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NASA NTRS1996

Discrete Deterministic and Stochastic Petri Nets

Petri nets augmented with timing specifications gained a wide acceptance in the area of performance and reliability evaluation of complex systems exhibiting concurrency, synchronization, and conflicts. The state space of time-extended Petri nets is mapped onto its basic underlying stochastic process, which can be shown to be Markovian under the assumption of exponentially distributed firing times. The integration of exponentially and non-exponentially distributed timing is still one of the major problems for the analysis and was first attacked for continuous time Petri nets at the cost of structural or analytical restrictions. We propose a discrete deterministic and stochastic Petri net (DDSPN) formalism with no imposed structural or analytical restrictions where transitions can fire either in zero time or according to arbitrary firing times that can be represented as the time to absorption in a finite absorbing discrete time Markov chain (DTMC). Exponentially distributed firing times are then approximated arbitrarily well by geometric distributions. Deterministic firing times are a special case of the geometric distribution. The underlying stochastic process of a DDSPN is then also a DTMC, from which the transient and stationary solution can be obtained by standard techniques. A comprehensive algorithm and some state space reduction techniques for the analysis of DDSPNs are presented comprising the automatic detection of conflicts and confusions, which removes a major obstacle for the analysis of discrete time models.

MATHEMATICAL MODELS↗
NASA NTRS2004

COSMOG: Cosmology Oriented Sub-mm Modeling of Galactic Foregrounds

With upcoming missions in mid- and far-Infrared there is a need for software packages to reliably simulate the planned observations. This would help in both planning the observation and scanning strategy and in developing the concepts of the far-off missions. As this workshop demonstrated, many of the new missions are to be in the far-IR range of the electromagnetic spectrum and at the same time will map the sky with a sub-arcsec angular resolution. We present here a computer package for simulating foreground maps for the planned sub-mm and far-IR missions. such as SPECS. The package allows to study confusion limits and simulate cosmological observations for specified sky location interactively and in real time. Most of the emission at wavelengths long-ward of approximately 50 microns is dominated by Galactic cirrus and Zodiacal dust emission. Stellar emission at these wavelengths is weak and is for now neglected. Cosmological sources (distant and not-so-distant) galaxies for specified cosmologies will be added. Briefly, the steps that the algorithm goes through is described.

Kashlinsky, A.↗
NASA NTRS2003

Optimal Feedback Control of Thermal Networks

An improved approach to the mathematical modeling of feedback control of thermal networks has been devised. Heretofore software for feedback control of thermal networks has been developed by time-consuming trial-and-error methods that depend on engineers expertise. In contrast, the present approach is a systematic means of developing algorithms for feedback control that is optimal in the sense that it combines performance with low cost of implementation. An additional advantage of the present approach is that a thermal engineer need not be expert in control theory. Thermal networks are lumped-parameter approximations used to represent complex thermal systems. Thermal networks are closely related to electrical networks commonly represented by lumped-parameter circuit diagrams. Like such electrical circuits, thermal networks are mathematically modeled by systems of differential-algebraic equations (DAEs) that is, ordinary differential equations subject to a set of algebraic constraints. In the present approach, emphasis is placed on applications in which thermal networks are subject to constant disturbances and, therefore, integral control action is necessary to obtain steady-state responses. The mathematical development of the present approach begins with the derivation of optimal integral-control laws via minimization of an appropriate cost functional that involves augmented state vectors. Subsequently, classical variational arguments provide optimality conditions in the form of the Hamiltonian equations for the standard linear-quadratic-regulator (LQR) problem. These equations are reduced to an algebraic Riccati equation (ARE) with respect to the augmented state vector. The solution of the ARE leads to the direct computation of the optimal proportional- and integral-feedback control gains. In cases of very complex networks, large numbers of state variables make it difficult to implement optimal controllers in the manner described in the preceding paragraph.

