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NASA NTRS1994

Preliminary estimates of Gulf Stream characteristics from TOPEX data and a precise gravimetric geoid

TOPEX sea surface height data has been used, with a gravimetric geoid, to calculate sea surface topography across the Gulf Stream. This topography was initially computed for nine tracks on cycles 21 to 29. Due to inaccurate geoid undulations on one track, results for eight tracks are reported. The sea surface topography estimates were used to calculate parameters that describe Gulf Stream characteristics from two models of the Gulf Stream. One model was based on a Gaussian representation of the velocity while the other was a hyperbolic representation of velocity or the sea surface topography. The parameters of the Gaussian velocity model fit were a width parameter, a maximum velocity value, and the location of the maximum velocity. The parameters of the hyperbolic sea surface topography model were the width, the height jump, position, and sea surface topography at the center of the stream. Both models were used for the eight tracks and nine cycles studied. Comparisons were made between the width parameters, the maximum velocities, and the height jumps. Some of the parameter estimates were found to be highly (0.9) correlated when the hyperbolic sea surface topography fit was carried out, but such correlations were reduced for either the Gaussian velocity fits or the hyperbolic velocity model fit. A comparison of the parameters derived from 1-year TOPEX data showed good agreement with values derived by Kelly (1991) using 2.5 years of Geosat data near 38 deg N, 66 deg W longitude. Accuracy of the geoid undulations used in the calculations was of order of +/- 16 cm with the accuracy of a geoid undulation difference equal to +/- 15 cm over a 100-km line in areas with good terrestrial data coverage. This paper demonstrates that our knowledge or geoid undulations and undulation differences, in a portion of the Gulf Stream region, is sufficiently accurate to determine characteristics of the jet when used with TOPEX altimeter data. The method used here has not been shown to be more accurate than methods that average altimeter data to form a reference surface used in analysis to obtain the Gulf Stream characteristics. However, the results show the geoid approach may be used in areas where lack of current meandering reduces the accuracy of the average surface procedure.

Rapp, Richard H.↗
NASA NTRS1992

Purposive discovery of operations

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements.

Sims, Michael H.↗
NASA NTRS2011

Toward Realistic Dynamics of Rotating Orbital Debris, and Implications for Lightcurve Interpretation

Optical observations of rotating space debris near GEO contain important information on size, shape, composition, and rotational states, but these aspects are difficult to extract due to data limitations and the high number of degrees of freedom in the modeling process. For tri-axial rigid debris objects created by satellite fragmentations, the most likely initial rotation state has a large component of initial angular velocity directed along the intermediate axis of inertia, leading to large angular reorientations of the body on the timescale of the rotation period. This lends some support to the simplest possible interpretation of light curves -- that they represent sets of random orientations of the objects of study. However, effects of internal friction and solar radiation are likely to cause significant modification of rotation states within a time as short as a few orbital periods. In order to examine the rotational dynamics of debris objects under the influences of these effects, a set of seven first-order coupled equations of motion were assembled in state form: three are Euler equations describing the rates of change of the components of angular velocity in the body frame, and four describe the rates of change of the components of the unit quaternion. Quaternions are a four-dimensional extension of complex numbers that form a seamless, singularity-free representation of body orientation on S3. The Euler equations contain explicit terms describing torque from solar radiation in terms of spherical harmonics, and terms representing effects of a prescribed rate of internal friction. Numerical integrations of these equations of motion are being performed, and results will be presented. Initial tests show that internal friction without solar radiation torque leads to rotation about the maximum principal axis of inertia, as required, and solar radiation torque is expected to lead to spin-up of objects. Because the axis of maximum rotational inertia tends to be roughly coincident with the normal to the largest projected cross-sectional area, internal friction is expected to lead to reduced variation of light curve amplitudes at a given phase angle, but a large dependence of the same on phase angle. At a given phase angle, databases are generated which contain reflected intensities for comprehensive sets of equally-likely orientations, represented as unit quaternions. When projected onto three dimensions (S2) and color-coded by intensity, the set is depicted as points within a solid, semi-transparent unit sphere, within which all possible reflected intensities for an object at a given phase angle may be inspected simultaneously. Rotational sequences are represented by trajectories through the sphere. Databases are generated for each of a set of phase angles separately, forming a comprehensive dataset of reflected intensities spanning all object orientations and solar phase angles. Symmetries in the problem suggest that preferred rotation states are likely, defined relative to the object-sun direction in inertial space and relative to the maximum principal axis of inertia in the body coordinate system. Such rotation states may greatly simplify the problem of light curve interpretation by reducing the number of degrees of freedom in the problem.

