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NASA NTRS2008

A Study of Visualization for Mathematics Education

Graphical representations such as figures, illustrations, and diagrams play a critical role in mathematics and they are equally important in mathematics education. However, graphical representations in mathematics textbooks are static, Le. they are used to illustrate only a specific example or a limited set. of examples. By using computer software to visualize mathematical principles, virtually there is no limit to the number of specific cases and examples that can be demonstrated. However, we have not seen widespread adoption of visualization software in mathematics education. There are currently a number of software packages that provide visualization of mathematics for research and also software packages specifically developed for mathematics education. We conducted a survey of mathematics visualization software packages, summarized their features and user bases, and analyzed their limitations. In this survey, we focused on evaluating the software packages for their use with mathematical subjects adopted by institutions of secondary education in the United States (middle schools and high schools), including algebra, geometry, trigonometry, and calculus. We found that cost, complexity, and lack of flexibility are the major factors that hinder the widespread use of mathematics visualization software in education.

Daugherty, Sarah C.↗
NASA NTRS2008

Scripting Module for the Satellite Orbit Analysis Program (SOAP)

This add-on module to the SOAP software can perform changes to simulation objects based on the occurrence of specific conditions. This allows the software to encompass simulation response of scheduled or physical events. Users can manipulate objects in the simulation environment under programmatic control. Inputs to the scripting module are Actions, Conditions, and the Script. Actions are arbitrary modifications to constructs such as Platform Objects (i.e. satellites), Sensor Objects (representing instruments or communication links), or Analysis Objects (user-defined logical or numeric variables). Examples of actions include changes to a satellite orbit ( v), changing a sensor-pointing direction, and the manipulation of a numerical expression. Conditions represent the circumstances under which Actions are performed and can be couched in If-Then-Else logic, like performing v at specific times or adding to the spacecraft power only when it is being illuminated by the Sun. The SOAP script represents the entire set of conditions being considered over a specific time interval. The output of the scripting module is a series of events, which are changes to objects at specific times. As the SOAP simulation clock runs forward, the scheduled events are performed. If the user sets the clock back in time, the events within that interval are automatically undone. This script offers an interface for defining scripts where the user does not have to remember the vocabulary of various keywords. Actions can be captured by employing the same user interface that is used to define the objects themselves. Conditions can be set to invoke Actions by selecting them from pull-down lists. Users define the script by selecting from the pool of defined conditions. Many space systems have to react to arbitrary events that can occur from scheduling or from the environment. For example, an instrument may cease to draw power when the area that it is tasked to observe is not in view. The contingency of the planetary body blocking the line of sight is a condition upon which the power being drawn is set to zero. It remains at zero until the observation objective is again in view. Computing the total power drawn by the instrument over a period of days or weeks can now take such factors into consideration. What makes the architecture especially powerful is that the scripting module can look ahead and behind in simulation time, and this temporal versatility can be leveraged in displays such as x-y plots. For example, a plot of a satellite s altitude as a function of time can take changes to the orbit into account.

Carnright, Robert↗
NASA NTRS2008

Range Imaging without Moving Parts

Range-imaging instruments of a type now under development are intended to generate the equivalent of three-dimensional images from measurements of the round-trip times of flight of laser pulses along known directions. These instruments could also provide information on characteristics of targets, including roughnesses and reflectivities of surfaces and optical densities of such semi-solid objects as trees and clouds. Unlike in prior range-imaging instruments based on times of flight along known directions, there would be no moving parts; aiming of the laser beams along the known directions would not be accomplished by mechanical scanning of mirrors, prisms, or other optical components. Instead, aiming would be accomplished by using solid-state devices to switch input and output beams along different fiber-optic paths. Because of the lack of moving parts, these instruments could be extraordinarily reliable, rugged, and long-lasting. An instrument of this type would include an optical transmitter that would send out a laser pulse along a chosen direction to a target. An optical receiver coaligned with the transmitter would measure the temporally varying intensity of laser light reflected from the target to determine the distance and surface characteristics of the target. The transmitter would be a combination of devices for generating precise directional laser illumination. It would include a pulsed laser, the output of which would be coupled into a fiber-optic cable with a fan-out and solid-state optical switches that would enable switching of the laser beam onto one or more optical fibers terminated at known locations in an array on a face at the focal plane of a telescope. The array would be imaged by the telescope onto the target space. The receiver optical system could share the aforementioned telescope with the transmitter or could include a separate telescope aimed in the same direction as that of the transmitting telescope. In either case, light reflected from the target would be focused by the receiver optical system onto an array of optical fibers matching the array in the transmitter. These optical fibers would couple the received light to one or more photodetector( s). Optionally, the receiver could include solid-state optical switches for choosing which optical fiber(s) would couple light to the photodetector(s). This instrument architecture is flexible and can be optimized for a wide variety of applications and levels of performance. For example, it is scalable to any number of pixels and pixel resolutions and is compatible with a variety of ranging and photodetection methodologies, including, for example, ranging by use of modulated (including pulsed and encoded) light signals. The use of fixed arrays of optical fibers to generate controlled illumination patterns would eliminate the mechanical complexity and much of the bulk of optomechanical scanning assemblies. Furthermore, digital control of the selection of the fiber-optic pathways for the transmitted beams could afford capabilities not seen in previous three-dimensional range-imaging systems. Instruments of this type could be specialized for use as, for example, proximity detectors, three-dimensional robotic vision systems, airborne terrain-mapping systems, and inspection systems.

