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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

Linear and nonlinear dynamic analysis by boundary element method

An advanced implementation of the direct boundary element method (BEM) applicable to free-vibration, periodic (steady-state) vibration and linear and nonlinear transient dynamic problems involving two and three-dimensional isotropic solids of arbitrary shape is presented. Interior, exterior, and half-space problems can all be solved by the present formulation. For the free-vibration analysis, a new real variable BEM formulation is presented which solves the free-vibration problem in the form of algebraic equations (formed from the static kernels) and needs only surface discretization. In the area of time-domain transient analysis, the BEM is well suited because it gives an implicit formulation. Although the integral formulations are elegant, because of the complexity of the formulation it has never been implemented in exact form. In the present work, linear and nonlinear time domain transient analysis for three-dimensional solids has been implemented in a general and complete manner. The formulation and implementation of the nonlinear, transient, dynamic analysis presented here is the first ever in the field of boundary element analysis. Almost all the existing formulation of BEM in dynamics use the constant variation of the variables in space and time which is very unrealistic for engineering problems and, in some cases, it leads to unacceptably inaccurate results. In the present work, linear and quadratic isoparametric boundary elements are used for discretization of geometry and functional variations in space. In addition, higher order variations in time are used. These methods of analysis are applicable to piecewise-homogeneous materials, such that not only problems of the layered media and the soil-structure interaction can be analyzed but also a large problem can be solved by the usual sub-structuring technique. The analyses have been incorporated in a versatile, general-purpose computer program. Some numerical problems are solved and, through comparisons with available analytical and numerical results, the stability and high accuracy of these dynamic analysis techniques are established.

Ahmad, Shahid↗
NASA NTRS1995

Three-dimensional ring current decay model

This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawnside and duskside of the inner magnetosphere spanning the L value range L = 2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H(+) fluxes at tens of keV, which are always overestimated. A newly invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion differential flux. Important features of storm time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (less than 10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, J(sub o)(1 + Ay(sup n)), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (less than 30 keV), both drift dispersion and charge exchange are important in determining n.

Fok, Mei-Ching↗
NASA NTRS2000

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Fink, P. W.↗
NASA NTRS1991

Systematic methods for knowledge acquisition and expert system development

Nine cooperating rule-based systems, collectively called AUTOCREW which were designed to automate functions and decisions associated with a combat aircraft's subsystems, are discussed. The organization of tasks within each system is described; performance metrics were developed to evaluate the workload of each rule base and to assess the cooperation between the rule bases. Simulation and comparative workload results for two mission scenarios are given. The scenarios are inbound surface-to-air-missile attack on the aircraft and pilot incapacitation. The methodology used to develop the AUTOCREW knowledge bases is summarized. Issues involved in designing the navigation sensor selection expert in AUTOCREW's NAVIGATOR knowledge base are discussed in detail. The performance of seven navigation systems aiding a medium-accuracy INS was investigated using Kalman filter covariance analyses. A navigation sensor management (NSM) expert system was formulated from covariance simulation data using the analysis of variance (ANOVA) method and the ID3 algorithm. ANOVA results show that statistically different position accuracies are obtained when different navaids are used, the number of navaids aiding the INS is varied, the aircraft's trajectory is varied, and the performance history is varied. The ID3 algorithm determines the NSM expert's classification rules in the form of decision trees. The performance of these decision trees was assessed on two arbitrary trajectories, and the results demonstrate that the NSM expert adapts to new situations and provides reasonable estimates of the expected hybrid performance.