Papalexandris, Miltiadis↗
NASA NTRS2003

Detecting Edges in Images by Use of Fuzzy Reasoning

A method of processing digital image data to detect edges includes the use of fuzzy reasoning. The method is completely adaptive and does not require any advance knowledge of an image. During initial processing of image data at a low level of abstraction, the nature of the data is indeterminate. Fuzzy reasoning is used in the present method because it affords an ability to construct useful abstractions from approximate, incomplete, and otherwise imperfect sets of data. Humans are able to make some sense of even unfamiliar objects that have imperfect high-level representations. It appears that to perceive unfamiliar objects or to perceive familiar objects in imperfect images, humans apply heuristic algorithms to understand the images

Dominguez, Jesus A.↗
NASA NTRS2019

Experimentally-Derived Bidirectional Reflectance Distribution Function Data in Support of the Orbital Debris Program Office

The NASA Orbital Debris Program Office (ODPO) has used various optical assets to acquire photometric data of Earth-orbiting objects to define the orbital debris environment. To better characterize and model optical data acquired from ground-based telescopes, the Optical Measurements Center (OMC) at NASA Johnson Space Center emulates illumination conditions seen in space by using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. One of the OMC goals is to improve the size calculation used for optical data by developing an optical-based Size Estimation Model. The current size estimation requires applying a Lambertian phase function, a set albedo value, and range to the observed magnitude. The first step to improving the sampled brightness of laboratory targets is to remove aspect-angle dependencies. Then, the volume of possible object viewing angles is sampled at 21 combinations of azimuth and zenith angles for each solar phase angle. Finally, the acquired images are input into an image processing program that generates approximations for the object’s Bidirectional Reflectance Distribution Function (BRDF) and phase function. The BRDF is a radiometric concept that identifies an object’s material composition by matching a BRDF approximated with photometric data collected by ground-based telescopes with a BRDF generated experimentally from a known object in the laboratory. This paper discusses the validation of experimental BRDF and phase function approximations produced in the OMC and how the findings will be incorporated into ODPO models. A Lambertian sphere is imaged and the subsequent experimental functions are scrutinized to confirm that they correspond to an object that has an isotropic luminance. With the image processing algorithm validated, test objects with varying optical properties are then imaged to confirm that the produced photometric functions are both unique and repeatable. Once the validation is complete, the OMC will be used to evaluate a subset of fragments from a hypervelocity impact test of a mock-up satellite and assess the appropriate phase function and size estimates using BRDF measurements for a large volume of targets composed of various shapes, sizes, and materials.

Orbital Debris Program Office (ODPO)↗
NASA NTRS2018

Optimal Control Prediction Method for Control Allocation

This paper proposes a novel prediction method for online optimal control allocation that extends the volume of moments achievable with the Moore-Penrose generalized inverse to the entire Attainable Moment Set. This method formulates the control allocation problem using selected basis vectors and associated gains which reduces the optimization problem dimensions and provides physical insight into the resulting optimal solutions. The proposed algorithm finds the entire family of unique optimal control solutions along the desired moment vector from the origin to the boundary of the Attainable Moment Set. Numerical results for the Moore-Penrose prediction method show that the unique minimal controls obtained yield the desired moment with near machine precision accuracy while maintaining control effectors within specified position limits. This method has been fully validated against the unique solution obtained on the boundary of the Attainable Moment Set using the Durham Direct Allocation method. Minimal control solutions obtained for moments in the interior of the Attainable Moment Set, similarly yield the desired moment to near machine precision while providing control solutions that are smaller (i.e. 2-norm) than solutions found with traditional control allocation algorithms (e.g. interior point methods) applied to the minimal control problem. Numerical simulations using a Matlab® autocoded executable (MEX) for the representative real world problem of 3-moments with 20 individual control effectors and prescribed control position limits show a mean computation speed of approximately 125 Hz which is sufficient to enable real-time flight allocation.

Acheson, Michael J.↗
NASA NTRS2001

Accuracy Assessment of Response Surface Approximations for Supersonic Turbine Design

There is a growing trend to employ CFD tools to supply the necessary information for design optimization of fluid dynamics components/systems. Such results are prone to uncertainties due to reasons including discretization. errors, incomplete convergence of computational procedures, and errors associated with physical models such as turbulence closures. Based on this type of information, gradient-based optimization algorithms often suffer from the noisy calculations, which can seriously compromise the outcome. Similar problems arise from the experimental measurements. Global optimization techniques, such as those based on the response surface (RS) concept are becoming popular in part because they can overcome some of these barriers. However, there are also fundamental issues related to such global optimization technique such as RS. For example, in high dimensional design spaces, typically only a small number of function evaluations are available due to computational and experimental costs. On the other hand, complex features of the design variables do not allow one to model the global characteristics of the design space with simple quadratic polynomials. Consequently a main challenge is to reduce the size of the region where we fit the RS, or make it more accurate in the regions where the optimum is likely to reside. Response Surface techniques using either polynomials or and Neural Network (NN) methods offer designers alternatives to conduct design optimization. The RS technique employs statistical and numerical techniques to establish the relationship between design variables and objective/constraint functions, typically using polynomials. In this study, we aim at addressing issues related to the following questions: (1) How to identify outliers associated with a given RS representation and improve the RS model via appropriate treatments? (2) How to focus on selected design data so that RS can give better performance in regions critical to design optimization? (3) How to combine NN and polynomial techniques for improving the accuracy of the RS model?