Blair, J. Bryan↗
NASA NTRS2008

Launching Science: Science Opportunities Provided by NASA's Constellation System

In 2004 NASA began implementation of the first phases of a new space exploration policy. This implementation effort included the development of a new human-carrying spacecraft, known as Orion; the Altair lunar lander; and two new launch vehicles, the Ares I and Ares V rockets.collectively called the Constellation System (described in Chapter 5 of this report). The Altair lunar lander, which is in the very preliminary concept stage, is not discussed in detail in the report. In 2007 NASA asked the National Research Council (NRC) to evaluate the science opportunities enabled by the Constellation System. To do so, the NRC established the Committee on Science Opportunities Enabled by NASA's Constellation System. In general, the committee interpreted "Constellation-enabled" broadly, to include not only mission concepts that required Constellation, but also those that could be significantly enhanced by Constellation. The committee intends this report to be a general overview of the topic of science missions that might be enabled by Constellation, a sort of textbook introduction to the subject. The mission concepts that are reviewed in this report should serve as general examples of kinds of missions, and the committee s evaluation should not be construed as an endorsement of the specific teams that developed the mission concepts or of their proposals. Additionally, NASA has a well-developed process for establishing scientific priorities by asking the NRC to conduct a "decadal survey" for a particular discipline. Any scientific mission that eventually uses the Constellation System will have to be properly evaluated by means of this decadal survey process. The committee was impressed with the scientific potential of many of the proposals that it evaluated. However, the committee notes that the Constellation System has been justified by NASA and selected in order to enable human exploration beyond low Earth orbit.not to enable science missions. Virtually all of the science mission concepts that could take advantage of Constellation s unique capabilities are likely to be prohibitively expensive. Several times in the past NASA has begun ambitious space science missions that ultimately proved too expensive for the agency to pursue. Examples include the Voyager-Mars mission and the Prometheus program and its Jupiter Icy Moons Orbiter spacecraft (both examples are discussed in Chapter 1). Finding: The scientific missions reviewed by the committee as appropriate for launch on an Ares V vehicle fall, with few exceptions, into the "flagship" class of missions. The preliminary cost estimates, based on mission concepts that at this time are not very detailed, indicate that the costs of many of the missions analyzed will be above $5 billion (in current dollars). The Ares V costs are not included in these estimates. All of the costs discussed in this report are presented in current-year (2008) dollars, not accounting for potential inflation that could occur between now and the decade in which these missions might be pursued. In general, preliminary cost estimates for proposed missions are, for many reasons, significantly lower than the final costs. Given the large cost estimates for many of the missions assessed in this report, the potentially large impacts on NASA's budget by many of these missions are readily apparent.

