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A describing function of the control moment gyros (CMG) frictional nonlinearity is derived using the analytic torque equation. Computer simulation of the simplified Large Space Telescope (LST) system with the analytic torque expression is discussed along with the transfer functions of the sampled-data LST system, and the discrete describing function of the GMC frictionality.
The digital IPS with wire cable and flex pivot nonlinearity is simulated on the digital computer to determine the effects of varying the sampling period T on the system stability, and to determine a range of optimal values of the parameters of the digital controller. The listing of the computer program is shown as well as the Dahl model for the flex pivot nonlinearity. For the wire cable nonlinearity, two ranges of values were used and the nominal values of the digital controller parameters are included.
Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) < x }. Utilizing the fixed-point semantics (denotational semantics), extended to probabilistic computations, we investigate the distribution functions of probabilistic automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.
One function of Continuous Air Monitor (CAM) samplers at LANL (Los Alamos National Laboratory) is to alert workers to the presence of airborne alpha-emitting (e.g.) plutonium particles.
Calculating the post glacial response of a viscoelastic Earth model using the exponential decay normal mode technique leads to intrinsic singularities if viscosity varies continuously as a function of radius. We develop a numerical implementation of the Complex Real Fourier transform (CRFT) method as an accurate and stable procedure to avoid these singularities. Using CRFT, we investigate the response of a set of Maxwell Earth models to surface loading. We find that the effect of expanding a layered viscosity structure into a continuously varying structure is to destroy the modes associated with the boundary between layers. Horizontal motion is more sensitive than vertical motion to the viscosity structure just below the lithosphere. Horizontal motion is less sensitive to the viscosity of the lower mantle than the vertical motion is. When the viscosity increases at 670 km depth by a factor of about 60, the response of the lower mantle is close to its elastic limit. Any further increase of the viscosity contrast at 670 km depth or further increase of viscosity as a continuous function of depth starting from 670 km depth is unlikely to be resolved.
The Exploration Supply Chain Simulation project was chartered by the NASA Exploration Systems Mission Directorate to develop a software tool, with proper data, to quantitatively analyze supply chains for future program planning. This tool is a discrete-event simulation that uses the basic supply chain concepts of planning, sourcing, making, delivering, and returning. This supply chain perspective is combined with other discrete or continuous simulation factors. Discrete resource events (such as launch or delivery reviews) are represented as organizational functional units. Continuous resources (such as civil service or contractor program functions) are defined as enabling functional units. Concepts of fixed and variable costs are included in the model to allow the discrete events to interact with cost calculations. The definition file is intrinsic to the model, but a blank start can be initiated at any time. The current definition file is an Orion Ares I crew launch vehicle. Parameters stretch from Kennedy Space Center across and into other program entities (Michaud Assembly Facility, Aliant Techsystems, Stennis Space Center, Johnson Space Center, etc.) though these will only gain detail as the file continues to evolve. The Orion Ares I file definition in the tool continues to evolve, and analysis from this tool is expected in 2008. This is the first application of such business-driven modeling to a NASA/government-- aerospace contractor endeavor.
It is noted that the distorsions introduced by the variation of distance between the sources and the measurement points can be important enough to create fake anomalies. The average amplitude of the anomalies at MAGSAT altitude is of the order of a few nT. Thus it is necessary to be careful in reducing MAGSAT data to a common elevation. The achievement of the corresponding anomaly map is of primary importance for the study of regional and long wave length anomalies. A method for the continuation of potential fields is described which consists in representing any harmonic function (in particular the anomaly is function of space coordinates) as a sum of elementary harmonic functions; the continuation being achieved by an inverse technique. Tests, made on a synthetic set of data, evaluate the method.
IRAS, IUE, and ground-based optical, NIR, mm and submm, and radio observations obtained mainly on Apr. 9-23, 1983, are reported for 19 active extragalactic sources and eight control sources. The overall spectra of the compact active sources are shown to be well represented by continuous-curvature functions such as parabolas. The spectra are found to be consistent with models involving continuous particle injection (with synchrotron losses) or first-order Fermi acceleration (with escape and synchrotron losses), but not with models using relativistic Maxwellian electron distributions.