Papila, Nilay↗
NASA NTRS2002

Evaluation of Methods to Estimate the Surface Downwelling Longwave Flux during Arctic Winter

Surface longwave radiation fluxes dominate the energy budget of nighttime polar regions, yet little is known about the relative accuracy of existing satellite-based techniques to estimate this parameter. We compare eight methods to estimate the downwelling longwave radiation flux and to validate their performance with measurements from two field programs in thc Arctic: the Coordinated Eastern Arctic Experiment (CEAREX ) conducted in the Barents Sea during the autumn and winter of 1988, and the Lead Experiment performed in the Beaufort Sea in the spring of 1992. Five of the eight methods were developed for satellite-derived quantities, and three are simple parameterizations based on surface observations. All of the algorithms require information about cloud fraction, which is provided from the NASA-NOAA Television and Infrared Observation Satellite (TIROS) Operational Vertical Sounder (TOVS) polar pathfinder dataset (Path-P): some techniques ingest temperature and moisture profiles (also from Path-P): one-half of the methods assume that clouds are opaque and have a constant geometric thickness of 50 hPa, and three include no thickness information whatsoever. With a somewhat limited validation dataset, the following primary conclusions result: (1) all methods exhibit approximately the same correlations with measurements and rms differences, but the biases range from -34 W sq m (16% of the mean) to nearly 0; (2) the error analysis described here indicates that the assumption of a 50-hPa cloud thickness is too thin by a factor of 2 on average in polar nighttime conditions; (3) cloud-overlap techniques. which effectively increase mean cloud thickness, significantly improve the results; (4) simple Arctic-specific parameterizations performed poorly, probably because they were developed with surface-observed cloud fractions; and (5) the single algorithm that includes an estimate of cloud thickness exhibits the smallest differences from observations.

Chiacchio, Marc↗
NASA NTRS1975

Joint pattern recognition/data compression concept for ERTS multispectral imaging

This paper describes a new technique which jointly applies clustering and source encoding concepts to obtain data compression. The cluster compression technique basically uses clustering to extract features from the measurement data set which are used to describe characteristics of the entire data set. In addition, the features may be used to approximate each individual measurement vector by forming a sequence of scalar numbers which define each measurement vector in terms of the cluster features. This sequence, called the feature map, is then efficiently represented by using source encoding concepts. A description of a practical cluster compression algorithm is given and experimental results are presented to show trade-offs and characteristics of various implementations. Examples are provided which demonstrate the application of cluster compression to multispectral image data of the Earth Resources Technology Satellite.

Hilbert, E. E.↗
NASA NTRS1991

Acquisition and tracking performance measurements for a high speed area array detector system

A proof-of-concept (POC) demonstration system has been developed which demonstrates acquisition, tracking and point-ahead angle sensing for a space optical communications terminal utilizing a single high speed area array detector. The detector is the 128 x 128 pixel Kodak HS-40 photodiode array. It has 64 parallel readout channels and can operate at frames rates up to 40,000 frames/sec with rms readout noise of 20 photoelectrons. A windowing scheme and special purpose digital signal processing electronics are employed to implement acquisition and tracking algorithms. The system operates at greater than 1 kHz sample (frame) rates. Acquisition can be performed in as little as 30 milliseconds with less than 1 picowatt of 0.85 micron beacon power on the detector. At the same power level, the rms tracking accuracy is approximately 1/16 pixel. Results of system analysis and measurements using the POC system are presented.