Belkin, Brenda L.↗
NASA NTRS2007

Robotic Vision-Based Localization in an Urban Environment

A system of electronic hardware and software, now undergoing development, automatically estimates the location of a robotic land vehicle in an urban environment using a somewhat imprecise map, which has been generated in advance from aerial imagery. This system does not utilize the Global Positioning System and does not include any odometry, inertial measurement units, or any other sensors except a stereoscopic pair of black-and-white digital video cameras mounted on the vehicle. Of course, the system also includes a computer running software that processes the video image data. The software consists mostly of three components corresponding to the three major image-data-processing functions: Visual Odometry This component automatically tracks point features in the imagery and computes the relative motion of the cameras between sequential image frames. This component incorporates a modified version of a visual-odometry algorithm originally published in 1989. The algorithm selects point features, performs multiresolution area-correlation computations to match the features in stereoscopic images, tracks the features through the sequence of images, and uses the tracking results to estimate the six-degree-of-freedom motion of the camera between consecutive stereoscopic pairs of images (see figure). Urban Feature Detection and Ranging Using the same data as those processed by the visual-odometry component, this component strives to determine the three-dimensional (3D) coordinates of vertical and horizontal lines that are likely to be parts of, or close to, the exterior surfaces of buildings. The basic sequence of processes performed by this component is the following: 1. An edge-detection algorithm is applied, yielding a set of linked lists of edge pixels, a horizontal-gradient image, and a vertical-gradient image. 2. Straight-line segments of edges are extracted from the linked lists generated in step 1. Any straight-line segments longer than an arbitrary threshold (e.g., 30 pixels) are assumed to belong to buildings or other artificial objects. 3. A gradient-filter algorithm is used to test straight-line segments longer than the threshold to determine whether they represent edges of natural or artificial objects. In somewhat oversimplified terms, the test is based on the assumption that the gradient of image intensity varies little along a segment that represents the edge of an artificial object.

Mchenry, Michael↗
NASA NTRS1994

A three-dimensional ring current decay model

This work is an extension of a previous ring current decay model. In the previous work, a two-dimensional kinetic model was constructed to study the temporal variations of the equatorially mirroring ring current ions, considering charge exchange and Coulomb drag losses along drift paths in a magnetic dipole field. In this work, particles with arbitrary pitch angle are considered. By bounce averaging the kinetic equation of the phase space density, information along magnetic field lines can be inferred from the equator. The three-dimensional model is used to simulate the recovery phase of a model great magnetic storm, similar to that which occurred in early February 1986. The initial distribution of ring current ions (at the minimum Dst) is extrapolated to all local times from AMPTE/CCE spacecraft observations on the dawn and dusk sides of the inner magnetosphere spanning the L value range L = 2.25 to 6.75. Observations by AMPTE/CCE of ring current distributions over subsequent orbits during the storm recovery phase are compared to model outputs. In general, the calculated ion fluxes are consistent with observations, except for H+ fluxes at tens of keV, which are always over-estimated. A newly-invented visualization idea, designated as a chromogram, is used to display the spatial and energy dependence of the ring current ion differential flux. Important features of storm-time ring current, such as day-night asymmetry during injection and drift hole on the dayside at low energies (less than 10 keV), are manifested in the chromogram representation. The pitch angle distribution is well fit by the function, j(sub o)(1+Ay(exp n)), where y is sine of the equatorial pitch angle. The evolution of the index n is a combined effect of charge exchange loss and particle drift. At low energies (less than 30 keV), both drift dispersion and charge exchange are important in determining n.

Fok, Mei-Ching↗
NASA NTRS2000

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗
NASA NTRS1996

Precision and Radiosonde Validation of Satellite Gridpoint Temperature Anomalies. Part I; MSU Channel 2: MSU Channel 2 - Pt. 1