Molded, conductive-epoxy recoverable fuse protects electronic circuits during overload conditions, and then permits them to continue to function immediately after the overload condition is removed. It has low resistance at ambient temperature, and high resistance at an elevated temperature.
The Tropical Rainfall Measuring Mission (TRMM) is in its sixth year of operation. This successful research mission, a joint U.S./Japan effort, has become-a key element in the routine monitoring of global precipitation. The package of rain measuring instrumentation, including the first meteorological radar in space, continues to function perfectly, and with the increase in orbital altitude (from 350 km to 400 km) the mission will hopefully continue for a number of years. The validation effort has been a combination of routine use of 1) ground-based radar and raingauge measurements for comparison with the satellite-based estimates, 2) the use of field experiment data for evaluation of the satellite data products and investigation of some of the assumptions in the satellite retrievals, and 3) use of other comparison data sets, including atoll and buoy gauges over ocean and research and operational gauge data sets over land. The status of the program will be described along with "lessons learned". Near term plans for improved validation products and new thrusts related to validation of TRMM-based multi-satellite products that extend into middle latitudes will be outlined.
Mathematical programming techniques provide a general approach to automated structural design. An iterative method is proposed in which design is treated as a hierarchy of subproblems, one being locally constrained and the other being locally unconstrained. It is assumed that the design space is locally convex in the case of good initial designs and that the objective and constraint functions are continuous, with continuous first derivatives. A general design algorithm is outlined for finding a move direction which will decrease the value of the objective function while maintaining a feasible design. The case of one-dimensional search in a two-variable design space is discussed. Possible applications are discussed. A major feature of the proposed algorithm is its application to problems which are inherently ill-conditioned, such as design of structures for optimum geometry.
Theodorsen's circulation function relates lift to downwash in unsteady two dimensional incompressible flow. A continued fraction representation for the circulation function is described. The continued fraction converges and has a particularly simple coefficient pattern.
The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.
The problem of obtaining an optimal control law, which is constrained to be a linear feedback of the available measurements, for both continuous and discrete time linear systems subjected to additive white process noise and measurement noise was Necessary conditions are obtained for minimizing a quadratic performance function for both finite and infinite terminal time cases. The feedback gains are constrained to be time invariant for the infinite terminal time cases. For all the cases considered, algorithms are derived for generating sequences of feedback gain matrices which successively improve the performance function. A continuous time numerical example is included for the purpose of demonstration.
An approach to incorporating artificial neural networks in nonlinear, adaptive control systems is described. The controller contains three principal elements: a nonlinear inverse dynamic control law whose coefficients depend on a comprehensive model of the plant, a neural network that models system dynamics, and a state estimator whose outputs drive the control law and train the neural network. Attention is focused on the system identification task, which combines an extended Kalman filter with generalized spline function approximation. Continual learning is possible during normal operation, without taking the system off line for specialized training. Nonlinear inverse dynamic control requires smooth derivatives as well as function estimates, imposing stringent goals on the approximating technique.
When a two-component system is cooled below the minimum temperature for its stability, it separates into two or more immiscible phases. The initial nucleation produces grains (if solid) or droplets (if liquid) of one of the phases dispersed in the other. The dynamics by which these nuclei proceed toward equilibrium is called Ostwald ripening. The dynamics of growth of the droplets depends upon the following factors: (1) The solubility of the droplet depends upon its radius and the interfacial energy between it and the surrounding (continuous) phase. There is a critical radius determined by the supersaturation in the continuous phase. Droplets with radii smaller than critical dissolve, while droplets with radii larger grow. (2) The droplets concentrate one component and reject the other. The rate at which this occurs is assumed to be determined by the interdiffusion of the two components in the continuous phase. (3) The Ostwald ripening is constrained by conservation of mass; e.g., the amount of materials in the droplet phase plus the remaining supersaturation in the continuous phase must equal the supersaturation available at the start. (4) There is a distribution of droplet sizes associated with a mean droplet radius, which grows continuously with time. This distribution function satisfies a continuity equation, which is solved asymptotically by a similarity transformation method.