Ojakangas, Gregory W.↗
NASA NTRS1992

Development of a residual acceleration data reduction and dissemination plan

A major obstacle in evaluating the residual acceleration environment in an orbiting space laboratory is the amount of data collected during a given mission: gigabytes of data will be available as SAMS units begin to fly regularly. Investigators taking advantage of the reduced gravity conditions of space should not be overwhelmed by the accelerometer data which describe these conditions. We are therefore developing a data reduction and analysis plan that will allow principal investigators of low-g experiments to create experiment-specific residual acceleration data bases for post-flight analysis. The basic aspects of the plan can also be used to characterize the acceleration environment of earth orbiting laboratories. Our development of the reduction plan is based on the following program of research: the identification of experiment sensitivities by order of magnitude estimates and numerical modelling; evaluation of various signal processing techniques appropriate for the reduction, supplementation, and dissemination of residual acceleration data; and testing and implementation of the plan on existing acceleration data bases. The orientation of the residual acceleration vector with respect to some set of coordinate axes is important for experiments with known directional sensitivity. Orientation information can be obtained from the evaluation of direction cosines. Fourier analysis is commonly used to transform time history data into the frequency domain. Common spectral representations are the amplitude spectrum which gives the average of the components of the time series at each frequency and the power spectral density which indicates the power or energy present in the series per unit frequency interval. The data reduction and analysis scheme developed involves a two tiered structure to: (1) identify experiment characteristics and mission events that can be used to limit the amount of accelerator data an investigator should be interested in; and (2) process the data in a way that will be meaningful to the experiment objectives. A general outline of the plan is given.

Rogers, Melissa J. B.↗
NASA NTRS2002

Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling

In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving ~he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required to obtain usable convergence from an iterative solver. The authors have examined the use of an Incomplete LU Threshold (ILUT) preconditioner . to solver linear systems stemming from higher order BEM/FEM formulations in 2D scattering problems. Although the resulting preconditioner provided aD excellent approximation to the system inverse, its size in terms of non-zero entries represented only a modest improvement when compared with the fill-in associated with a sparse direct solver. Furthermore, the fill-in of the preconditioner could not be substantially reduced without the occurrence of instabilities. In addition to the results for these 2D problems, the authors will present iterative solution data from the application of the ILUT preconditioner to 3D problems.

Fink, P. W.↗
NASA NTRS1998

Modelling and Estimation of Dynamic Ocean Topography Within Global Geopotential Solutions

In this poster, we will present a report on the ongoing investigation "Improved Gravitational and Dynamic Height Models Through the use of Oceanographic Data." we have used a two year mean (1993-1994) of the Dynamic ocean Topography (DOT) field implied by the Semtner and Chervin POCM_4B model, and developed normal equations in surface spherical harmonics to degree and order 30. These normal equations, were combined with normal equations derived from TOPEX and ERS-1 altimeter data over the same time period. Combination solutions (based on satellite tracking data, altimeter data, surface gravity data and OCM data) were were developed Test solutions were obtained estimating the DOT field to 2Ox2O and 3ox3O. These solutions were tested with independent DOT values computed over 38 WOCE hydrographic sections, which contained a total of 3072 stations and represented 216000 km of travelled lines. The weighted standard deviation of the differences between the DOT obtained from the hydrographic data and and the field estimated from the joint combination solutions was computed for each of the test models, the weighted standard deviation for the baseline combination solution excluding the POCM4_B data was 9.7 cm for a DOT solution to 30x30, where introducing the POCM4_B data into the combination model reduced the standard deviation to 9.2 cm, indicating the the introduction of oceanographic information benefits the solution for the dynamic ocean topography. We will discuss the weighting schemes applied and the method of solution. Another aspect of our investigation involves testing alternate parametric representations of the dynamic height field. We looked at the alternative representations in terms of the Proudman functions (PF), and compared these to the use of spherical harmonics (SH) to represent the dynamic ocean topography, using once again the 1993 and 1994 output of the POCM4_B OCM as the reference model. A significant advantage of PF's over SH's is that the former require no "fill-in" values over areas where the DOT is undefined. We show that the PF and SH results using equal number of parameters agree quite well in overall content. In addition, PFs appear better suited for representation of high frequency signals close to the signal boundary. The development of the PF solutions for the DOT will be described and the statistics of the comparisons will be presented.

Lemoine, Frank G.↗
NASA NTRSDate not supplied

Multiscale Modeling of Reconstructed Tricalcium Silicate using NASA Multiscale Analysis Tool