In Part 1 of this study, monthly 2.5 deg. gridpoint anomalies in the TIROS-N (Television and Infrared Operational Satellite-N) series Microwave Sounding Unit (MSU) channel 2 brightness temperatures during 1979-88 are evaluated with multiple satellites and radiosonde data for their climate temperature monitoring capability. The MSU anomalies we computed about a 10-year mean annual cycle at each grid point, with the MSUs intercalibrated to a common arbitrary level. The intercalibrations remove relative biases between instruments of up to several tenths of a degree celsius. The monthly gridpoint anomaly agreement between concurrently operating satellites reveals single-satellite precision on generally better than 0.07 C in the tropics and better than 0.15 C at higher latitudes. Monthly anomalies in radiosonde channel 2 brightness temperatures computed with the radiative transfer equation compare very closely to the MSU measured anomalies in all climate zones, with correlations generally from 0.94 to 0.98 and standard errors of 0.15 C in the tropics to 0.30 C at high latitudes. Simplification of these radiative transfer calculations to a static weighting profile applied to the radiosonde temperature profile leads to an average degradation of only 0.02 deg. in the monthly skill. In terms of a more traditionally measured quantity, the MSU channel 2 anomalies match best with either the radiosonde 100-20-kPa or 100-15-kPa layer anomalies. No significant spurious trends were found in the 10-yr satellite dataset compared to the radiosondes that would indicate a calibration drift in either system. Thus, sequentially launched, overlapping passive microwave radiometers provide a useful system for monitoring intraseasonal to interannual climate anomalies and offer hope for monitoring of interdecadal trends from space. The Appendix includes previously unpublished details of the MSU gridpoint anomaly dataset construction. Part II of this study addresses the removal from channel 2 of the temperature influence above the 30-kPa level, providing a sharper and thus potentially more useful weighting function for monitoring lower tropospheric temperatures.

Spencer, Roy W.↗
NASA NTRS2010

Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations: Viscous Fluxes

Discretization of the viscous terms in current finite-volume unstructured-grid schemes are compared using node-centered and cell-centered approaches in two dimensions. Accuracy and complexity are studied for four nominally second-order accurate schemes: a node-centered scheme and three cell-centered schemes - a node-averaging scheme and two schemes with nearest-neighbor and adaptive compact stencils for least-square face gradient reconstruction. The grids considered range from structured (regular) grids to irregular grids composed of arbitrary mixtures of triangles and quadrilaterals, including random perturbations of the grid points to bring out the worst possible behavior of the solution. Two classes of tests are considered. The first class of tests involves smooth manufactured solutions on both isotropic and highly anisotropic grids with discontinuous metrics, typical of those encountered in grid adaptation. The second class concerns solutions and grids varying strongly anisotropically over a curved body, typical of those encountered in high-Reynolds number turbulent flow simulations. Tests from the first class indicate the face least-square methods, the node-averaging method without clipping, and the node-centered method demonstrate second-order convergence of discretization errors with very similar accuracies per degree of freedom. The tests of the second class are more discriminating. The node-centered scheme is always second order with an accuracy and complexity in linearization comparable to the best of the cell-centered schemes. In comparison, the cell-centered node-averaging schemes may degenerate on mixed grids, have a higher complexity in linearization, and can fail to converge to the exact solution when clipping of the node-averaged values is used. The cell-centered schemes using least-square face gradient reconstruction have more compact stencils with a complexity similar to that of the node-centered scheme. For simulations on highly anisotropic curved grids, the least-square methods have to be amended either by introducing a local mapping based on a distance function commonly available in practical schemes or modifying the scheme stencil to reflect the direction of strong coupling. The major conclusion is that accuracies of the node centered and the best cell-centered schemes are comparable at equivalent number of degrees of freedom.