Source record↗
NASA NTRS2008

Some Expected Characteristics of Lunar Dust: A Geological View Applied to Engineering

Compared to the Earth the geologic nature of the lunar regolith is quite distinct. Even though similar minerals exist on the Earth and Moon, they may have very different properties due to the absence of chemical modification in the lunar environment. The engineering properties of the lunar regolith reflect aspects of the parent rock and the consequences of hypervelocity meteor bombardment. On scales relevant to machinery and chemical processing for In-Situ Resource Utilization, ISRU (such as water production), the lunar regolith compositional range is much more restricted than terrestrial material. This fact impacts predictions of properties required by design engineers for constructing equipment for lunar use. In this paper two examples will be covered. 1) Abrasion is related to hardness and hardness is a commonly measured property for both minerals and engineering materials. Although different hardness scales are routinely employed for minerals and engineering materials, a significant amount of literature is available relating the two. As one example, we will discuss how to relate hardness to abrasion for the design of lunar equipment. We also indicate how abundant the various mineral phases are and typical size distributions for lunar regolith which will impact abrasive nature. 2) Mineral characteristics that may seem trivial to the non-geologist or material scientist may have significant bearing on ISRU processing technologies. As a second example we discuss the impact of traces of F-, Cl-, and OH-, H2O, CO2, and sulfur species which can radically alter melting points and the corrosive nature of reaction products thereby significantly changing bulk chemistry and associated processing technologies. For many engineering uses, a simulant s fidelity to bulk lunar regolith chemistry may be insufficient. Therefore, simulant users need to engage in continuing dialogue with simulant developers and geoscientists.

Street, Kenneth W.↗
NASA NTRS2008

Dielectric Elastomer Actuated Systems and Methods

The system of the present invention includes an actuator having at least two electrodes, an elastomeric dielectric film disposed between the two electrodes, and a frame attached to the elastomeric dielectric film. The frame provides a linear actuation force characteristic over a displacement range. The displacement range is preferably the stroke of the actuator. The displacement range can be about 5 mm and greater. Further, the frame can include a plurality of configurations, for example, at least a rigid members coupled to a flexible member wherein the frame provides an elastic restoring force. In preferred embodiments, the rigid member can be, but is not limited to, curved beams, parallel beams, rods and plates. In a preferred embodiment the actuator can further include a passive element disposed between two flexible members such as, for example, links to tune a stiffness characteristic of the actuator. The passive element can be a bi-stable element. Further, the actuator can include a plurality of layers of the elastomeric dielectric film integrated into the frame. The elastomeric film can be made of different materials such as, for example, acrylic, silicone and latex.

Dubowsky, Steven↗
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 NTRS2008

Some Expected Characteristics of Lunar Dust: A Geological View Applied to Engineering

Compared to the Earth the geologic nature of the lunar regolith is quite distinct. Even though similar minerals exist on the Earth and Moon, they may have very different properties due to the absence of chemical modification in the lunar environment. The engineering properties of the lunar regolith reflect aspects of the parent rock and the consequences of hypervelocity meteor bombardment. On scales relevant to machinery and chemical processing for In-Situ Resource Utilization, ISRU (such as water production), the lunar regolith compositional range is much more restricted than terrestrial material. This fact impacts predictions of properties required by design engineers for constructing equipment for lunar use. In this paper two examples will be covered. 1) Abrasion is related to hardness and hardness is a commonly measured property for both minerals and engineering materials. Although different hardness scales are routinely employed for minerals and engineering materials, a significant amount of literature is available relating the two. As one example, we will discuss how to relate hardness to abrasion for the design of lunar equipment. We also indicate how abundant the various mineral phases are and typical size distributions for lunar regolith which will impact abrasive nature. 2) Mineral characteristics that may seem trivial to the non-geologist or material scientist may have significant bearing on ISRU processing technologies. As a second example we discuss the impact of traces of fluoride, chloride, and hydroxide, water, carbon dioxide, and sulfur species which can radically alter melting points and the corrosive nature of reaction products thereby significantly changing bulk chemistry and associated processing technologies. For many engineering uses, a simulant's fidelity to bulk lunar regolith chemistry may be insufficient. Therefore, simulant users need to engage in continuing dialogue with simulant developers and geoscientists.

Street, Kenneth W.↗
NASA NTRS2009

When Failure Means Success: Accepting Risk in Aerospace Development

Over the last three decades, NASA has been diligent in qualifying systems for human space flight. As the Agency transitions from operating the Space Shuttle, its employees must learn to accept higher risk levels to generate the data needed to certify its next human space flight system. The Marshall Center s Engineering workforce is developing the Ares I crew launch vehicle and designing the Ares V cargo launch vehicle for safety, reliability, and cost-effective operations. This presentation will provide a risk retrospective, using first-hand examples from the Delta Clipper-Experimental Advanced (DC-XA) and the X-33 single-stage-to-orbit flight demonstrators, while looking ahead to the upcoming Ares I-X uncrewed test flight. The DC-XA was successfully flown twice in 26 hours, setting a new turnaround-time record. Later, one of its 3 landing gears did not deploy, it tipped over, and was destroyed. During structural testing, the X-33 s advanced composite tanks were unable to withstand the forces to which it was subjected and the project was later cancelled. These are examples of successful failures, as the data generated are captured in databases used by vehicle designers today. More recently, the Ares I-X flight readiness review process was streamlined in keeping with the mission's objectives, since human lives are not at stake, which reflects the beginning of a cultural change. Failures are acceptable during testing, as they provide the lessons that actually lead to mission success. These and other examples will stimulate the discussion of when to accept risk in aerospace projects.

