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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Finite element methods in probabilistic mechanics

Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.

Liu, Wing Kam↗
NASA NTRS1988

Compact radio sources in the galactic plane

The preliminary results of a search for infrared counterparts to compact continuum radio sources found within 0.5 deg of the Galactic plane are presented. Out of 75 positions searched, nine very red sources, each with a probability of less than 0.01 of being a random field star, were found. Most of the nine sources are characterized by deep silicate absorption features at 10 microns and a red energy distribution that continues to rise beyond 25 microns. Six of the sources are best explained as late O or early B stars exciting a compact H II region. The radio emission is close to that expected for the rate of emission of ionizing photons for a normal main-sequence star. Although these H II regions are compact, they are not sufficiently dusty in the immediate environment of the star to significantly reduce the ionizing flux. Three of the sources show considerably more emission than expected for a main-sequence star, indicating they are either hotter than a main-sequence star with the same luminosity or the radio emision is nonthermal and coming from a more exotic object.

Jones, Terry Jay↗
NASA NTRS1988

International Conference on Advances in Communication and Control Systems, 1st, Washington, DC, June 18-20, 1987, Proceedings

Theoretical models of communication and control systems are discussed in reviews and reports. Topics addressed include smoothing and identification for random fields, the information and coding capacities of mismatched Gaussian channels, recursive least-squares estimation and Kalman filtering by systolic arrays, Kemp echo digital filters, a periodic test-scheduling scheme for communication and queuing processes, and receivers for direct-sequence systems. Consideration is given to a distributed-parameter model for detecting cracks in rotors, active control of aeroelastic systems governed by functional differential equations, robust multivariable control of large space structures, finite-rank relatively bounded perturbations of semigroup generators, and sensitivity analysis of convex optimal-control problems.

Declaris, Nicholas↗
NASA NTRS1989

A tesselated probabilistic representation for spatial robot perception and navigation

The ability to recover robust spatial descriptions from sensory information and to efficiently utilize these descriptions in appropriate planning and problem-solving activities are crucial requirements for the development of more powerful robotic systems. Traditional approaches to sensor interpretation, with their emphasis on geometric models, are of limited use for autonomous mobile robots operating in and exploring unknown and unstructured environments. Here, researchers present a new approach to robot perception that addresses such scenarios using a probabilistic tesselated representation of spatial information called the Occupancy Grid. The Occupancy Grid is a multi-dimensional random field that maintains stochastic estimates of the occupancy state of each cell in the grid. The cell estimates are obtained by interpreting incoming range readings using probabilistic models that capture the uncertainty in the spatial information provided by the sensor. A Bayesian estimation procedure allows the incremental updating of the map using readings taken from several sensors over multiple points of view. An overview of the Occupancy Grid framework is given, and its application to a number of problems in mobile robot mapping and navigation are illustrated. It is argued that a number of robotic problem-solving activities can be performed directly on the Occupancy Grid representation. Some parallels are drawn between operations on Occupancy Grids and related image processing operations.

Elfes, Alberto↗
NASA NTRS1989

Advances in image compression and automatic target recognition; Proceedings of the Meeting, Orlando, FL, Mar. 30, 31, 1989

Various papers on image compression and automatic target recognition are presented. Individual topics addressed include: target cluster detection in cluttered SAR imagery, model-based target recognition using laser radar imagery, Smart Sensor front-end processor for feature extraction of images, object attitude estimation and tracking from a single video sensor, symmetry detection in human vision, analysis of high resolution aerial images for object detection, obscured object recognition for an ATR application, neural networks for adaptive shape tracking, statistical mechanics and pattern recognition, detection of cylinders in aerial range images, moving object tracking using local windows, new transform method for image data compression, quad-tree product vector quantization of images, predictive trellis encoding of imagery, reduced generalized chain code for contour description, compact architecture for a real-time vision system, use of human visibility functions in segmentation coding, color texture analysis and synthesis using Gibbs random fields.

Tescher, Andrew G.↗
NASA NTRS1991

Statistics of primordial density perturbations from discrete seed masses

The statistics of density perturbations for general distributions of seed masses with arbitrary matter accretion is examined. Formal expressions for the power spectrum, the N-point correlation functions, and the density distribution function are derived. These results are applied to the case of uncorrelated seed masses, and power spectra are derived for accretion of both hot and cold dark matter plus baryons. The reduced moments (cumulants) of the density distribution are computed and used to obtain a series expansion for the density distribution function. Analytic results are obtained for the density distribution function in the case of a distribution of seed masses with a spherical top-hat accretion pattern. More generally, the formalism makes it possible to give a complete characterization of the statistical properties of any random field generated from a discrete linear superposition of kernels. In particular, the results can be applied to density fields derived by smoothing a discrete set of points with a window function.