To study microstructure characteristics of cementitious materials hydrated in space; previously, cement binder formations were processed under microgravity conditions and was further compared against ground-based experiments. For accurate estimation of process-structure-property linkage, particularly on samples hydrated in the microgravity environment, it is desired to have a high-fidelity volumetric representation of the microstructure. However, owing to small sample size and high porosity of the space-returned samples, conventional experimental characterization techniques are not viable. Hence, a deep learning-based reconstruction algorithm was employed to obtain high fidelity 3D volumes from sparse high resolution 2D Scanning Electron Microscopy (SEM) images, as inputs to micromechanics-based modeling. This machine learning-based reconstruction methodology validated against low-order statistical descriptors, captured the microstructural topology of both sample types (ground, 1g and microgravity, μg). Due to the lack of gravity, hydration products of the samples processed in space differed from those processed-on ground. Such AI-generated virtual samples were analyzed in a multiscale recursive micromechanics approach using the NASA Multiscale Analysis Tool (NASMAT). Here, we present a methodology to rapidly integrate and evaluate these AI-generated volumes in NASMAT. The synthesized microstructural volumes are directly employed as Representative Volume Elements (RVEs) to preserve the fidelity (1 pixel = 0.54 m). Invariably, analysis of such largescale problems (5123 voxels) requires huge amount of computational resources. By taking advantage of the NASMAT architecture, we also focused on systematic multiscale integration of these AI-reconstructed virtual volumes to reduce the computational demands. In this work, this methodology is demonstrated on the ground-based, 1g samples. The estimated stiffness value of 15.90 GPa is comparable to experimentally obtained modulus of hydrated tricalcium silicate sample. The workflow presented here paves the way for utilizing the NASMAT tool to perform multiscale analyses of other multi-phase material systems using either 3D virtual datasets synthesized using AI or obtained via micro-CT.

Machine Learning↗
NASA NTRS2021

Validation Assessment for the Soil Moisture Active Passive (SMAP) Level 4 Carbon (L4_C) Data Product Version 5

The post-launch Cal/Val phase of the SMAP mission is guided by two primary objectives for each science product team: 1) to calibrate, verify, and improve the performance of the science algorithms, and 2) validate accuracies of the science data products as specified in the SMAP Level-1 mission science requirements. Algorithm science and product maintenance activities during the SMAP extended mission phase have also involved periodic algorithm calibration and product refinements to maintain or enhance product consistency and performance as well as science utility. This report provides an assessment of the latest (Version 5) SMAP Level 4 Carbon (L4_C) product. The L4_C Version 5 (v5) global record now spans more than six years (March 2015 – present) of SMAP operations and has benefited from five major reprocessing updates to the operational product. These reprocessing events and L4_C product release updates have incorporated various algorithm refinements and calibration adjustments to account for similar refinements to the upstream GEOS land model assimilation system, SMAP brightness temperatures, and MODIS vegetation inputs used for L4_C processing. The SMAP L4_C algorithms utilize a terrestrial carbon flux model informed by daily surface and root zone soil moisture information contributed from the SMAP Level 4 Soil Moisture (L4_SM) product along with optical remote sensing-based (e.g. MODIS-based) land cover and canopy fractional photosynthetic active radiation (fPAR), and other ancillary biophysical data. The carbon flux model estimates global daily net ecosystem CO2 exchange (NEE) and the component carbon fluxes, namely, vegetation gross primary production (GPP) and soil heterotrophic respiration (Rh). Other L4_C product elements include surface (~0-5 cm depth) soil organic carbon (SOC) stocks and associated environmental constraints to these processes, including soil moisture-related controls on GPP and ecosystem respiration (Kimball et al. 2014, Jones et al. 2017). The L4_C product addresses SMAP carbon cycle science objectives by: 1) providing a direct link between terrestrial carbon fluxes and underlying freeze/thaw and soil moisture-related constraints to these processes, 2) documenting primary connections between terrestrial water, energy and carbon cycles, and 3) improving understanding of terrestrial carbon sink activity. The SMAP L4_C algorithms and operational product are mature and at a CEOS Validation Stage 4 level (Jackson et al. 2012) based on extensive validation of the multi-year record against a diverse array of independent benchmarks, well characterized global