Short, R. C.↗
NASA NTRS2001

Cloud Spatial Structure and 3D Radiative Transfer

Cloud radiative properties are sensitive to drop size and other parameters of cloud micro-structure, but also to cloud shape, spacing, and other parameters of cloud macro-structure, including internal fractal structure. New information on cloud structure is being derived from a variety of cloud radars and lidars. Ongoing field programs such as DoE/ARM (atmospheric radiation measurement) are improving the measurement and modelling of physical and radiative properties of clouds. A parallel effort is underway to improve cloud remote sensing, especially from the new suite of EOS (Earth observing system) instruments which are beginning to provide higher spectral, spatial resolution, and/or angular resolution. Key parameters for improving pixel-scale retrievals are cloud thickness and photon mean-free-path, which together determine the scale of 'radiative smoothing' of cloud fluxes and radiances. This scale has been observed as a change in the spatial spectrum of Landsat cloud radiances, and was also recently found with the Goddard micropulse lidar, by searching for returns from directions nonparallel to the incident beam. 'Offbeam' Lidar returns are now being used to estimate the cloud 'radiative Green's function' (G). G depends on cloud thickness and may be used to retrieve that important quantity. G is also being applied to improving simple estimates of cloud radiative properties that are based on the 'Independent Pixel Approximation' or IPA. This and other measurements of 3D (three dimensional) transfer in clouds, coupled with Monte Carlo and other 3D transfer methods, are beginning to provide a better understanding of the dependence of radiation on cloud inhomogeneity, and to suggest new retrieval and parameterization algorithms which take account of cloud inhomogeneity. An international 'Intercomparison of 3D Radiation Codes' (I3RC) program is underway to coordinate and evaluate the variety of 3D radiative transfer methods now available, and to make them more widely available. Information is on the Web at: http://climate.gsfc.nasa.gov/I3RC. Input consists of selected cloud fields derived from data sources such as radar, microwave and satellite, and from models involved in the GEWEX Cloud Systems Studies. Output is selected radiative quantities that characterize the large-scale properties of the fields of radiative fluxes and heating. Several example cloud fields will be used to illustrate the effects of cloud inhomogeneity and 3D radiation.

Cahalan, Robert F.↗
NASA NTRS2010

Automatic Identification of Solar X-Ray Bright Points in Hinode X-Ray Data

We have automated a method that is used to find point sources in Chandra X-ray telescope data, to identify solar bright points in Hinode X-ray data. This tool, called lextrct, first identifies candidate sources that are brighter than the surrounding background. The algorithm also allows selected pixels to be excluded from the source-finding, thus allowing saturated pixels (from flares and/or active regions) to be ignored. We then use lextrct to fit the sources to two-dimensional, elliptical Gaussians. The size and orientation give an approximation of the shape of the bright points. We are in the process of analyzing observations through the Al_poly filter with a four-second exposure time, to obtain a catalogue of bright points, which will include their sizes, lifetimes, intensities, and position on the solar disk

Adams, M. L.↗
NASA NTRS2016

Improving Photometric Calibration of Meteor Video Camera Systems

Current optical observations of meteors are commonly limited by systematic uncertainties in photometric calibration at the level of approximately 0.5 mag or higher. Future improvements to meteor ablation models, luminous efficiency models, or emission spectra will hinge on new camera systems and techniques that significantly reduce calibration uncertainties and can reliably perform absolute photometric measurements of meteors. In this talk we discuss the algorithms and tests that NASA's Meteoroid Environment Office (MEO) has developed to better calibrate photometric measurements for the existing All-Sky and Wide-Field video camera networks as well as for a newly deployed four-camera system for measuring meteor colors in Johnson-Cousins BV RI filters. In particular we will emphasize how the MEO has been able to address two long-standing concerns with the traditional procedure, discussed in more detail below.

Ehlert, Steven↗
NASA NTRS2016

The Frequency of Giant Impacts on Earth-Like Worlds

The late stages of terrestrial planet formation are dominated by giant impacts that collectively influence the growth, composition, and habitability of any planets that form. Hitherto, numerical models designed to explore these late stage collisions have been limited by assuming that all collisions lead to perfect accretion, and many of these studies lack the large number of realizations needed to account for the chaotic nature of N-body systems. We improve on these limitations by performing 280 simulations of planet formation around a Sun-like star, half of which used an N-body algorithm that has recently been modified to include fragmentation and hit-and-run (bouncing) collisions. We find that when fragmentation is included, the final planets formed are comparable in terms of mass and number; however, their collision histories differ significantly and the accretion time approximately doubles. We explored impacts onto Earth-like planets, which we parameterized in terms of their specific impact energies. Only 15 of our 164 Earth-analogs experienced an impact that was energetic enough to strip an entire atmosphere. To strip about half of an atmosphere requires energies comparable to recent models of the Moon-forming giant impact. Almost all Earth-analogs received at least one impact that met this criteria during the 2 Gyr simulations and the median was three giant impacts. The median time of the final giant impact was 43 Myr after the start of the simulations, leading us to conclude that the time-frame of the Moon-forming impact is typical among planetary systems around Sun-like stars.

