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NASA NTRSDate not supplied

A Framework for the Analysis of Deep Neural Networks in Autonomous Aerospace Applications using Bayesian Statistics

Deep Neural Networks (DNNs) are considered to be key components in many autonomous systems. Applications range from vision-based obstacle avoidance to intelligent/learning control and planning. Safety-critical applications as found in the aerospace domain require that the behavior of the DNN is validated and tested rigorously for safety of the autonomous system (AUS). In this paper, we present a framework to support testing of DNNs and the analysis of the network structure. Our framework employs techniques from statistical modeling and active learning to effectively generate test cases for DNN safety testing and performance analysis. We will present results of a case study on a physics-based Deep recurrent residual neural network (DR-RNN), which has been trained to emulate the aerodynamics behavior of a fixed-wing aircraft.

Deep Neural networks↗
NASA NTRS1979

A statistical model for the initial stellar mass function

The nonlinear stages of the fragmentation of a collapsing molecular cloud are modeled by coagulation theory. Several distinct physical processes are discussed, including protostellar fragment coalescence, gas accretion, and binary formation. This work confirms and extends the earlier result of Nakano (1966) that an approximately self-similar limiting form of the mass spectrum develops after several mean initial collision times. An approximate solution to the velocity-averaged coagulation equation is given for an arbitrary power-law dependence of the coalescence rate on mass, with dimensional dependence proportional to m to the power lambda; i.e., the asymptotic mass spectrum varies as m to the -3 lambda/2 power at small masses and cuts off exponentially at large masses, the characteristic mass depending on the number of collision times elapsed. Simple physical arguments suggest that lambda may increase with increasing mass, but is restricted to the range from 2/3 to 4/3. A large fraction of collisions could result in binary formation.

Silk, J.↗
NASA NTRS2019

On the Calculation of Exact Cumulative Distribution Statistics for Burgers Equation

A mathematical procedure is presented for the calculation of exact cumulative distribution statistics for a viscosity-free variant of Burgers nonlinear partial differential equation (PDE) in one space dimension and time subject to sinusoidal initial data with uncertain (random variable) amplitude or phase shift. Analytical solutions of nonlinear PDEs with uncertain initial and/or boundary data are invaluable benchmarks in assessing approximate uncertainty quantification techniques. The Burgers equation solution with uncertain initial data results in nonsmooth solution behavior in both physical and random variable dimensions which provides a severe test for approximate uncertainty quantification techniques. Mathematical proofs are provided to verify that exact cumulative distribution statistics can be systematically and robustly obtained for all forward time.

Burgers↗
NASA NTRS1982

Criteria for the use of regression analysis for remote sensing of sediment and pollutants

An examination of limitations, requirements, and precision of the linear multiple-regression technique for quantification of marine environmental parameters is conducted. Both environmental and optical physics conditions have been defined for which an exact solution to the signal response equations is of the same form as the multiple regression equation. Various statistical parameters are examined to define a criteria for selection of an unbiased fit when upwelled radiance values contain error and are correlated with each other. Field experimental data are examined to define data smoothing requirements in order to satisfy the criteria of Daniel and Wood (1971). Recommendations are made concerning improved selection of ground-truth locations to maximize variance and to minimize physical errors associated with the remote sensing experiment.

Whitlock, C. H.↗
NASA NTRS1995

Theoretical and experimental models of the diffuse radar backscatter from Mars

The general objective for this work was to develop a theoretically and experimentally consistent explanation for the diffuse component of radar backscatter from Mars. The strength, variability, and wavelength independence of Mars' diffuse backscatter are unique among our Moon and the terrestrial planets. This diffuse backscatter is generally attributed to wavelength-scale surface roughness and to rock clasts within the Martian regolith. Through the combination of theory and experiment, the authors attempted to bound the range of surface characteristics that could produce the observed diffuse backscatter. Through these bounds they gained a limited capability for data inversion. Within this umbrella, specific objectives were: (1) To better define the statistical roughness parameters of Mars' surface so that they are consistent with observed radar backscatter data, and with the physical and chemical characteristics of Mars' surface as inferred from Mariner 9, the Viking probes, and Earth-based spectroscopy; (2) To better understand the partitioning between surface and volume scattering in the Mars regolith; (3) To develop computational models of Mars' radio emission that incorporate frequency dependent, surface and volume scattering.