Dumbacher, Daniel L.↗
NASA NTRS2009

Hybrid NN/SVM Computational System for Optimizing Designs

A computational method and system based on a hybrid of an artificial neural network (NN) and a support vector machine (SVM) (see figure) has been conceived as a means of maximizing or minimizing an objective function, optionally subject to one or more constraints. Such maximization or minimization could be performed, for example, to optimize solve a data-regression or data-classification problem or to optimize a design associated with a response function. A response function can be considered as a subset of a response surface, which is a surface in a vector space of design and performance parameters. A typical example of a design problem that the method and system can be used to solve is that of an airfoil, for which a response function could be the spatial distribution of pressure over the airfoil. In this example, the response surface would describe the pressure distribution as a function of the operating conditions and the geometric parameters of the airfoil. The use of NNs to analyze physical objects in order to optimize their responses under specified physical conditions is well known. NN analysis is suitable for multidimensional interpolation of data that lack structure and enables the representation and optimization of a succession of numerical solutions of increasing complexity or increasing fidelity to the real world. NN analysis is especially useful in helping to satisfy multiple design objectives. Feedforward NNs can be used to make estimates based on nonlinear mathematical models. One difficulty associated with use of a feedforward NN arises from the need for nonlinear optimization to determine connection weights among input, intermediate, and output variables. It can be very expensive to train an NN in cases in which it is necessary to model large amounts of information. Less widely known (in comparison with NNs) are support vector machines (SVMs), which were originally applied in statistical learning theory. In terms that are necessarily oversimplified to fit the scope of this article, an SVM can be characterized as an algorithm that (1) effects a nonlinear mapping of input vectors into a higher-dimensional feature space and (2) involves a dual formulation of governing equations and constraints. One advantageous feature of the SVM approach is that an objective function (which one seeks to minimize to obtain coefficients that define an SVM mathematical model) is convex, so that unlike in the cases of many NN models, any local minimum of an SVM model is also a global minimum.

Rai, Man Mohan↗
NASA NTRS2009

An Assessment of GEO Orbital Debris Photometric Properties Derived from Laboratory-Based Measurements

Optical observations of orbital debris offer insights that differ from radar measurements (specifically the size parameter and wavelength regime). For example, time-dependent photometric data yield lightcurves in multiple bandpasses that aid in material identification and possible periodic orientations. This data can also be used to help identify shapes and optical properties at multiple phase angles. Capitalizing on optical data products and applying them to generate a more complete understanding of orbital space objects, is a key objective of NASA s Optical Measurement Program, and a primary driver for creation of the Optical Measurements Center (OMC). The OMC attempts to emulate space-based illumination conditions using equipment and techniques that parallel telescopic observations and source-target-sensor orientations. The OMC uses a 300 Watt Xenon arc lamp as a solar simulator, a CCD camera with Johnson/Bessel colored filters, and a robotic arm to orientate/rotate objects to simulate an object's orbit/rotational period. A high-resolution, high bandwidth (350nm-2500nm) Analytical Spectral Devices (ASD) spectrometer is also employed to baseline various material types. Since observation of GEO targets are generally restricted to the optical regime (due to radar range limitations), analysis of their properties is tailored to those revealed by optical data products. In this connection, much attention has been directed towards understanding the lightcurves of orbital debris with high area-to-mass (A/m) ratios (greater than 0.9 square meters per kilogram). A small population of GEO debris was recently identified, which exhibits the properties of high A/m objects, such as variable eccentricities and inclinations a dynamical characteristic generally resulting from varying solar radiation pressure on high A/m objects. Materials such as multi-layered insulation (MLI) and solar panels are two examples of materials with high area-to mass ratios. Lightcurves for such objects can vary greatly (even for the same object under different illumination conditions). For example, specular reflections from multiple facets of the target surface (e.g. Mylar or Aluminized Kapton) can lead to erratic, orientation-dependent light curves. This paper will investigate published color photometric data for a series of orbital debris targets and compare it to the empirical photometric measurements generated in the OMC. The specific materials investigated (known to exist in GEO) are: an intact piece of MLI, separated layers of MLI, and multiple solar cells materials. Using the data acquired over specific rotational angles through different filters (B, V, R, I), a color index is acquired (B-R, R-I). As a secondary check, the spectrometer is used to define color indexes for the same material. Using these values and their associated lightcurves, this laboratory data is compared to observational data obtained on the 1m telescope of the Astronomical Institute of the University of Bern (AUIB) and the 0.9 m Small and Moderate Aperture Research Telescope System (SMARTS) telescope at Cerro Tololo Inter-American Observatory (CTIO). We will present laboratory generated lightcurves with color indexes of the high A/m materials alongside telescopic data of targets with high A/m values. We will discuss the relationship of laboratory to telescope data in the context of classification of GEO debris objects.

