temperature anisotropies of the cosmic microwave background. The sky, when viewed in the microwave, is very uniform, with a nearly perfect blackbody spectrum at 2.7 degrees. Very small amplitude brightness fluctuations (to one part in a million!!) trace small density perturbations in the early universe (roughly 300,000 years after the Big Bang), which later grow through gravitational instability to the large-scale structure seen in redshift surveys... In this talk, I will discuss a Bayesian formulation of this problem; discuss a Gibbs sampling approach to numerically sampling from the Bayesian posterior, and the application of this approach to the first-year data from the Wilkinson Microwave Anisotropy Probe. I will also comment on recent algorithmic developments for this approach to be tractable for the even more massive data set to be returned from the Planck satellite.

Bayesian inference↗
NASA NTRS2010

Vibration Response Predictions for Heavy Panel Mounted Components from Panel Acreage Environment Specifications

The development of new launch vehicles in the Aerospace industry often relies on response measurements taken from previously developed vehicles during various stages of liftoff and ascent, and from wind tunnel models. These measurements include sound pressure levels, dynamic pressures in turbulent boundary layers and accelerations. Rigorous statistical scaling methods are applied to the data to derive new environments and estimate the performance of new skin panel structures. Scaling methods have proven to be reliable, particularly for designs similar to the vehicles used as the basis for scaling, and especially in regions of smooth acreage without exterior protuberances or heavy components mounted to the panel. To account for response attenuation of a panel-mounted component due to its apparent mass at higher frequencies, the vibroacoustics engineer often reduces the acreage vibration according to a weight ratio first suggested by Barrett. The accuracy of the reduction is reduced with increased weight of the panel-mounted component, and does not account for low-frequency amplification of the component/panel response as a system. A method is proposed that combines acreage vibration from scaling methods with finite element analysis to account for the frequency-dependent dynamics of heavy panel-mounted components. Since the acreage and mass-loaded skins respond to the same dynamic input pressure, such pressure may be eliminated in favor of a frequency-dependent scaling function applied to the acreage vibration to predict the mass-loaded panel response. The scaling function replaces the Barrett weight ratio, and contains all of the dynamic character of the loaded and unloaded skin panels. The solution simplifies for spatially uncorrelated and fully correlated input pressures. Since the prediction uses finite element models of the loaded and unloaded skins, a rich suite of response data are available to the design engineer, including interface forces, stress and strain, as well as acceleration and displacement. An extension of the method is also developed to incorporate the effect of a local protuberance near a heavy component. Acreage environments from traditional scaling methods with and without protuberance effects serve as the basis for the extension. Authors:

Harrison, Phillip↗
NASA NTRS2004

The Elegance of Disordered Granular Packings: A Validation of Edwards' Hypothesis

We have found a way to analyze Edwards' density of states for static granular packings in the special case of round, rigid, frictionless grains assuming constant coordination number. It obtains the most entropic density of single grain states, which predicts several observables including the distribution of contact forces. We compare these results against empirical data obtained in dynamic simulations of granular packings. The agreement between theory and the empirics is quite good, helping validate the use of statistical mechanics methods in granular physics. The differences between theory and empirics are mainly due to the variable coordination number, and when the empirical data are sorted by that number we obtain several insights that suggest an underlying elegance in the density of states

Metzger, Philip T.↗
NASA NTRS2011

Applications of the BIOPHYS Algorithm for Physically-Based Retrieval of Biophysical, Structural and Forest Disturbance Information

Canopy reflectance model inversion using look-up table approaches provides powerful and flexible options for deriving improved forest biophysical structural information (BSI) compared with traditional statistical empirical methods. The BIOPHYS algorithm is an improved, physically-based inversion approach for deriving BSI for independent use and validation and for monitoring, inventory and quantifying forest disturbance as well as input to ecosystem, climate and carbon models. Based on the multiple-forward mode (MFM) inversion approach, BIOPHYS results were summarized from different studies (Minnesota/NASA COVER; Virginia/LEDAPS; Saskatchewan/BOREAS), sensors (airborne MMR; Landsat; MODIS) and models (GeoSail; GOMS). Applications output included forest density, height, crown dimension, branch and green leaf area, canopy cover, disturbance estimates based on multi-temporal chronosequences, and structural change following recovery from forest fires over the last century. Good correspondences with validation field data were obtained. Integrated analyses of multiple solar and view angle imagery further improved retrievals compared with single pass data. Quantifying ecosystem dynamics such as the area and percent of forest disturbance, early regrowth and succession provide essential inputs to process-driven models of carbon flux. BIOPHYS is well suited for large-area, multi-temporal applications involving multiple image sets and mosaics for assessing vegetation disturbance and quantifying biophysical structural dynamics and change. It is also suitable for integration with forest inventory, monitoring, updating, and other programs.