England, A. W.↗
NASA NTRS2003

NASA GPM GV Science Requirements

An important scientific objective of the NASA portion of the GPM Mission is to generate quantitatively-based error characterization information along with the rainrate retrievals emanating from the GPM constellation of satellites. These data must serve four main purposes: (1) they must be of sufficient quality, uniformity, and timeliness to govern the observation weighting schemes used in the data assimilation modules of numerical weather prediction models; (2) they must extend over that portion of the globe accessible by the GPM core satellite to which the NASA GV program is focused - (approx.65 degree inclination); (3) they must have sufficient specificity to enable detection of physically-formulated microphysical and meteorological weaknesses in the standard physical level 2 rainrate algorithms to be used in the GPM Precipitation Processing System (PPS), i.e., algorithms which will have evolved from the TRMM standard physical level 2 algorithms; and (4) they must support the use of physical error modeling as a primary validation tool and as the eventual replacement of the conventional GV approach of statistically intercomparing surface rainrates fiom ground and satellite measurements. This approach to ground validation research represents a paradigm shift vis-&-vis the program developed for the TRMM mission, which conducted ground validation largely as a statistical intercomparison process between raingauge-derived or radar-derived rainrates and the TRMM satellite rainrate retrievals -- long after the original satellite retrievals were archived. This approach has been able to quantify averaged rainrate differences between the satellite algorithms and the ground instruments, but has not been able to explain causes of algorithm failures or produce error information directly compatible with the cost functions of data assimilation schemes. These schemes require periodic and near-realtime bias uncertainty (i.e., global space-time distributed conditional accuracy of the retrieved rainrates) and local error covariance structure (i.e., global space-time distributed error correlation information for the local 4-dimensional space-time domain -- or in simpler terms, the matrix form of precision error). This can only be accomplished by establishing a network of high quality-heavily instrumented supersites selectively distributed at a few oceanic, continental, and coastal sites. Economics and pragmatics dictate that the network must be made up of a relatively small number of sites (6-8) created through international cooperation. This presentation will address some of the details of the methodology behind the error characterization approach, some proposed solutions for expanding site-developed error properties to regional scales, a data processing and communications concept that would enable rapid implementation of algorithm improvement by the algorithm developers, and the likely available options for developing the supersite network.

Smith, E.↗
NASA NTRS2007

GRO J1655-40: Early Stages of the 2005 Outburst

The black-hole X-ray binary transient GRO J1655-40 underwent an outburst beginning in early 2005. We present the results of our multi-wavelength observational campaign to study the early outburst spectral and temporal evolution, which combines data from X-ray (RXTE, INTEGRAL), radio (VLA) and optical (ROTSE, SMARTS) instruments. During the reported period the source left quiescence and went through four major accreting black hole states: low-hard, hard intermediate, soft intermediate and high-soft. We investigated dipping behavior in the RXTE band and compare our results to the 1996-1997 case, when the source was predominantly in the high-soft state, finding significant differences. We consider the evolution of the low frequency quasi-periodic oscillations and find that the frequency strongly correlates with the spectral characteristics, before shutting off prior to the transition to the high-soft state. We model the broad-band high-energy spectrum in the context of empirical models, as well as more physically motivated thermal and bulk-motion Comptonization and Compton reflection models. RXTE and INTEGRAL data together support a statistically significant high energy cut-off in the energy spectrum at approximately equal to 100 - 200 keV during the low-hard state. The RXTE data alone also show it very significantly during the transition, but cannot see one in the high-soft state spectra. We consider radio, optical and X-ray connections in the context of possible synchrotron and synchrotron self-Compton origins of X-ray emission in low-hard and intermediate states. In this outburst of GRO J1655-40, the radio flux does not rise strongly with the X-ray flux.