Diskin, Boris↗
NASA NTRS1999

Ames Optimized TCA Configuration

Configuration design at Ames was carried out with the SYN87-SB (single block) Euler code using a 193 x 49 x 65 C-H grid. The Euler solver is coupled to the constrained (NPSOL) and the unconstrained (QNMDIF) optimization packages. Since the single block grid is able to model only wing-body configurations, the nacelle/diverter effects were included in the optimization process by SYN87's option to superimpose the nacelle/diverter interference pressures on the wing. These interference pressures were calculated using the AIRPLANE code. AIRPLANE is an Euler solver that uses a unstructured tetrahedral mesh and is capable of computations about arbitrary complete configurations. In addition, the buoyancy effects of the nacelle/diverters were also included in the design process by imposing the pressure field obtained during the design process onto the triangulated surfaces of the nacelle/diverter mesh generated by AIRPLANE. The interference pressures and nacelle buoyancy effects are added to the final forces after each flow field calculation. Full details of the (recently enhanced) ghost nacelle capability are given in a related talk. The pseudo nacelle corrections were greatly improved during this design cycle. During the Ref H and Cycle 1 design activities, the nacelles were only translated and pitched. In the cycle 2 design effort the nacelles can translate vertically, and pitch to accommodate the changes in the lower surface geometry. The diverter heights (between their leading and trailing edges) were modified during design as the shape of the lower wing changed, with the drag of the diverter changing accordingly. Both adjoint and finite difference gradients were used during optimization. The adjoint-based gradients were found to give good direction in the design space for configurations near the starting point, but as the design approached a minimum, the finite difference gradients were found to be more accurate. Use of finite difference gradients was limited by the CPU time limit available on the Cray machines. A typical optimization run using finite difference gradients can use only 30 to 40 design variables and one optimization iteration within the 8 hour queue limit for the chosen grid size and convergence level. The efficiency afforded by the adjoint method allowed for 50-120 design variables and 5-10 optimization iterations in the 8 hour queue. Geometric perturbations to the wing and fuselage were made using the Hicks/Henne (HH) shape functions. The HH functions were distributed uniformly along the chords of the wing defining sections and lofted linearly. During single-surface design, constraints on thickness and volume at selected wing stations were imposed. Both fuselage camber and cross-sectional area distributions were permitted to change during design. The major disadvantage to the use of these functions is the inherent surface waviness produced by repeated use of such functions. Many smoothing operations were required following optimization runs to produce a configuration with reasonable smoothness. Wagner functions were also used on the wing sections but were never used on the fuselage. The Wagner functions are a family of increasingly oscillatory functions that have also been used extensively in airfoil design. The leading and trailing edge regions of the wing were designed by use of polynomial and monomial functions respectively. Twist was attempted but was abandoned because of little performance improvement available from changing the baseline twist.

Cliff, Susan E.↗
NASA NTRS2011

High-Efficiency Ka-Band Waveguide Two-Way Asymmetric Power Combiner

NASA is planning a number of Space Exploration, Earth Observation and Space Science missions where Ka-band solid-state power amplifiers (SSPAs) could have a role. Monolithic microwave integrated circuit (MMIC) based SSPAs with output powers on the order of 10 W at Ka-band frequencies would be adequate to satisfy the data transmission rate requirements at the distances involved. MMICs are a type of integrated circuit fabricated on a GaAs wafer, which operates at micro wave frequencies and performs the function of signal amplification. The highest power Ka-band (31.8 to 32.3 GHz) SSPA to have flown in space had an output power of 2.6 W with an overall efficiency of 14.3 percent. This SSPA was built around discrete GaAs pHEMT (high electron mobility transistor) devices and flew aboard the Deep Space One spacecraft. State-of-the-art GaAs pHEMT-based MMIC power amplifiers (PAs) can deliver RF power at Ka-band frequencies anywhere from 3 W with a power added efficiency (PAE) of 32 percent to 6 W with a PAE of 26 percent. However, to achieve power levels higher than 6 W, the output of several MMIC PAs would need to be combined using a high-efficiency power combiner. Conventional binary waveguide power combiners, based on short-slot and magic-T circuits, require MMIC PAs with identical amplitude and phase characteristics for high combining efficiency. However, due to manufacturing process variations, the output powers of the MMIC PAs tend to be unequal, and hence the need to develop unequal power combiners. A two-way asymmetric magic-T based power combiner for MMIC power amplifiers, which can take in unequal inputs, has been successfully designed, fabricated, and characterized over NASA s Deep Space Network (DSN) frequency range of 31.8 to 32.3 GHz. The figure is a transparent view of the a sym - metric combiner that shows the 4-port configuration and the internal structure. The rod, post, and iris are positioned by design to achieve the desired asymmetric power ratio, phase equality, and port isolation. Although the combiner was designed for an input power ratio of 2:1, it can be custom-designed for any arbitrary power ratio and frequency range. The manufactured prototype combiner was precision machined from aluminum and is less than 2 in.3 (32.8 cm3). Previously investigated rectangular waveguide unequal power combiners were based on shunt/series coupling slots, E-plane septums, or H-plane T-junctions. All the prior art unequal power combiners operated at or below X-band (10 GHz) frequencies and were primarily used in the feed network of antenna arrays. The only reported asymmetric magic-T was developed as a 2:1 power divider for operation at a much lower frequency, around 500 MHz. The measured power ratio when tested as a power divider was very close to 2 and the phase balance was within 2.6, resulting in near ideal performance. When tested as a combiner using two MMIC SSPAs with a 2:1 power output ratio, an efficiency greater than 90 percent was demonstrated over the 500 MHz DSN frequency range. The return loss at the combiner output port (1) was greater than 18 dB and the input port (2 and 3) isolation was greater than 22 dB. The results show the asymmetric combiner to be a good candidate for high-efficiency power combining of two or more SSPAs needed to achieve the 6 to 10 W required by space communications systems of future NASA missions.