Peddle, Derek R.↗
NASA NTRS2014

Satellite Sounder Data Assimilation for Improving Alaska Region Weather Forecast

Data assimilation has been demonstrated very useful in improving both global and regional numerical weather prediction. Alaska has very coarser surface observation sites. On the other hand, it gets much more satellite overpass than lower 48 states. How to utilize satellite data to improve numerical prediction is one of hot topics among weather forecast community in Alaska. The Geographic Information Network of Alaska (GINA) at University of Alaska is conducting study on satellite data assimilation for WRF model. AIRS/CRIS sounder profile data are used to assimilate the initial condition for the customized regional WRF model (GINA-WRF model). Normalized standard deviation, RMSE, and correlation statistic analysis methods are applied to analyze one case of 48 hours forecasts and one month of 24-hour forecasts in order to evaluate the improvement of regional numerical model from Data assimilation. The final goal of the research is to provide improved real-time short-time forecast for Alaska regions.

Zhu, Jiang↗
NASA NTRS2014

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability↗
NASA NTRS2014

Assume-Guarantee Abstraction Refinement Meets Hybrid Systems

Compositional verification techniques in the assume- guarantee style have been successfully applied to transition systems to efficiently reduce the search space by leveraging the compositional nature of the systems under consideration. We adapt these techniques to the domain of hybrid systems with affine dynamics. To build assumptions we introduce an abstraction based on location merging. We integrate the assume-guarantee style analysis with automatic abstraction refinement. We have implemented our approach in the symbolic hybrid model checker SpaceEx. The evaluation shows its practical potential. To the best of our knowledge, this is the first work combining assume-guarantee reasoning with automatic abstraction-refinement in the context of hybrid automata.

Reliability↗
NASA NTRS1973

Use of Polarization Lidar for Investigation of Meteorological Formations

This paper presents the results of theoretical and experimental, investigations of depolarization characteristics of different meteorological formations. Experimental investigations are carried out with a monostatic lidar. The ruby laser radiation is polarized in a vertical plane. The radiation reflected is accepted by a lens system of 150 rom in diameter and a viewing angle of 12' and further it is divided by Wollaston prism into the components polarized orthogonally. In this case the principal plane of the prism is exposed parallel with the laser polarization plane. Investigations show the degree of radiation polarization, reflected from water clouds, to be changed within 1/0.7 (seldom up to 0.6) depending on their density. In most cases a signal reflected from the cloud leading edge is polarized completely. The time shift is observed between polarized and crosspolarized components of a Fignal, reflected from a cloud, depending on the density of a meteorological object. While penetrating into the cloud depth a degree of polarization decreases up to 0.8-0.7, and the character of this decrease is different for various types of clouds. For crystal clouds the shift between the components of the reflected signal is not observed and the magnitude of polarization degree amounts to 0.1/0.3 in comparison with water clouds. The polarization degree of radiation reflected by fog is not less than 0.6, and that in the rains of average intensity (about 5 mm/h) is always about 1. The authors have suggested an algorithm of numerical solution of nonstationary transfer equation in the vector form to forecast the influence of multiple scattering effects on polarization characteristics of the lidar light signal. The method of statistical simulation (Monte-Carlo technique) forms the basis of the algorithm. Numerical estimates obtained for a model of stratocumulus at lambda = 0.6943 microns under boundary conditions close to the conditions of natural experiment being discussed proved to be in a good agreement with the results of observation. Specifically, Fig. 1 shows the profiles of polarization (p) versus depth (L) of the following drop formations: fog (curve 1) with horizontal meteorological visibility of 4 km two stratocumulus at a height of 1100 m with the attenuation factors delta = 0.01m(exp -1) (curve 2) and delta = 0.05m(exp -1) (curve 3). Curve 3 shows the results of numerical estimates and the value of their statistical error.

Balin, Yu. S.↗