Shaposhnikov, N.↗
NASA NTRS2008

Verification of Atmospheric Signals Associated with Major Seismicity by Space and Terrestrial Observations

Observations from the last twenty years suggest the existence of electromagnetic (EM) phenomena during or preceding some earthquakes [Haykawa et a!, 2004; Pulinets at al, 1999,2004, 2006, Ouzounov et all 2007 and Liu et all 20041. Both our previous studies [Pulinets at al, 2005, 2006, Ouzounov et al, 2006, 20071 and the latest review by the Earthquake Remote Precursor Sensing panel [ERPS; 2003- 20051; have shown that there were precursory atmospheric TIR signals observed on the ground and in space associated with several recent earthquakes. [Tramutoli at al, 2005, 2006, Cervone et al, 2006, Ouzounov et all 2004,2006JT.o study these signals, we applied both multi parameter statistical analysis and data mining methods that require systematic measurements from an Integrated Sensor Web of observations of several physical and environmental parameters. These include long wave earth infra-red radiation, ionospheric electrical and magnetic parameters, temperature and humidity of the boundary layer, seismicity and may be associated with major earthquakes. Our goal is to verify the earthquake atmospheric correlation in two cases: (i) backward analysis - 2000-2008 hindcast monitoring of multi atmospheric parameters over the Kamchatka region, Russia ; and (ii) forward real-time alert analysis over different seismo-tectonic regions for California, Turkey, Taiwan and Japan. Our latest results, from several post-earthquake independent analyses of more then 100 major earthquakes, show that joint satellite and some ground measurements, using an integrated web, could provide a capability for observing pre-earthquake atmospheric signals by combining the information from multiple sensors into a common framework. Using our methodology, we evaluated and compared the observed signals preceding the latest M7.9 Sichuan earthquake (0511212008), M8.0 earthquake in Peru (0811512007), M7.6 Kashmir earthquake (1010812005) and M9.0 Sumatra earthquake (1212812004). We found evidence of the systematic appearance of both atmospheric and ionospheric anomalies preceding most of the major events during the period of our analysis 2001 -2008.

Taylor, Patrick↗
NASA NTRS2021

Assimilation of Lidar Planetary Boundary Layer Height Observations

Lidar backscatter and wind retrievals of the planetary boundary layer height (PBLH) are assimilated into 22 hourly forecasts from the NASA Unified - Weather and Research Forecast (NU-WRF) model during the Plains Elevated Convection Convection at Night (PECAN) campaign on July 11, 2015 in Greensburg, Kansas, using error statistics collected from the model profiles to compute the necessary covariance matrices. Two separate forecast runs using different PBL physics schemes were employed, and comparisons with 6 independent radiosonde profiles were made for each run. Both of the forecast runs accurately predicted the PBLH and the state variable profiles within the planetary boundary layer during the early morning, and the assimilation had a small impact during this time. In the late afternoon, the forecast runs showed decreased accuracy as the convective boundary layer developed. However, assimilation of the Doppler lidar PBLH observations were found to improve the temperature and V velocity profiles relative to independent radiosonde profiles. Water vapor was overcorrected, leading to increased differences with independent data. Errors in the U velocity were made slightly larger. The computed forecast error covariances between the PBLH and state variables were found to rise in the late afternoon, leading to the larger improvements in the afternoon. This work represents the first effort to assimilate PBLH into forecast states using ensemble methods.

Andrew Tangborn↗
NASA NTRS1993

Second quantization in bit-string physics

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Noyes, H. Pierre↗
NASA NTRS1988

Heterogeneous physicochemistry of the winter polar stratosphere

Present chemical theories of the Antarctic ozone hole assume that heterogeneous reactions involving polar stratospheric clouds (PSCs) are the precursor of springtime ozone depletions. However, none of the theories quantify the rates of proposed heterogeneous processed, and none utilize the extensive data base on PSC's. Thus, all of the theories must be considered incomplete until the heterogeneous mechanisms are properly defined. A unified treatment developed of the cloud related processes, both physical and chemical, and the importance of these processes using observation data is calibrated. The rates are compared competitive heterogeneous processes to place reasonable limits on critical mechanisms such as the denitrification and dechlorination of the polar winter stratosphere. Among the subjects addressed here are the physical/chemical properties of PSC's including their relevant microphysical, optical and compositional characteristics, mass transfer rates of gaseous constituents to cloud particles, adsorption, accommodation and sticking coefficients on cloud particles, time constants for condensation, absorption and other microphysical processes, effects of solubility and vapor pressure on cloud composition, the statistics of cloud processing of chemically active condensible species, rate limiting steps in heterogeneous chemical reactions, and the nonlinear dependence of ozone loss on physical and chemical parameters.