Rodriquez-Cowardin, H.↗
NASA NTRS2009

Human/Automation Trade Methodology for the Moon, Mars and Beyond

It is possible to create a consistent trade methodology that can characterize operations model alternatives for crewed exploration missions. For example, a trade-space that is organized around the objective of maximizing Crew Exploration Vehicle (CEV) independence would have the input as a classification of the category of analysis to be conducted or decision to be made, and a commitment to a detailed point in a mission profile during which the analysis or decision is to be made. For example, does the decision have to do with crew activity planning, or life support? Is the mission phase trans-Earth injection, cruise, or lunar descent? Different kinds of decision analysis of the trade-space between human and automated decisions will occurs at different points in a mission's profile. The necessary objectives at a given point in time during a mission will call for different kinds of response with respect to where and how computers and automation are expected to help provide an accurate, safe, and timely response. In this paper, a consistent methodology for assessing the trades between human and automated decisions on-board will be presented and various examples discussed.

Korsmeyer, David J.↗
NASA NTRS2009

Constructing LDPC Codes from Loop-Free Encoding Modules

A method of constructing certain low-density parity-check (LDPC) codes by use of relatively simple loop-free coding modules has been developed. The subclasses of LDPC codes to which the method applies includes accumulate-repeat-accumulate (ARA) codes, accumulate-repeat-check-accumulate codes, and the codes described in Accumulate-Repeat-Accumulate-Accumulate Codes (NPO-41305), NASA Tech Briefs, Vol. 31, No. 9 (September 2007), page 90. All of the affected codes can be characterized as serial/parallel (hybrid) concatenations of such relatively simple modules as accumulators, repetition codes, differentiators, and punctured single-parity check codes. These are error-correcting codes suitable for use in a variety of wireless data-communication systems that include noisy channels. These codes can also be characterized as hybrid turbolike codes that have projected graph or protograph representations (for example see figure); these characteristics make it possible to design high-speed iterative decoders that utilize belief-propagation algorithms. The present method comprises two related submethods for constructing LDPC codes from simple loop-free modules with circulant permutations. The first submethod is an iterative encoding method based on the erasure-decoding algorithm. The computations required by this method are well organized because they involve a parity-check matrix having a block-circulant structure. The second submethod involves the use of block-circulant generator matrices. The encoders of this method are very similar to those of recursive convolutional codes. Some encoders according to this second submethod have been implemented in a small field-programmable gate array that operates at a speed of 100 megasymbols per second. By use of density evolution (a computational- simulation technique for analyzing performances of LDPC codes), it has been shown through some examples that as the block size goes to infinity, low iterative decoding thresholds close to channel capacity limits can be achieved for the codes of the type in question having low maximum variable node degrees. The decoding thresholds in these examples are lower than those of the best-known unstructured irregular LDPC codes constrained to have the same maximum node degrees. Furthermore, the present method enables the construction of codes of any desired rate with thresholds that stay uniformly close to their respective channel capacity thresholds.