Wintucky, E. G.↗
NASA NTRS1995

Implications of Gamma-Ray Transparency Constraints in Blazars: Minimum Distances and Gamma-Ray Collimation

We develop a general expression for the gamma - gamma absorption coefficient, alpha(sub gamma(gamma)) for gamma-rays propagating in an arbitrary direction at an arbitrary point in space above an X-ray-emitting accretion disk. The X-ray intensity is assumed to vary as a power law in energy and radius between the outer disk radius, R(sub 0), and the inner radius, R(sub ms) which is the radius of marginal stability for a Schwarzschild black hole. We use our result for alpha(sub gamma(gamma)) to calculate the gamma - gamma optical depth, tau(sub gamma(gamma)) for gamma - rays created at height z and propagating at angle Phi relative to the disk axis, and we show that for Phi = 0 and z greater than or approx equal to R(sub 0), tau(sub gamma(gamma)) proportional to Epsilon(sup alpha)z(sup -2(alpha) - 3), where alpha is the X-ray spectral index and Epsilon is the gamma - ray energy. As an application, we use our formalism to compute the minimum distance between the central black hole and the site of production of the gamma-rays detected by EGRET during the 1991 June flare of 3C 279. In order to obtain an upper limit, we assume that all of the X-rays observed contemporaneously by Ginga were emitted by the disk. Our results suggest that the observed gamma - rays may have originated within less than or approx equal to 45 GM/sq c from a black hole of mass greater than or approx equal to 10(exp 9) solar mass, perhaps in active plasma located above the central funnel of the accretion disk. This raises the possibility of establishing a direct connection between the production of the observed gamma - rays and the accretion of material onto the black hole. We also consider the variation of the optical depth as a function of the angle of propagation Phi. Our results indicate that the "focusing" of the gamma - rays along the disk axis due to pair production is strong enough to explain the observed degree of alignment in blazar sources. If the gamma - rays are produced isotropically in gamma - ray blazars, then these objects should appear as bright MeV sources when viewed along off-axis lines of sight.

Becker, Peter A.↗
NASA NTRSDate not supplied

An Optimization Approach to Support Science Decision Making for Lunar Surface Exploration