Turco, R. P.↗
NASA NTRS2008

Comparison of CERES-MODIS Stratus Cloud Properties with Ground-Based Measurements at the DOE ARM Southern Great Plains Site

Overcast stratus cloud properties derived for the Clouds and the Earth's Radiant Energy system (CERES) Project using Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) data are compared with observations taken at the Atmospheric Radiation Measurement (ARM) Southern Great Plains site from March 2000 through December 2004. Retrievals from ARM surface-based data were averaged over a 1-hour interval centered at the time of each satellite overpass, and the CERES-MODIS cloud properties were averaged within a 30-km x 30 km box centered on the ARM SGP site. Two datasets were analyzed: all of the data (ALL) which include multilayered, single-layered, and slightly broken stratus decks and a subset, single-layered unbroken decks (SL). The CERES-MODIS effective cloud heights were determined from effective cloud temperature using a lapse rate method with the surface temperature specified as the 24-h mean surface air temperature. For SL stratus, they are, on average, within the ARM radar-lidar estimated cloud boundaries and are 0.534 +/- 0.542 km and 0.108 +/- 0.480 km lower than the cloud physical tops and centers, respectively, and are comparable for day and night observations. The mean differences and standard deviations are slightly larger for ALL data, but not statistically different to those of SL data. The MODIS-derived effective cloud temperatures are 2.7 +/- 2.4 K less than the surface-observed SL cloud center temperatures with very high correlations (0.86-0.97). Variations in the height differences are mainly caused by uncertainties in the surface air temperatures, lapse rates, and cloud-top height variability. The biases are mainly the result of the differences between effective and physical cloud top, which are governed by cloud liquid water content and viewing zenith angle, and the selected lapse rate, -7.1 K km(exp -1). Based on a total of 43 samples, the means and standard deviations of the differences between the daytime Terra and surface retrievals of effective radius r(sub e), optical depth, and liquid water path for SL stratu are 0.1 +/- 1.9 micrometers (1.2 +/- 23.5%), -1.3 +/- 9.5 (-3.6 +/-26.2%), and 0.6 +/- 49.9 gm (exp -2) (0.3 +/- 27%), respectively, while the corresponding correlation coefficients are 0.44, 0.87, and 0.89. For Aqua, they are 0.2 +/- 1.9 micrometers (2.5 +/- 23.4%), 2.5 +/- 7.8 (7.8 +/- 24.3%), and 28.1 +/- 52.7 gm (exp -2) (17.2 +/- 32.2%), as well as 0.35, 0.96, and 0.93 from a total of 21 cases. The results for ALL cases are comparable. Although a bias in R(sub e) was expected because the satellite retrieval of effective radius only represents the top of the cloud, the surface-based radar retrievals revealed that the vertical profile of r(sub e) is highly variable with smaller droplets occurring at cloud top in some cases. The larger bias in optical depth and liquid water path for Aqua is due, at least partially, to differences in the Terra and Aqua MODIS visible channel calibrations. methods for improving the cloud-top height and microphysical property retrievals are suggested.

Dong, Xiquan↗
NASA NTRS1991

Evaluation of an efficient statistical transport model for turbulent droplet dispersion in dilute combusting sprays

Evaluation of an efficient statistical transport model for turbulent droplet dispersion is made for a dilute spray of methanol droplets injected into a turbulent, axisymmnetric methane-fuelled diffusion flame burning in stagnant air. In the dispersion model, a computational parcel representing a group of physical particles (droplets) is considered to have a normal probability density function (pdf) in space. The mean is determined by Lagrangian tracking through a sequence of stochastically generated turbulent eddies and the variance is evaluated from a statistical formulation based on the linearized particle equations of motion. The basic validity of this model is established through comparison with available experimental data and with theoretical predictions using a conventional stochastic direct modeling approach. The conclusion of the evaluation is that the proposed dispersion model compares favorably with experimental data and provides a valid technique for simulating turbulent combusting sprays with significant computational savings over conventional methods.