Divsalar, Dariush↗
NASA NTRS2008

Increasing the Cost-efficiency of the DSN

JPL has operated the Deep Space Network (DSN) on behalf of NASA since the 1960's. Over the last two decades, the DSN budget has generally declined in real-year dollars while the aging assets required more attention, and the missions became more complex. As a result, the budget has been increasingly consumed by Operations and Maintenance (O and M), significantly reducing the funding wedge available for technology investment and for enhancing the DSN capability and capacity. Responding to this budget squeeze, the DSN launched an effort to improve the cost-efficiency of the O and M. In this paper we: Analyze the components of O&M. We note for example that, for the DSN, less than 20% of the staff engage in the traditional human-in-front-a-console role, so any effort to increase the cost efficiency must go beyond reducing the number of "Real-time operators." Explain the underlying organizational and cultural structures. Any cost-efficiency activities changes either accept, or carefully modify these structures. For example, the DSN O&M is based on the concept that there are three nearly identical antenna complexes separated by approximately 1200 in latitude and that each antenna complex is operated by a different contractor (driven by international agreements). Explore planned changes in the customer interface, e.g. web-based automated scheduling, and the processes required for a transition. Changes have to be evaluated in the larger end-to-end context, e.g. do the changes provide a net cost-efficiency for the DSN and the missions, or do they merely shift cost from the DSN to the missions. Consider possible significant changes in real-time pass management, e.g. full-remoting of operations, and lights-dim operations, while maintaining (or improving) the performance metrics of the DSN. Investigate how procedural and administrative changes could increase cost-efficiency, in conjunction with changes in the customer interfaces and real-time pass management. Examples would be handling of inter-governmental agreements, improved sharing of resources with other agencies, and better use of commercial (rather than government) resources

Deep Space Network (DSN)↗
NASA NTRS2007

Automated Knowledge Discovery From Simulators

A computational method, SimLearn, has been devised to facilitate efficient knowledge discovery from simulators. Simulators are complex computer programs used in science and engineering to model diverse phenomena such as fluid flow, gravitational interactions, coupled mechanical systems, and nuclear, chemical, and biological processes. SimLearn uses active-learning techniques to efficiently address the "landscape characterization problem." In particular, SimLearn tries to determine which regions in "input space" lead to a given output from the simulator, where "input space" refers to an abstraction of all the variables going into the simulator, e.g., initial conditions, parameters, and interaction equations. Landscape characterization can be viewed as an attempt to invert the forward mapping of the simulator and recover the inputs that produce a particular output. Given that a single simulation run can take days or weeks to complete even on a large computing cluster, SimLearn attempts to reduce costs by reducing the number of simulations needed to effect discoveries. Unlike conventional data-mining methods that are applied to static predefined datasets, SimLearn involves an iterative process in which a most informative dataset is constructed dynamically by using the simulator as an oracle. On each iteration, the algorithm models the knowledge it has gained through previous simulation trials and then chooses which simulation trials to run next. Running these trials through the simulator produces new data in the form of input-output pairs. The overall process is embodied in an algorithm that combines support vector machines (SVMs) with active learning. SVMs use learning from examples (the examples are the input-output pairs generated by running the simulator) and a principle called maximum margin to derive predictors that generalize well to new inputs. In SimLearn, the SVM plays the role of modeling the knowledge that has been gained through previous simulation trials. Active learning is used to determine which new input points would be most informative if their output were known. The selected input points are run through the simulator to generate new information that can be used to refine the SVM. The process is then repeated. SimLearn carefully balances exploration (semi-randomly searching around the input space) versus exploitation (using the current state of knowledge to conduct a tightly focused search). During each iteration, SimLearn uses not one, but an ensemble of SVMs. Each SVM in the ensemble is characterized by different hyper-parameters that control various aspects of the learned predictor - for example, whether the predictor is constrained to be very smooth (nearby points in input space lead to similar output predictions) or whether the predictor is allowed to be "bumpy." The various SVMs will have different preferences about which input points they would like to run through the simulator next. SimLearn includes a formal mechanism for balancing the ensemble SVM preferences so that a single choice can be made for the next set of trials.