Scherrer, Robert J.↗
NASA NTRS1991

Unsupervised segmentation of polarimetric SAR data using the covariance matrix

An unsupervised selection of polarimetric features useful for the segmentation and analysis of polarimetric synthetic aperture radar (SAR) data is presented. The technique is based on multidimensional clustering of the parameters composing the polarimetric covariance matrix of the data. Clustering is performed on the logarithm of these quantities. Once the polarimetric cluster centers have been determined, segmentation of the polarimetric data into regions is performed using a maximum likelihood polarimetric classifier. Segmentation maps are further improved using a Markov random field to describe the statistics of the regions and computing the maximum of the product of the local conditional densities. Examples with real polarimetric SAR imagery are given to illustrate the potential of this method.

Rignot, Eric↗
NASA NTRS1993

Probabilistic finite elements for fatigue and fracture analysis

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Belytschko, Ted↗
NASA NTRS1992

Classification with spatio-temporal interpixel class dependency contexts

A contextual classifier which can utilize both spatial and temporal interpixel dependency contexts is investigated. After spatial and temporal neighbors are defined, a general form of maximum a posterior spatiotemporal contextual classifier is derived. This contextual classifier is simplified under several assumptions. Joint prior probabilities of the classes of each pixel and its spatial neighbors are modeled by the Gibbs random field. The classification is performed in a recursive manner to allow a computationally efficient contextual classification. Experimental results with bitemporal TM data show significant improvement of classification accuracy over noncontextual pixelwise classifiers. This spatiotemporal contextual classifier should find use in many applications of remote sensing, especially when the classification accuracy is important.

Jeon, Byeungwoo↗
NASA NTRS1993

Maximum a posteriori classification of multifrequency, multilook, synthetic aperture radar intensity data

We present a maximum a posteriori (MAP) classifier for classifying multifrequency, multilook, single polarization SAR intensity data into regions or ensembles of pixels of homogeneous and similar radar backscatter characteristics. A model for the prior joint distribution of the multifrequency SAR intensity data is combined with a Markov random field for representing the interactions between region labels to obtain an expression for the posterior distribution of the region labels given the multifrequency SAR observations. The maximization of the posterior distribution yields Bayes's optimum region labeling or classification of the SAR data or its MAP estimate. The performance of the MAP classifier is evaluated by using computer-simulated multilook SAR intensity data as a function of the parameters in the classification process. Multilook SAR intensity data are shown to yield higher classification accuracies than one-look SAR complex amplitude data. The MAP classifier is extended to the case in which the radar backscatter from the remotely sensed surface varies within the SAR image because of incidence angle effects. The results obtained illustrate the practicality of the method for combining SAR intensity observations acquired at two different frequencies and for improving classification accuracy of SAR data.

Rignot, E.↗
NASA NTRS1994

Improved image decompression for reduced transform coding artifacts

The perceived quality of images reconstructed from low bit rate compression is severely degraded by the appearance of transform coding artifacts. This paper proposes a method for producing higher quality reconstructed images based on a stochastic model for the image data. Quantization (scalar or vector) partitions the transform coefficient space and maps all points in a partition cell to a representative reconstruction point, usually taken as the centroid of the cell. The proposed image estimation technique selects the reconstruction point within the quantization partition cell which results in a reconstructed image which best fits a non-Gaussian Markov random field (MRF) image model. This approach results in a convex constrained optimization problem which can be solved iteratively. At each iteration, the gradient projection method is used to update the estimate based on the image model. In the transform domain, the resulting coefficient reconstruction points are projected to the particular quantization partition cells defined by the compressed image. Experimental results will be shown for images compressed using scalar quantization of block DCT and using vector quantization of subband wavelet transform. The proposed image decompression provides a reconstructed image with reduced visibility of transform coding artifacts and superior perceived quality.

Orourke, Thomas P.↗
NASA NTRS1995

On the joint spectral density of bivariate random sequences

For univariate random sequences, the power spectral density acts like a probability density function of the frequencies present in the sequence. This dissertation extends that concept to bivariate random sequences. For this purpose, a function called the joint spectral density is defined that represents a joint probability weighing of the frequency content of pairs of random sequences. Given a pair of random sequences, the joint spectral density is not uniquely determined in the absence of any constraints. Two approaches to constraining the sequences are suggested: (1) assume the sequences are the margins of some stationary random field, (2) assume the sequences conform to a particular model that is linked to the joint spectral density. For both approaches, the properties of the resulting sequences are investigated in some detail, and simulation is used to corroborate theoretical results. It is concluded that under either of these two constraints, the joint spectral density can be computed from the non-stationary cross-correlation.