Litchford, Ron J.↗
NASA NTRS2021

New giant planet beyond the snow line for an extended MOA exoplanet microlens sample

Characterizing a planet detected by microlensing is hard if the planetary signal is weak or the lens-source relative trajectory is far from caustics. However, statistical analyses of planet demography must include those planets to accurately determine occurrence rates. As part of a systematic modelling effort in the context of a >10-yr retrospective analysis of MOA’s survey observations to build an extended MOA statistical sample, we analyse the light curve of the planetary microlensing event MOA-2014-BLG-472. This event provides weak constraints on the physical parameters of the lens, as a result of a planetary anomaly occurring at low magnification in the light curve. We use a Bayesian analysis to estimate the properties of the planet, based on a refined Galactic model and the assumption that all Milky Way’s stars have an equal planet-hosting probability. We find that a lens consisting of a 1.9(+2.2,−1.2)M(J) giant planet orbiting a 0.31(+0.36,−0.19)Mꙩ host at a projected separation of 0.75±0.24au is consistent with the observations and is most likely, based on the Galactic priors. The lens most probably lies in the Galactic bulge, at 7.2(+0.6,−1.7)kpc from Earth. The accurate measurement of the measured planet-to-host star mass ratio will be included in the next statistical analysis of cold planet demography detected by microlensing.

Clément Ranc↗
NASA NTRS2015

Preliminary Statistics from the NASA Alphasat Beacon Receiver in Milan, Italy

NASA Glenn Research Center (GRC) and the Politecnico di Milano (POLIMI) have initiated a joint propagation campaign within the framework of the Alphasat propagation experiment to characterize rain attenuation, scintillation, and gaseous absorption effects of the atmosphere in the 40 gigahertz band. NASA GRC has developed and installed a K/Q-band (20/40 gigahertz) beacon receiver at the POLIMI campus in Milan, Italy, which receives the 20/40 gigahertz signals broadcast from the Alphasat Aldo Paraboni TDP no. 5 beacon payload. The primary goal of these measurements is to develop a physical model to improve predictions of communications systems performance within the Q-band. Herein, we provide an overview of the design and data calibration procedure, and present 6 months of preliminary statistics of the NASA propagation terminal, which has been installed and operating in Milan since May 2014. The Q-band receiver has demonstrated a dynamic range of 40 decibels at an 8-hertz sampling rate. A weather station with an optical disdrometer is also installed to characterize rain drop size distribution for correlation with physical based models.

RF propagation↗
NASA NTRS1974

Instrumental and analytic techniques for separating protons from electrons in the cosmic ray flux

Techniques are being investigated to aid in distinguishing between electrons and the large background of interacting protons which simulate electron-induced electromagnetic cascades. For cosmic ray primaries, incident on the HECRE ionization spectrometer, statistical criteria are employed to test the cascade curves with the incident energy and starting point as free parameters. The physical significance of the distribution of apparent cascade starting points is being studied using Monte Carlo 100-GeV protons. The proposed use of a CsI detector module (totally-active and high Z) to further discriminate against protons is described.

Crannell, C. J.↗
NASA NTRS1975

Reexamination of the correlation of galaxies and QSO's

It is shown that the correlation of the separation in the sky between certain QSO's and the nearest bright galaxy to them with the galaxy's redshift could be an artifact of the sampling procedure or small number statistics. The overall association between 3C QSO's and bright galaxies remains as suggestive, but not compelling, evidence for a physical relationship.

Noerdlinger, P. D.↗
NASA NTRS1981

Correlation function studies for snow and ice

The random medium model is used to characterize snow and ice fields in the interpretation of active and passive microwave remote sensing data. A correlation function is used to describe the random permittivity fluctuations with the associated mean and variance and correlation lengths; and several samples are investigated to determine typical correlation functions for snow and ice. It is shown that correlation functions are extracted directly from appropriate ground truth data, and an exponential correlation function is observed for snow and ice with lengths corresponding to the actual size of ice particles or air bubbles. Thus, given that a medium has spatially stationary statistics and a small medium, the random medium model can interpret remote sensing data where theoretical parameters correspond to actual physical parameters of the terrain.

Vallese, F.↗