performance, and systematic refinements gained from five major reprocessing events. There are no Level-1 mission science requirements for the L4_C product; however, self-imposed requirements have been established focusing on NEE as the primary product field for validation, and on demonstrating L4_C accuracy and success in meeting product science requirements (Jackson et al. 2012). The other L4_C product fields also have strong utility for carbon science applications (e.g., Liu et al. 2019, Endsley et al. 2020); however, analysis of these other fields is considered secondary relative to primary validation activities focusing on NEE. The L4_C targeted accuracy requirements are to meet or exceed a mean unbiased root-mean-square error (ubRMSE, or standard deviation of the error) for NEE of 1.6 g C m-2 d-1 and 30 g C m-2 yr-1, emphasizing northern (≥45°N) boreal and arctic ecosystems; this accuracy is similar to that of tower eddy covariance measurement-based observations (Baldocchi 2008). Methods used for the latest v5 L4_C product performance and validation assessment have been established from the SMAP Cal/Val plan and previous studies (Jackson et al. 2012, Jones et al. 2017) and include: 1) consistency evaluations of the product fields against earlier product releases (version 4 or earlier); 2) comparisons of daily carbon flux estimates with independent tower eddy 4covariance measurement-based daily carbon (CO2) flux observations from core tower validation sites (CVS); and 3) consistency checks against other global carbon products, including soil carbon inventory records, global GPP records derived from tower observation upscaling methods, and satellite-based observations of canopy solar induced chlorophyll fluorescence (SIF) as a surrogate for GPP. Metrics used to evaluate relative agreement between L4_C product fields and observational benchmarks include correlation (r-value), RMSE differences, bias and model sensitivity diagnostics. Following these validation criteria, the present report provides a validation assessment of the latest L4_C product release (v5). Detailed descriptions of the L4_C algorithm and additional global product accuracy and performance results are given elsewhere (Jones et al. 2017, Endsley et al. 2020). The v5 L4_C product replaces earlier product versions and continues to show: (i) accuracy and performance levels meeting or exceeding SMAP L4_C science requirements; (ii) improvement over the previous product version (version 4); and (iii) suitability for a diversity of science applications. Example L4_C applications from the recent literature include clarifying environmental trends and controls on the northern terrestrial carbon sink (Liu et al. 2019), diagnosing drought-related impacts on ecosystem productivity (Li et al. 2020), and regional monitoring of cropland conditions for projecting annual yields (Wurster et al. 2020). 2EXPECTED L4_C ALGORITHM AND PRODUCTPERFORMANCE The L4_C algorithm performance, including variance and uncertainty estimates of model outputs, was determined during the mission pre-launch phase through spatially explicit model sensitivity studies using available model inputs similar to those currently being used for operational production and evaluating the resulting model simulations over the observed range of northern (≥45 °N) and global conditions (Kimball et al. 2012, Entekhabi et al. 2014). The L4_C algorithm options were also evaluated during the mission prelaunch phase, including deriving canopy fPAR from lower order NDVI (Normalized Difference Vegetation Index) inputs in lieu of using MODIS (MOD15) fPAR; and including an explicit model representation of boreal fire disturbance recovery impacts. These results indicated that the L4_C accuracy requirements (i.e., NEE ubRMSE ≤ 30 g C m-2 yr-1or ≤ 1.6 g C m-2 d-1) could be met from the baseline algorithms over more than 82% and 89% of global and northern vegetated land areas, respectively (Yi et al. 2013, Kimball et al. 2014). The global L4_C algorithm error budget for NEE derived during the mission prelaunch phase indicated that the estimated NEE ubRMSE uncertainty is proportional to GPP and is therefore larger in higher biomass productivity areas, including forests and croplands (Kimball et al. 2014). Likewise, NEE ubRMSE uncertainty is expected to be lower in less-productive areas, including grasslands and shrublands. Expected model NEE ubRMSE levels were also generally within targeted accuracy levels for characteristically less-productive boreal and Arctic biomes, even though relative model error as a proportion of total productivity (NEE RMSE / GPP) may be large in these areas. The estimated NEE uncertainty was lower than expected in some warmer tropical high biomass productivity areas (e.g. Amazon rainforest) because of reduced low temperature and moisture constraints to the L4_C respiration calculations so that the bulk of model uncertainty is contributed by GPP in these areas. Model NEE uncertainty in the African Congo was estimated to