Next Generation Air Transportation System (NextGen) concepts of operation may require aircraft to fly planned trajectories in four dimensions three spatial dimensions and time. A prototype 4D flight management capability is being developed by NASA to facilitate the development of these concepts. New trajectory generation functions extend today's flight management system (FMS) capabilities that meet a single Required Time of Arrival (RTA) to trajectory solutions that comply with multiple RTA constraints. When a solution is not possible, a constraint management capability relaxes constraints to achieve a trajectory solution that meets the most important constraints as specified by candidate NextGen concepts. New flight guidance functions provide continuous guidance to the aircraft s flight control system to enable it to fly specified 4D trajectories. Guidance options developed for research investigations include a moving time window with varying tolerances that are a function of proximity to imposed constraints, and guidance that recalculates the aircraft s planned trajectory as a function of the estimation of current compliance. Compliance tolerances are related to required navigation performance (RNP) through the extension of existing RNP concepts for lateral containment. A conceptual temporal RNP implementation and prototype display symbology are proposed.
Ongoing collaborative research efforts between NASA's Neuroscience and Cardiovascular Laboratories, and the Institute of Biomedical Problems' (IBMP) Sensory-Motor and Countermeasures Laboratories have been measuring functional sensorimotor, cardiovascular and strength responses following bed rest, dry immersion, short duration (Space Shuttle) and long duration (Mir and International Space Station) space flights. While the unloading paradigms associated with dry immersion and bed rest does serve as acceptable flight analogs, testing of crew responses following the long duration flights previously has not been possible until a minimum of 24 hours after landing. As a result, it is not possible to estimate the nonlinear trend of the early (<24 hr) recovery process, nor is it possible to accurately assess the full impact of the decrements associated with long duration flight. To overcome these limitations, both the Russian and U.S. sides have implemented testing at landing site. By joint agreement, this research effort has been identified as the functional Field Test (FT). For practical reasons the FT has been divided into two phases: the full FT and a preliminary pilot version (PFT) of the FT that is reduced in both length and scope. The primary goal of this research is to determine functional abilities in long duration space flight crews beginning as soon after landing as possible (< 2 hr) with one to three immediate follow-up measurements on the day of landing. This goal has both sensorimotor and cardiovascular elements, including evaluations of NASA's new anti-orthostatic compression garment and the Russian Kentavr garment. Functional sensorimotor measurements will include, but are not limited to, assessment of hand/eye coordination, ability to egress from a seated position, walk normally without falling, measurement of dynamic visual acuity, ability to discriminate different forces generated with both the hands and legs, recovery from a fall, a coordinated walk involving tandem heel-to-toe placement, and determination of postural ataxia while standing. The cardiovascular portion of the investigation includes blood pressure and heart rate measurements during a timed stand test in conjunction with postural ataxia testing (quiet stance sway) as well as cardiovascular responses during other functional tasks. In addition to the immediate post-landing collection of data for the full FT, postflight data will be acquired at a minimum of one to three more other times within the 24 hr following landing and continue until functional sensorimotor and cardiovascular responses have returned to preflight normative values. The PFT represents a single trial run comprised of jointly agreed upon subset of tests from the full FT and relies heavily on IBMP's Sensory-Motor and Countermeasures Laboratories for content and implementation. The PFT was first conducted following the September 2013 landing of the Soyuz spacecraft (34S) and again following the landing of Soyuz 35S in November. Testing included: (1) a sit-tostand test, (2) recovery from a fall where the crewmember began in the prone position on the ground and then stood for 3 min while cardiovascular stability was determined and postural ataxia data were acquired, and (3) a tandem heel-to-toe walk test to determine changes in the central locomotor program. Video, cardiovascular parameters (heart rate and blood pressure), data from body-worn inertial sensors and severity of postflight motion sickness were collected for analysis. In summary, the level of functional deficit is expected to be most profound during the acquisition of gravity loads immediately after landing when the demands for crew intervention in response to emergency operations will be greatest. Clearly measureable performance parameters such as ability to perform a seat egress, recover from a fall or the ability to see clearly when walking, and related physiological data (orthostatic responses) are required to provide an evidence base for characterizing programmatic risks and the degree of variability among crewmembers for exploration missions where the crew will be unassisted after landing. Overall, these early functional and related physiological measurements will allow estimation of nonlinear sensorimotor and cardiovascular recovery trends to an accuracy that has not been previously captured in over 50 years of space flight.