Introduction: Scientific exploration is one of the three pillars of NASA’s Moon2Mars architecture, with crew surface extra vehicular activities (EVA) serving a critical enabling function. Development of surface EVA operational planning and execution, specifically integrating science and flight control teams (FCT), is currently being explored through analog scenarios. This integration, exercised, for example, through the Joint EVA and Hu-man Surface Mobility Test Team (JETT), allows for science input on EVA activities in near real-time through a Science Evaluation Room (SER), or Arte-mis science backroom, which integrates with the broader FCT through the Science Officer. The SER works within the FCT to support dynamic EVA planning in response to changes in operational constraints as well as science opportunities and re-prioritization, increasing the mission science return and accelerating the accomplishment of the Moon2Mars science objectives. The SER works within the FCT to provide recommendations to traverse execution in near real-time. One challenge is the requirement to deliver SER inputs to the FCT on operationally relevant timelines. Failure to do so may result in suboptimal execution of science exploration EVAs or even loss of key science objectives. To close this gap, we present a network optimization tool to allow the SER to provide rapid input to the FCT in response to changes in operational constraints or science opportunities. Inputs are predicated on approved science objectives, and clear rationale must be provided to the FCT for any requested change. Accordingly, this tool incorporates the Science Traceability Matrix (STM), SER prioritization scheme, and station characterization and action planning with operational constraints such as duration, traverse speed, and distance to maximize science objectives based on SER priorities, consistent with FCT operational requirements. Method: As a proof of concept, we used an existing linear programing software package used to simulate optimal routes through cellular metabolism. We built a Demonstrative Model with three STM objectives and four stations on a region of the Moon. The objectives were given an arbitrary prioritization and mapped to the stations through four possible crew actions. (Figs. 1 and 2). This station to STM mapping is consistent with the method used by the JETT5 Science Team to develop analog surface EVA science planning. We used a grid system with the landing site at the origin and the four stations placed across the positive x,y quadrant. Actions were assigned to each station and the accomplishment of those actions resulted in a numerical “reward” based on the ability of that action to achieve science objectives. The aggregate reward from each individual STM objective contributes to a global score (Science Yield), weighted by its priority. Operational constraints included a requirement to start and end at the landing site, 5 minutes each for initial station characterization and “clean up,” and variable total EVA time, traverse rate (fixed to 0.5 meters per second in our example), and time to perform each action (10, 5, 7, and 15 min for actions 1, 2, 3, and 4, respectively). Additional constraints and variables will be added in the future (e.g., sample mass, number of stations, traverse route constraints, illumination). Optimization. We converted the connections (arcs) between these stations (nodes) into a mixed integer linear programming optimization problem (arcs = constraints, nodes = variables) with the objective to maximize Science Yield. For any action, the Science Yield is equal to the relevance of that action to an STM objective [3, 2, and 1 point(s) for High, Med., and Low relevance, respectively], multiplied by the STM Objective Priority [3, 2, and 1 point(s) for High, Med., and Low priority, respectively]. This resulted in a model that computes the optimal station and action combination to maximize the Science Yield. These weightings can be adjusted by the SER as desired. Results: We explored three test cases for the Demonstrative Model. First, we set the maximum EVA duration to 120 minutes and computed the optimal route (Fig. 3A). The model suggested per-forming Actions 1 and 2 at Station P01, followed by Actions 1 and 2 at Station P02, and finally Actions 1 and 3 at Station P04 before returning to the Landing Site. Second, we adjusted the STM Objective Priori-ty order and computed the new optimal route (Fig. 3B). Under this situation, the model suggested per-forming all Actions at Station P02 followed by all Actions at Station P03. The previous test cases were relevant to SER planning activities. Next, we explored providing mid-EVA replanning input to the FCT. Scenario: While executing the Route in Fig. 3A the crew finishes at Station P01 and FCT decides that the EVA needs to finish in 45 minutes back at the Landing Site. FCT asks SER to recommend changes to the plan to accommodate this operation-al change. Using the model and incorporating these new constraints (start at Station P01, max. time of 45 min), the model suggested performing Actions 2 and 4 at Station P03 (Fig. 4), requiring 41 minutes to complete and return to the Landing Site. Interestingly, Station 3 was not part of the original route. Using the model, we determined the EVA would need 66 minutes, instead of 45, in order for the original Station P04 to yield a larger Science Yield than Station P03. The parametrization and simulation was per-formed in less than a minute, demonstrating the operational relevance of the approach. Future Efforts: The results from the Demonstrative Model suggest this tool can accelerate SER decision making on operationally relevant timelines. Use in analog activities, such as JETT5 or follow-ons, which have over a dozen stations for a crew to explore and over a dozen actions per station, will provide needed validation of the utility of this tool for planning EVAs, replanning mid-EVA, or planning follow-on EVAs based on previous results. Further integration with FCT execution monitoring tools may provide additional efficiency gains, al-lowing rapid and iterative exploration of operation-al and science decision space by the FCT and SER.