Aalfs, David D.↗
NASA NTRS1994

Wiener filtering of the COBE Differential Microwave Radiometer data

We derive an optimal linear filter to suppress the noise from the cosmic background explorer satellite (COBE) Differential Microwave Radiometer (DMR) sky maps for a given power spectrum. We then apply the filter to the first-year DMR data, after removing pixels within 20 deg of the Galactic plane from the data. We are able to identify particular hot and cold spots in the filtered maps at a level 2 to 3 times the noise level. We use the formalism of constrained realizations of Gaussian random fields to assess the uncertainty in the filtered sky maps. In addition to improving the signal-to-noise ratio of the map as a whole, these techniques allow us to recover some information about the cosmic microwave background anisotropy in the missing Galactic plane region. From these maps we are able to determine which hot and cold spots in the data are statistically significant, and which may have been produced by noise. In addition, the filtered maps can be used for comparison with other experiments on similar angular scales.

Bunn, Emory F.↗
NASA NTRS1997

The STIS parallel survey: Introduction and first results

The installation of the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST) allows for the first time two-dimensional optical and ultraviolet slitless spectroscopy of faint objects from space. The STIS Parallel Survey (SPS) routinely obtains broad band images and slitless spectra of random fields in parallel with HST observations using other instruments. The SPS is designed to study a wide variety of astrophysical phenomena, including the rate of star formation in galaxies at intermediate to high redshift through the detection of emission-line galaxies. We present the first results of the SPS, which demonstrate the capability of STIS slitless spectroscopy to detect and identify high-redshift galaxies.

Gardner, Jonathan P.↗
NASA NTRS1997

Evolution of Structure in the Intergalactic Medium and the Nature of the LY-Alpha Forest

We have performed a detailed statistical study of the evolution of structure in a photoionized intergalactic medium (IGM) using analytical simulations to extend the calculation into the mildly nonlinear density regime found to prevail at z = 3. Our work is based on a simple fundamental conjecture: that the probability distribution function of the density of baryonic diffuse matter in the universe is described by a lognormal (LN) random field. The LN distribution has several attractive features and follows plausibly from the assumption of initial linear Gaussian density and velocity fluctuations at arbitrarily early times. Starting with a suitably normalized power spectrum of primordial fluctuations in a universe dominated by cold dark matter (CDM), we compute the behavior of the baryonic matter, which moves slowly toward minima in the dark matter potential on scales larger than the Jeans length. We have computed two models that succeed in matching observations. One is a nonstandard CDM model with OMEGA = 1, h = 0.5, and GAMMA = 0.3, and the other is a low-density flat model with a cosmological constant (LCDM), with OMEGA = 0.4, OMEGA(sub LAMBDA) = 0.6, and h = 0.65. In both models, the variance of the density distribution function grows with time, reaching unity at about z = 4, where the simulation yields spectra that closely resemble the Ly-alpha forest absorption seen in the spectra of high-z quasars. The calculations also successfully predict the observed properties of the Ly-alpha forest clouds and their evolution from z = 4 down to at least z = 2, assuming a constant intensity for the metagalactic UV background over this redshift range. However, in our model the forest is not due to discrete clouds, but rather to fluctuations in a continuous intergalactic medium. At z = 3; typical clouds with measured neutral hydrogen column densities N(sub H I) = 10(exp 13.3), 10(exp 13.5), and 10(exp 11.5) /sq cm correspond to fluctuations with mean total densities approximately 10, 1, and 0.1 times the universal mean baryon density. Perhaps surprisingly, fluctuations whose amplitudes are less than or equal to the mean density still appear as "clouds" because in our model more than 70% of the volume of the IGM at z = 3 is filled with gas at densities below the mean value.

Bi, Hongguang↗
NASA NTRS2001

Probabilistic Structural Analysis and Reliability Using NESSUS With Implemented Material Strength Degradation Model