SMAP↗
NASA NTRS2000

Low-dimensional Representation of Error Covariance

Ensemble and reduced-rank approaches to prediction and assimilation rely on low-dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time-independent systems are used to identify factors that cause the steady-state analysis error covariance to admit a low-dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix, a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady-state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time-dependent systems. If much of the steady-state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady-state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting nonmodal transient growth. Failure to observe growing modes leads to increased steady-state analysis error variances. Leading eigenvectors of the steady-state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest-order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady-state analysis error covariance matrix.

Tippett, Michael K.↗
NASA NTRS1996

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance x,ary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are (1) determining, what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major U.S. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimility with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider un-modelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Patrick, Nicholas J. M.↗
NASA NTRS1996

Decision-Aiding and Optimization for Vertical Navigation of Long-Haul Aircraft

Most decisions made in the cockpit are related to safety, and have therefore been proceduralized in order to reduce risk. There are very few which are made on the basis of a value metric such as economic cost. One which can be shown to be value based, however, is the selection of a flight profile. Fuel consumption and flight time both have a substantial effect on aircraft operating cost, but they cannot be minimized simultaneously. In addition, winds, turbulence, and performance vary widely with altitude and time. These factors make it important and difficult for pilots to (a) evaluate the outcomes associated with a particular trajectory before it is flown and (b) decide among possible trajectories. The two elements of this problem considered here are: (1) determining what constitutes optimality, and (2) finding optimal trajectories. Pilots and dispatchers from major u.s. airlines were surveyed to determine which attributes of the outcome of a flight they considered the most important. Avoiding turbulence-for passenger comfort-topped the list of items which were not safety related. Pilots' decision making about the selection of flight profile on the basis of flight time, fuel burn, and exposure to turbulence was then observed. Of the several behavioral and prescriptive decision models invoked to explain the pilots' choices, utility maximization is shown to best reproduce the pilots' decisions. After considering more traditional methods for optimizing trajectories, a novel method is developed using a genetic algorithm (GA) operating on a discrete representation of the trajectory search space. The representation is a sequence of command altitudes, and was chosen to be compatible with the constraints imposed by Air Traffic Control, and with the training given to pilots. Since trajectory evaluation for the GA is performed holistically, a wide class of objective functions can be optimized easily. Also, using the GA it is possible to compare the costs associated with different airspace design and air traffic management policies. A decision aid is proposed which would combine the pilot's notion of optimality with the GA-based optimization, provide the pilot with a number of alternative pareto-optimal trajectories, and allow him to consider unmodelled attributes and constraints in choosing among them. A solution to the problem of displaying alternatives in a multi-attribute decision space is also presented.

Patrick, Nicholas J. M.↗
NASA NTRS2020

Analysis of Sample Acquisition Dynamics Using Discrete Element Method

The analysis presented in this paper is conducted in the framework of the Ocean Worlds Autonomy Testbed for Exploration Research and Simulation (OceanWATERS) project, currently under development at NASA Ames Research Center. OceanWATERS aims at designing a simulation environment which allows for testing autonomy of scientific lander missions to the icy moons of our solar system. Mainly focused on reproducing the end effector interaction with the inherent terrain, this paper introduces a novel discrete element method (DEM)-based approach to determine forces and torques acting on the lander’s scoop during the sample acquisition process. An accurate force feedback from the terrain on the scoop is required by fault-detection and autonomous decision-making algorithms to identify when the requested torque on the robotic arm’s joints exceeds the maximum available torque. Knowledge of the terrain force feedback significantly helps evaluating the arm’s links structural properties and properly selecting actuators for the joints. Models available in literature constitute a partial representation of the dynamics of the interaction. As an example, Balovnev derived an analytical expression of the vertical and horizontal force acting on a bucket while collecting a sample as a function of its geometry and velocity, soil parameters and reached depth. Although the model represents an adequate approximation of the two force components, it ignores the direction orthogonal to the scoop motion and neglects the torque. This work relies on DEM analysis to compensate for analytical models’ deficiencies and inaccuracies, i. e. provide force and torque 3D vectors, defined in the moving reference (body) frame attached to the scoop, at each instant of the sample collection process. Results from the first presented analysis relate to the specific OceanWATERS sampling strategy, which consists of collecting the sample through five consecutive passes with increasing depth, each pass following the same circularlinear- circular trajectory. Data is collected given a specific scoop design interacting with two types of bulk materials, which may characterize the surface of icy planetary bodies: snow and ice. Although specifically concerned with the OceanWATERS design, this first analysis provides the expected force trends for similar sampling strategies and allows to deduce phenomenological information about the general scooping process. In order to further instruct the community on the use of DEM tools as a solution to the sampling collection problem, two more analyses have been carried out, mainly focused on reducing the DEM computation time, which increases with a decrease in particle size. After running a set of identical simulations, where the only changing parameter is the size of the spherical particle, it is observed that the resulting force trajectories, starting from a given particle size, converge to the true trend. It is deducible that a further decrease in size yields negligible improvements in the accuracy, while it sensibly increases computation time. A final analysis aims at discussing limitations of approximating bulk material particles having a complex shape, e. g. ice fragments, with spheres, by comparing force trends resulting in the two cases for the same simulation scenario.

Catanoso, Damiana↗
NASA NTRS2016

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization↗
NASA NTRS1998

LAPS Lidar Measurements at the ARM Alaska Northslope Site (Support to FIRE Project)

This report consists of data summaries of the results obtained during the May 1998 measurement period at Barrow Alaska. This report does not contain any data interpretation or analysis of the results which will follow this activity. This report is forwarded with a data set on magnetic media which contains the reduced data from the LAPS lidar in 15 minute intervals. The data was obtained during the period 15-30 May 1998. The measurement period overlapped with several aircraft flights conducted by NASA as part of the FIRE project. The report contains a summary list of the data obtained plus figures that have been prepared to help visualize the measurement periods. The order of the presentation is as follows: Section 1. A copy of the Statement of Work for the planned activity of the second measurement period at the ARM Northslope site is provided. Section 2. A list of the data collection periods shows the number of one minute data records stored during each hour of operation and the corresponding size (Mbytes) of the one hour data folders. The folder and file names are composed from the year, month, day, hour and minute. The date/time information is given in UTC for easier comparison with other data sets. Section 3. A set of 4 comparisons between the LAPS lidar results and the sondes released by the ARM scientists from a location nearby the lidar. The lidar results show the +/- 1 sigma statistical error on each of the independent 75 m altitude bins of the data. This set of 4 comparisons was used to set and validate the calibration value which was then used for the complete data set. Section 4. A set of false color figures with up to 10 hours of specific humidity measurements are shown in each graph. Two days of measurements are shown on each page. These plots are crude representations of the data and permit a survey which indicates when the clouds were very low or where interesting events may occur in the results. These plots are prepared using the real time sequence plot program which has no smoothing in either the altitude or time (except that you are allowed to pick the integration time and time step. All of these plots were prepared with 15 minute integration and 5 minute time step. Section 5. A set of time sequence data for all of the extended observation periods are shown with a smoothing algorithm from the Matlab plotting library. Most of these data are integrated for 5 minutes and stepped at I minute intervals but several plots are shown with both 15 minute integration and 5 minute steps. The upper level on these data was selected and converted to the white background where the error in the specific humidity reached 25%. Section 6. The set of one hour integrated plots shown with up to 4 hours per page are provided- from the real time analysis snapshot program. The only difference in these plots and the real time display is that the plots are stopped at an altitude where the error appears to be too large for the data to contain any meaningful information.