terrestrial planet formation↗
NASA NTRS1976

A block iterative finite element algorithm for numerical solution of the steady-state, compressible Navier-Stokes equations

An iterative method for numerically solving the time independent Navier-Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss-Seidel principle in block form to the systems of nonlinear algebraic equations which arise in construction of finite element (Galerkin) models approximating solutions of fluid dynamic problems. The C deg-cubic element on triangles is employed for function approximation. Computational results for a free shear flow at Re = 1,000 indicate significant achievement of economy in iterative convergence rate over finite element and finite difference models which employ the customary time dependent equations and asymptotic time marching procedure to steady solution. Numerical results are in excellent agreement with those obtained for the same test problem employing time marching finite element and finite difference solution techniques.

Cooke, C. H.↗
NASA NTRS1994

Climatic, eustatic, and tectnoic controls on Quarternary deposits and landforms, Red Sea coast, Egypt

The degree to which local climatic variations, eustatic sea level fluctuations, and tectonic uplift have influenced the development of Quaternary marine and fluvial landforms and deposits along the Red Sea coast, Eastern Desert, was investigated using a combination of remote sensing and field data, age determinations of corals, and numerical simulations. False color composites generated from Landsat Thematic Mapper and SPOT image data, digital elevation models derived from sterophotogrammetric analysis of SPOT data, and field observations document that a approximately 10-km wide swath inland from the coast is covered in many places with coalescing alluvial fans of Quaternary age. Wadis cutting through the fans exhibit several pairs of fluvial terraces, and wadi walls expose alluvium interbedded with corraline limestone deposits Further, three distinct coral terraces are evident along the coatline. Climatic, eustatic, and tectonic uplift controls on the overall system were simulated using a cellular automata algorithm with the following characteristics: (1) uplift as a function of position and time, as defined by the elevations and ages of corals; (2) climatic variations driven by insolation changes associated with Milankovitch cycles; (3) sea level fluctuations based on U/Th ages of coral terraces and eustatic data; and (4) parametrized fluvial erosion and deposition. Results imply that the fans and coralline limestones were generated in a setting in which the tectonic uplift rate decreased over the Quarternary to negligible values at present. Coralline limestones formed furing eustatic highstands when alluvium was trapped uspstream and wadis filled with debris. During lowstands, wadis cut into sedimentary deposits; coupled with continuing uplift, fans were dissected, leaving remnant surfaces, and wadi-related terraces were generated by down cutting. Only landforms from the past three to four eustatic sea level cycles (i.e., approximately 300 to 400 kyr) are likely to have survived erosion and deposition associated with fluvial processes.

Arvidson, Raymond↗
NASA NTRS1975

Design data collection with Skylab microwave radiometer-scatterometer S-193, volume 2

The author has identified the following significant results. Skylab S-193 radiometer/scatterometer produced terrain responses with various polarizations and observation angles for cells of 100 to 400 sq km area. Classification of the observations into natural categories was achieved by K-means and spatial clustering algorithms. Microwave data acquired over the Great Salt Lake Desert area by sensors aboard Skylab and Nimbus 5 indicate that the microwave emission and backscatter were strongly influenced by contributions from subsurface layers of sediment saturated with brine. Correlations were noted between microwave backscatter response at approximately 33 deg from scatterometer (operating at 13.9 GHz) and the configuration of ground targets in Brazil as discerned from coarse scale maps. With limited, available ground truth, these correlations were sufficient to permit the production of image-like displays which bear a marked resemblance to known terrain features in several instances.

Moore, R. K.↗
NASA NTRS1979

Atmospheric scattering corrections to solar radiometry

Whenever a solar radiometer is used to measure direct solar radiation, some diffuse sky radiation invariably enters the detector's field of view along with the direct beam. Therefore, the atmospheric optical depth obtained by the use of Bouguer's transmission law (also called Beer-Lambert's law), that is valid only for direct radiation, needs to be corrected by taking account of the scattered radiation. This paper discusses the correction factors needed to account for the diffuse (i,e., singly and multiply scattered) radiation and the algorithms developed for retrieving aerosol size distribution from such measurements. For a radiometer with a small field of view (half-cone angle of less than 5 deg) and relatively clear skies (optical depths less than 0.4), it is shown that the total diffuse contribution represents approximately 1% of the total intensity.

Box, M. A.↗