This project included both research and education objectives. The goal of this project was to advance innovative research and education objectives in theoretical and computational probabilistic structural analysis, reliability, and life prediction for improved reliability and safety of structural components of aerospace and aircraft propulsion systems. Research and education partners included Glenn Research Center (GRC) and Southwest Research Institute (SwRI) along with the University of Texas at San Antonio (UTSA). SwRI enhanced the NESSUS (Numerical Evaluation of Stochastic Structures Under Stress) code and provided consulting support for NESSUS-related activities at UTSA. NASA funding supported three undergraduate students, two graduate students, a summer course instructor and the Principal Investigator. Matching funds from UTSA provided for the purchase of additional equipment for the enhancement of the Advanced Interactive Computational SGI Lab established during the first year of this Partnership Award to conduct the probabilistic finite element summer courses. The research portion of this report presents the cumulation of work performed through the use of the probabilistic finite element program, NESSUS, Numerical Evaluation and Structures Under Stress, and an embedded Material Strength Degradation (MSD) model. Probabilistic structural analysis provided for quantification of uncertainties associated with the design, thus enabling increased system performance and reliability. The structure examined was a Space Shuttle Main Engine (SSME) fuel turbopump blade. The blade material analyzed was Inconel 718, since the MSD model was previously calibrated for this material. Reliability analysis encompassing the effects of high temperature and high cycle fatigue, yielded a reliability value of 0.99978 using a fully correlated random field for the blade thickness. The reliability did not change significantly for a change in distribution type except for a change in distribution from Gaussian to Weibull for the centrifugal load. The sensitivity factors determined to be most dominant were the centrifugal loading and the initial strength of the material. These two sensitivity factors were influenced most by a change in distribution type from Gaussian to Weibull. The education portion of this report describes short-term and long-term educational objectives. Such objectives serve to integrate research and education components of this project resulting in opportunities for ethnic minority students, principally Hispanic. The primary vehicle to facilitate such integration was the teaching of two probabilistic finite element method courses to undergraduate engineering students in the summers of 1998 and 1999.

Bast, Callie C.↗
NASA NTRS2015

A High Performance Computing Approach to Tree Cover Delineation in 1-m NAIP Imagery Using a Probabilistic Learning Framework

Tree cover delineation is a useful instrument in deriving Above Ground Biomass (AGB) density estimates from Very High Resolution (VHR) airborne imagery data. Numerous algorithms have been designed to address this problem, but most of them do not scale to these datasets, which are of the order of terabytes. In this paper, we present a semi-automated probabilistic framework for the segmentation and classification of 1-m National Agriculture Imagery Program (NAIP) for tree-cover delineation for the whole of Continental United States, using a High Performance Computing Architecture. Classification is performed using a multi-layer Feedforward Backpropagation Neural Network and segmentation is performed using a Statistical Region Merging algorithm. The results from the classification and segmentation algorithms are then consolidated into a structured prediction framework using a discriminative undirected probabilistic graphical model based on Conditional Random Field, which helps in capturing the higher order contextual dependencies between neighboring pixels. Once the final probability maps are generated, the framework is updated and re-trained by relabeling misclassified image patches. This leads to a significant improvement in the true positive rates and reduction in false positive rates. The tree cover maps were generated for the whole state of California, spanning a total of 11,095 NAIP tiles covering a total geographical area of 163,696 sq. miles. The framework produced true positive rates of around 88% for fragmented forests and 74% for urban tree cover areas, with false positive rates lower than 2% for both landscapes. Comparative studies with the National Land Cover Data (NLCD) algorithm and the LiDAR canopy height model (CHM) showed the effectiveness of our framework for generating accurate high-resolution tree-cover maps.

Segments↗
NASA NTRS2016

DeepSAT: A Deep Learning Approach to Tree-Cover Delineation in 1-m NAIP Imagery for the Continental United States

High resolution tree cover classification maps are needed to increase the accuracy of current land ecosystem and climate model outputs. Limited studies are in place that demonstrates the state-of-the-art in deriving very high resolution (VHR) tree cover products. In addition, most methods heavily rely on commercial softwares that are difficult to scale given the region of study (e.g. continents to globe). Complexities in present approaches relate to (a) scalability of the algorithm, (b) large image data processing (compute and memory intensive), (c) computational cost, (d) massively parallel architecture, and (e) machine learning automation. In addition, VHR satellite datasets are of the order of terabytes and features extracted from these datasets are of the order of petabytes. In our present study, we have acquired the National Agriculture Imagery Program (NAIP) dataset for the Continental United States at a spatial resolution of 1-m. This data comes as image tiles (a total of quarter million image scenes with ~60 million pixels) and has a total size of ~65 terabytes for a single acquisition. Features extracted from the entire dataset would amount to ~8-10 petabytes. In our proposed approach, we have implemented a novel semi-automated machine learning algorithm rooted on the principles of "deep learning" to delineate the percentage of tree cover. Using the NASA Earth Exchange (NEX) initiative, we have developed an end-to-end architecture by integrating a segmentation module based on Statistical Region Merging, a classification algorithm using Deep Belief Network and a structured prediction algorithm using Conditional Random Fields to integrate the results from the segmentation and classification modules to create per-pixel class labels. The training process is scaled up using the power of GPUs and the prediction is scaled to quarter million NAIP tiles spanning the whole of Continental United States using the NEX HPC supercomputing cluster. An initial pilot over the state of California spanning a total of 11,095 NAIP tiles covering a total geographical area of 163,696 sq. miles has produced true positive rates of around 88 percent for fragmented forests and 74 percent for urban tree cover areas, with false positive rates lower than 2 percent for both landscapes.

Imagery↗