Philbrick, C. Russell↗
NASA NTRS2006

Tilt and Translation Motion Perception during Pitch Tilt with Visual Surround Translation

The central nervous system must resolve the ambiguity of inertial motion sensory cues in order to derive an accurate representation of spatial orientation. Previous studies suggest that multisensory integration is critical for discriminating linear accelerations arising from tilt and translation head motion. Visual input is especially important at low frequencies where canal input is declining. The NASA Tilt Translation Device (TTD) was designed to recreate postflight orientation disturbances by exposing subjects to matching tilt self motion with conflicting visual surround translation. Previous studies have demonstrated that brief exposures to pitch tilt with foreaft visual surround translation produced changes in compensatory vertical eye movement responses, postural equilibrium, and motion sickness symptoms. Adaptation appeared greatest with visual scene motion leading (versus lagging) the tilt motion, and the adaptation time constant appeared to be approximately 30 min. The purpose of this study was to compare motion perception when the visual surround translation was inphase versus outofphase with pitch tilt. The inphase stimulus presented visual surround motion one would experience if the linear acceleration was due to foreaft self translation within a stationary surround, while the outofphase stimulus had the visual scene motion leading the tilt by 90 deg as previously used. The tilt stimuli in these conditions were asymmetrical, ranging from an upright orientation to 10 deg pitch back. Another objective of the study was to compare motion perception with the inphase stimulus when the tilts were asymmetrical relative to upright (0 to 10 deg back) versus symmetrical (10 deg forward to 10 deg back). Twelve subjects (6M, 6F, 22-55 yrs) were tested during 3 sessions separated by at least one week. During each of the three sessions (out-of-phase asymmetrical, in-phase asymmetrical, inphase symmetrical), subjects were exposed to visual surround translation synchronized with pitch tilt at 0.1 Hz for a total of 30 min. Tilt and translation motion perception was obtained from verbal reports and a joystick mounted on a linear stage. Horizontal vergence and vertical eye movements were obtained with a binocular video system. Responses were also obtained during darkness before and following 15 min and 30 min of visual surround translation. Each of the three stimulus conditions involving visual surround translation elicited a significantly reduced sense of perceived tilt and strong linear vection (perceived translation) compared to pre-exposure tilt stimuli in darkness. This increase in perceived translation with reduction in tilt perception was also present in darkness following 15 and 30 min exposures, provided the tilt stimuli were not interrupted. Although not significant, there was a trend for the inphase asymmetrical stimulus to elicit a stronger sense of both translation and tilt than the out-of-phase asymmetrical stimulus. Surprisingly, the inphase asymmetrical stimulus also tended to elicit a stronger sense of peak-to-peak translation than the inphase symmetrical stimulus, even though the range of linear acceleration during the symmetrical stimulus was twice that of the asymmetrical stimulus. These results are consistent with the hypothesis that the central nervous system resolves the ambiguity of inertial motion sensory cues by integrating inputs from visual, vestibular, and somatosensory systems.

O'Sullivan, Brita M.↗
NASA NTRS2015

An Upper Bound on Orbital Debris Collision Probability When Only One Object has Position Uncertainty Information