Science Operations↗
NASA NTRS2011

Broadband Achromatic Phase Shifter for a Nulling Interferometer

Nulling interferometry is a technique for imaging exoplanets in which light from the parent star is suppressed using destructive interference. Light from the star is divided into two beams and a phase shift of radians is introduced into one of the beams. When the beams are recombined, they destructively interfere to produce a deep null. For monochromatic light, this is implemented by introducing an optical path difference (OPD) between the two beams equal to lambda/2, where lambda is the wavelength of the light. For broadband light, however, a different phase shift will be introduced at each wavelength and the two beams will not effectively null when recombined. Various techniques have been devised to introduce an achromatic phase shift a phase shift that is uniform across a particular bandwidth. One popular technique is to use a series of dispersive elements to introduce a wavelength-dependent optical path in one or both of the arms of the interferometer. By intelligently choosing the number, material and thickness of a series of glass plates, a nearly uniform, arbitrary phase shift can be introduced between two arms of an interferometer. There are several constraints that make choosing the number, type, and thickness of materials a difficult problem, such as the size of the bandwidth to be nulled. Several solutions have been found for bandwidths on the order of 20 to 30 percent (Delta(lambda)/lambda(sub c)) in the mid-infrared region. However, uniform phase shifts over a larger bandwidth in the visible regime between 480 to 960 nm (67 percent) remain difficult to obtain at the tolerances necessary for exoplanet detection. A configuration of 10 dispersive glass plates was developed to be used as an achromatic phase shifter in nulling interferometry. Five glass plates were placed in each arm of the interferometer and an additional vacuum distance was also included in the second arm of the interferometer. This configuration creates a phase shift of pi radians with an average error of 5.97 x 10(exp -8) radians and standard deviation of 3.07 x 10(exp -4) radians. To reduce ghost reflections and interference effects from neighboring elements, the glass plates are tilted such that the beam does not strike each plate at normal incidence. Reflections will therefore walk out of the system and not contribute to the intensity when the beams are recombined. Tilting the glass plates, however, introduces several other problems that must be mitigated: (1) the polarization of a beam changes when refracted at an interface at non-normal incidence; (2) the beam experiences lateral chromatic spread as it traverses multiple glass plates; (3) at each surface, wavelength- dependent intensity losses will occur due to reflection. For a fixed angle of incidence, each of these effects must be balanced between each arm of the interferometer in order to ensure a deep null. The solution was found using a nonlinear optimization routine that minimized an objective function relating phase shift, intensity difference, chromatic beam spread, and polarization difference to the desired parameters: glass plate material and thickness. In addition to providing a uniform, broadband phase shift, the configuration achieves an average difference in intensity transmission between the two arms of the interferometer of 0.016 percent with a standard deviation of 3.64 x 10(exp -4) percent, an average difference in polarization between the two arms of the interferometer of 5.47 x 10(exp -5) percent with a standard deviation of 1.57 x 10(exp -6) percent, and an average chromatic beam shift between the two arms of the interferometer of -47.53 microns with a wavelength-by-wavelength spread of 0.389 microns.

Bolcar, Matthew R.↗
NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗
NASA NTRS2014