Burl, Michael↗
NASA NTRS2007

Loss-of-Control-Inhibitor Systems for Aircraft

Systems to provide improved tactile feedback to aircraft pilots are being developed to help the pilots maintain harmony between their control actions and the positions of aircraft control surfaces, thereby helping to prevent loss of control. A system of this type, denoted a loss-of-control-inhibitor system (LOCIS) can be implemented as a relatively simple addition to almost any pre-existing flight-control system. The LOCIS concept offers at least a partial solution to the problem of (1) keeping a pilot aware of the state of the control system and the aircraft and (2) maintaining sufficient control under conditions that, as described below, have been known to lead to loss of control. Current commercial aircraft exhibit uneven responses of primary flight-control surfaces to aggressive pilot control commands, leading to deterioration of pilots ability to control their aircraft. In severe cases, this phenomenon can result in loss of control and consequent loss of aircraft. For an older aircraft equipped with a purely mechanical control system, the loss of harmony between a pilot s command action and the control- surface response can be attributed to compliance in the control system (caused, for example, by stretching of control cables, flexing of push rods, or servo-valve distortion). In a newer aircraft equipped with a fly-by-wire control system, the major contributions to loss of harmony between the pilot and the control surfaces are delays attributable to computer cycle time, control shaping, filtering, aliasing, servo-valve distortion, and actuator rate limiting. In addition, a fly-by-wire control system provides no tactile feedback that would enable the pilot to sense such features of the control state as surface flutter, surface jam, position limiting, actuator rate limiting, and control limiting imposed by the aircraft operational envelope. Hence, for example, when a pilot is involved in aggressive closed-loop maneuvering, as when encountering a wake-vortex upset on final landing approach, the control-surface delay can lead to loss of control. Aggressive piloting can be triggered and exacerbated by control-system anomalies, which the pilot cannot diagnose because of the lack of symptoms caused by the absence of feedback through the controls. The purpose served by a LOCIS is to counteract these adverse effects by providing real-time feedback that notifies the pilot that the aircraft is tending to lag the pilot s commands. A LOCIS (see figure) includes cockpit control input-position sensors, control-surface output-position sensors, variable dampers (for example, shock absorbers containing magneto-rheological fluids such that the damping forces can be varied within times of the order of milliseconds by varying applied magnetic fields) attached to the cockpit control levers, electromagnet coils to apply the magnetic fields, and feedback control circuits to drive the electromagnet coils. The feedback control gains are chosen so that the current applied to each electromagnet coil results in a damping force that increases in a suitable nonlinear manner (e.g., exponentially) with the difference between the actual and commanded positions of the affected control surface. The increasing damping force both alerts the pilot to the onset of a potentially dangerous situation and resists the pilot s effort to command a control surface to change position at an excessive rate

AHarrah, Ralph C.↗
NASA NTRS2010

Modeling Social Influence via Combined Centralized and Distributed Planning Control

Real world events are driven by a mixture of both centralized and distributed control of individual agents based on their situational context and internal make up. For example, some people have partial allegiances to multiple, contradictory authorities, as well as to their own goals and principles. This can create a cognitive dissonance that can be exploited by an appropriately directed psychological influence operation (PSYOP). An Autonomous Dynamic Planning and Execution (ADP&E) approach is proposed for modeling both the unperturbed context as well as its reaction to various PSYOP interventions. As an illustrative example, the unrest surrounding the Iranian elections in the summer of 2009 is described in terms applicable to an ADP&E modeling approach. Aspects of the ADP&E modeling process are discussed to illustrate its application and advantages for this example.

Vaccaro, James↗
NASA NTRS2010

Offset Compound Gear Drive

The Offset Compound Gear Drive is an in-line, discrete, two-speed device utilizing a special offset compound gear that has both an internal tooth configuration on the input end and external tooth configuration on the output end, thus allowing it to mesh in series, simultaneously, with both a smaller external tooth input gear and a larger internal tooth output gear. This unique geometry and offset axis permits the compound gear to mesh with the smaller diameter input gear and the larger diameter output gear, both of which are on the same central, or primary, centerline. This configuration results in a compact in-line reduction gear set consisting of fewer gears and bearings than a conventional planetary gear train. Switching between the two output ratios is accomplished through a main control clutch and sprag. Power flow to the above is transmitted through concentric power paths. Low-speed operation is accomplished in two meshes. For the purpose of illustrating the low-speed output operation, the following example pitch diameters are given. A 5.0 pitch diameter (PD) input gear to 7.50 PD (internal tooth) intermediate gear (0.667 reduction mesh), and a 7.50 PD (external tooth) intermediate gear to a 10.00 PD output gear (0.750 reduction mesh). Note that it is not required that the intermediate gears on the offset axis be of the same diameter. For this example, the resultant low-speed ratio is 2:1 (output speed = 0.500; product of stage one 0.667 reduction and stage two 0.750 stage reduction). The design is not restricted to the example pitch diameters, or output ratio. From the output gear, power is transmitted through a hollow drive shaft, which, in turn, drives a sprag during which time the main clutch is disengaged.

Stevens, Mark A.↗