Upper bounds on high speed satellite collision probability, P (sub c), have been investigated. Previous methods assume an individual position error covariance matrix is available for each object. The two matrices being combined into a single, relative position error covariance matrix. Components of the combined error covariance are then varied to obtain a maximum P (sub c). If error covariance information for only one of the two objects was available, either some default shape has been used or nothing could be done. An alternative is presented that uses the known covariance information along with a critical value of the missing covariance to obtain an approximate but useful P (sub c) upper bound. There are various avenues along which an upper bound on the high speed satellite collision probability has been pursued. Typically, for the collision plane representation of the high speed collision probability problem, the predicted miss position in the collision plane is assumed fixed. Then the shape (aspect ratio of ellipse), the size (scaling of standard deviations) or the orientation (rotation of ellipse principal axes) of the combined position error ellipse is varied to obtain a maximum P (sub c). Regardless as to the exact details of the approach, previously presented methods all assume that an individual position error covariance matrix is available for each object and the two are combined into a single, relative position error covariance matrix. This combined position error covariance matrix is then modified according to the chosen scheme to arrive at a maximum P (sub c). But what if error covariance information for one of the two objects is not available? When error covariance information for one of the objects is not available the analyst has commonly defaulted to the situation in which only the relative miss position and velocity are known without any corresponding state error covariance information. The various usual methods of finding a maximum P (sub c) do no good because the analyst defaults to no knowledge of the combined, relative position error covariance matrix. It is reasonable to think, given an assumption of no covariance information, an analyst might still attempt to determine the error covariance matrix that results in an upper bound on the P (sub c). Without some guidance on limits to the shape, size and orientation of the unknown covariance matrix, the limiting case is a degenerate ellipse lying along the relative miss vector in the collision plane. Unless the miss position is exceptionally large or the at-risk object is exceptionally small, this method results in a maximum P (sub c) too large to be of practical use. For example, assuming that the miss distance is equal to the current ISS alert volume along-track (+ or -) distance of 25 kilometers and that the at-risk area has a 70 meter radius. The maximum (degenerate ellipse) P (sub c) is about 0.00136. At 40 kilometers, the maximum P (sub c) would be 0.00085 which is still almost an order of magnitude larger than the ISS maneuver threshold of 0.0001. In fact, a miss distance of almost 340 kilometers is necessary to reduce the maximum P (sub c) associated with this degenerate ellipse to the ISS maneuver threshold value. Such a result is frequently of no practical value to the analyst. Some improvement may be made with respect to this problem by realizing that while the position error covariance matrix of one of the objects (usually the debris object) may not be known the position error covariance matrix of the other object (usually the asset) is almost always available. Making use of the position error covariance information for the one object provides an improvement in finding a maximum P (sub c) which, in some cases, may offer real utility. The equations to be used are presented and their use discussed.

Frisbee, Joseph H., Jr.↗
NASA NTRS2015

AMO EXPRESS: A Command and Control Experiment for Crew Autonomy Onboard the International Space Station

NASA is investigating a range of future human spaceflight missions, including both Mars-distance and Near Earth Object (NEO) targets. Of significant importance for these missions is the balance between crew autonomy and vehicle automation. As distance from Earth results in increasing communication delays, future crews need both the capability and authority to independently make decisions. However, small crews cannot take on all functions performed by ground today, and so vehicles must be more automated to reduce the crew workload for such missions. NASA's Advanced Exploration Systems Program funded Autonomous Mission Operations (AMO) project conducted an autonomous command and control experiment on-board the International Space Station that demonstrated single action intelligent procedures for crew command and control. The target problem was to enable crew initialization of a facility class rack with power and thermal interfaces, and involving core and payload command and telemetry processing, without support from ground controllers. This autonomous operations capability is enabling in scenarios such as initialization of a medical facility to respond to a crew medical emergency, and representative of other spacecraft autonomy challenges. The experiment was conducted using the Expedite the Processing of Experiments for Space Station (EXPRESS) rack 7, which was located in the Port 2 location within the U.S Laboratory onboard the International Space Station (ISS). Activation and deactivation of this facility is time consuming and operationally intensive, requiring coordination of three flight control positions, 47 nominal steps, 57 commands, 276 telemetry checks, and coordination of multiple ISS systems (both core and payload). Utilization of Draper Laboratory's Timeliner software, deployed on-board the ISS within the Command and Control (C&C) computers and the Payload computers, allowed development of the automated procedures specific to ISS without having to certify and employ novel software for procedure development and execution. The procedures contained the ground procedure logic and actions as possible to include fault detection and recovery capabilities. The autonomous operations concept includes a reduction of the amount of data a crew operator is required to verify during activation or de-activation, as well as integration of procedure execution status and relevant data in a single integrated display. During execution, the auto-procedures (via Timerliner) provide a step-by-step messaging paradigm and a high-level status upon termination. This messaging and high-level status is the only data generated for operator display. To enhance situational awareness of the operator, the Web-based Procedure Display (WebPD) provides a novel approach to the issues of procedure display and execution tracking. WebPD is a web based application that serves as the user interface for electronic procedure execution. It incorporates several aspects of the HTML5 standard. Procedures are written in a dialect of XML called Procedure Representation Language (PRL). WebPD tracks execution status in the procedure or procedures being displayed. WebPD aggregates and simplifies the auto-sequence execution status information, and formatted to be easily followed and understood by an operator who is not dedicated to actively monitoring the task. WebPD also provides an integrated data and control interface to pause or halt the execution in order to provide a check point of operation and to examine progress before starting the next sequence of activities. For this demonstration, the procedure was initiated and monitored from the ground. As the Timeliner sequences executed, their high-level execution status was written to PLMDM memory. This memory is read and downlinked via Ku-Band at a 1 Hz rate. The data containing the high-level execution status is de-commutated on the ground, and rebroadcast for WebPD consumption. A future demonstration will be performed onboard, with ISS astronauts initiating the operations instead of ground controllers. The AMO EXPRESS experiment demonstrated activation and de-activation of EXPRESS rack 7, providing the capability of future single button activations and deactivations of facility class racks. The experiment achieved numerous technical and operations 'firsts' for the ISS