Clearance Analysis of Node 3 Aft CBM to the Stowed FGB Solar Array

In early 2011, the ISS Vehicle Configuration Office began considering the relocation of the Permanent Multipurpose Module (PMM) to the aft facing Common Berthing Mechanism (CBM) on Node 3 to open a berthing location for visiting vehicles on the Node 1 nadir CBM. In this position, computer-aided design (CAD) models indicated that the aft end of the PMM would be only a few inches from the stowed Functional Cargo Block (FGB) port solar array. To validate the CAD model clearance analysis, in the late summer of 2011 the Image Science and Analysis Group (ISAG) was asked to determine the true geometric relationship between the on-orbit aft facing Node 3 CBM and the FGB port solar array. The desired measurements could be computed easily by photogrammetric analysis if current imagery of the ISS hardware were obtained. Beginning in the fall of 2011, ISAG used the Dynamic Onboard Ubiquitous Graphics (DOUG) program to design a way to acquire imagery of the aft face of Node 3, the aft end-cone of Node 1, the port side of pressurized mating adapter 1 (PMA1), and the port side of the FGB out to the tip of the port solar array using cameras on the Space Station Remote Manipulator System (SSRMS). This was complicated by the need to thread the SSRMS under the truss, past Node 3 and the Cupola, and into the space between the aft side of Node 3 and the FGB solar array to acquire more than 100 images from multiple positions. To minimize the number of SSRMS movements, the Special Purpose Dexterous Manipulator (SPDM) would be attached to the SSRMS. This would make it possible to park the SPDM in one position and acquire multiple images by changing the viewing orientation of the SPDM body cameras using the pan/tilt units on which the cameras are mounted. Using this implementation concept, ISAG identified four SSRMS/SPDM positions from which all of the needed imagery could be acquired. Based on a photogrammetric simulation, it was estimated that the location of the FGB solar array could be measured within an accuracy of about 1 in. in each axis relative to the ISS Analysis Coordinate System (ISSACS). In October 2011, a proposed image-acquisition plan was drafted by ISAG and released for review. The ISS Robotics flight control team (ROBO) proposed minor changes to SPDM positions 1 and 4 to meet ISS proximity requirements. The updated image acquisition plan and draft chit were presented to and approved by the Systems Working Group (SWG) November 18 and were sent to the Vehicle Configuration Board (VCB) in early December 2011. Working with ROBO on 3 successive days (February 21, 22, and 23), ISAG collected 161 images of the ISS. Approximately 40 images were collected from each of the four different SSRMS/SPDM positions, with each set mapping the region from the Node 3 end cone, across Node 1, along the forward port side portion of the FGB, and out the port side FGB solar arrays. From this imagery, the best 80 images were selected for use in the analysis. The images were radiometrically enhanced to improve color and contrast and loaded into the FotoG analysis software along with the camera parameters and control data, which consisted of the coordinates for 54 handrail attachment bolts on the aft face of Node 3, in the ISSACS coordinate system. The results of this analysis produced the measured coordinates of 116 points distributed across the face of the FGB solar array panels (see figure 3) along with propagated uncertainty estimates in each coordinate axis. These results were sent to the ISS Vehicle Configuration Office, which sent them to the Configuration Analysis Modeling and Mass Properties (CAMMP) team for comparison with the Russian-provided CAD model for the retracted FGB solar arrays. The CAMMP analysis unexpectedly showed that the measured location of the port FGB solar array was up to 41-in. further outboard than the design and was slightly twisted about its rotational axis. The unexpected comparison results produced some initial concern regarding the accuracy of the photogrammetric measurements. To verify the measured results, ISAG personnel conducted a second analysis using just the imagery of the solar arrays in an arbitrary coordinate system defined by the three corner points of the inboard-most panel, with the design distance between points A1 and A10 as the only scale. The new measurements agreed with the original results to within less than 1 in. RMS in each axis, confirming the original solar array measurements. ISAG produced a final report for the ISS Vehicle Configuration Office documenting an apparent anomaly in the retracted configuration of the port FGB solar arrays. A copy of the measurement report was translated and sent to the Russian Space Agency. During a Vehicle Integrated Performance and Resources (VIPeR) teleconference September 24, 2012, the Russians acknowledged receipt of a translated copy of the ISAG report. The Russian representative stated that the head of the solar array design team claimed that the measured configuration was impossible unless the structure was physically broken. The Russians acknowledged that they had no expertise in photogrammetry, so the analysis technique employed was a "black box" to them, and they did not know how to use the ISAG results. They asked for a single image in which the overextension of the port solar array could be obviously seen. On November 10, 2012, during a face-to-face meeting with their Russian counterparts at JSC, ISAG presented nadir-view imagery of the FGB acquired during Space Shuttle rendezvous. Using the known width of the pressurized portion of the FGB as a scale, this analysis clearly showed that the port FGB solar array was extended outboard further than the Russian design for the retracted solar array.

Liddle, Donn↗