Stetson, Howard K.↗
NASA NTRS2018

GMI-IPS: Python Processing Software for Aircraft Campaigns

NASA's Atmospheric Tomography Mission (ATom) seeks to understand the impact of anthropogenic air pollution on gases in the Earth's atmosphere. Four flight campaigns are being deployed on a seasonal basis to establish a continuous global-scale data set intended to improve the representation of chemically reactive gases in global atmospheric chemistry models. The Global Modeling Initiative (GMI), is creating chemical transport simulations on a global scale for each of the ATom flight campaigns. To meet the computational demands required to translate the GMI simulation data to grids associated with the flights from the ATom campaigns, the GMI ICARTT Processing Software (GMI-IPS) has been developed and is providing key functionality for data processing and analysis in this ongoing effort. The GMI-IPS is written in Python and provides computational kernels for data interpolation and visualization tasks on GMI simulation data. A key feature of the GMI-IPS, is its ability to read ICARTT files, a text-based file format for airborne instrument data, and extract the required flight information that defines regional and temporal grid parameters associated with an ATom flight. Perhaps most importantly, the GMI-IPS creates ICARTT files containing GMI simulated data, which are used in collaboration with ATom instrument teams and other modeling groups. The initial main task of the GMI-IPS is to interpolate GMI model data to the finer temporal resolution (1-10 seconds) of a given flight. The model data includes basic fields such as temperature and pressure, but the main focus of this effort is to provide species concentrations of chemical gases for ATom flights. The software, which uses parallel computation techniques for data intensive tasks, linearly interpolates each of the model fields to the time resolution of the flight. The temporally interpolated data is then saved to disk, and is used to create additional derived quantities. In order to translate the GMI model data to the spatial grid of the flight path as defined by the pressure, latitude, and longitude points at each flight time record, a weighted average is then calculated from the nearest neighbors in two dimensions (latitude, longitude). Using SciPya's Regular Grid Interpolator, interpolation functions are generated for the GMI model grid and the calculated weighted averages. The flight path points are then extracted from the ATom ICARTT instrument file, and are sent to the multi-dimensional interpolating functions to generate GMI field quantities along the spatial path of the flight. The interpolated field quantities are then written to a ICARTT data file, which is stored for further manipulation. The GMI-IPS is aware of a generic ATom ICARTT header format, containing basic information for all flight campaigns. The GMI-IPS includes logic to edit metadata for the derived field quantities, as well as modify the generic header data such as processing dates and associated instrument files. The ICARTT interpolated data is then appended to the modified header data, and the ICARTT processing is complete for the given flight and ready for collaboration. The output ICARTT data adheres to the ICARTT file format standards V1.1. The visualization component of the GMI-IPS uses Matplotlib extensively and has several functions ranging in complexity. First, it creates a model background curtain for the flight (time versus model eta levels) with the interpolated flight data superimposed on the curtain. Secondly, it creates a time-series plot of the interpolated flight data. Lastly, the visualization component creates averaged 2D model slices (longitude versus latitude) with overlaid flight track circles at key pressure levels. The GMI-IPS consists of a handful of classes and supporting functionality that have been generalized to be compatible with any ICARTT file that adheres to the base class definition. The base class represents a generic ICARTT entry, only defining a single time entry and 3D spatial positioning parameters. Other classes inherit from this base class; several classes for input ICARTT instrument files, which contain the necessary flight positioning information as a basis for data processing, as well as other classes for output ICARTT files, which contain the interpolated model data. Utility classes provide functionality for routine procedures such as: comparing field names among ICARTT files, reading ICARTT entries from a data file and storing them in data structures, and returning a reduced spatial grid based on a collection of ICARTT entries. Although the GMI-IPS is compatible with GMI model data, it can be adapted with reasonable effort for any simulation that creates Hierarchical Data Format (HDF) files. The same can be said of its adaptability to ICARTT files outside of the context of the ATom mission. The GMI-IPS contains just under 30,000 lines of code, eight classes, and a dozen drivers and utility programs. It is maintained with GIT source code management and has been used to deliver processed GMI model data for the ATom campaigns that have taken place to date.

Damon, M. R.↗