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At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Evaluating Image Classification Deep Convolutional Neural Network Architectures for Remaining Useful Life Estimation of Turbofan Engines

Accurate estimation of the remaining useful life (RUL) is a key component of condition-based maintenance (CBM) and prognosis and health management (PHM). Data-based models for the estimation of RUL are of particular interest because expert knowledge of systems is not always available, and physical modeling is often not feasible. Additionally, using data-based models, which make decisions based on raw sensor data, allow features to be learned instead of manually determined. In this work, deep convolutional neural network (CNN) architectures are investigated for their ability to estimate the RUL of turbofan engines. To improve the accuracy of the models, CNN architectures, which have proven successful in image classification, are implemented and tested. Specifically, the blocks used in the Visual Geometry Group (VGG) architecture, inception modules used in the GoogLeNet architecture, and residual blocks used in the ResNet architecture are incorporated. To account for varying flight lengths, the input to the models is a window of time series data collected from the engine under test. Window locations at the climb, cruise, and descent stages are considered. To further improve the RUL estimations, multiple overlapping windows at each location are used. This increases the amount of training data available and is found to increase the accuracy of the resulting RUL estimations by averaging the estimates from all overlapping segments. The model is trained and tested using the new Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS) data set, and high prognosis accuracy was achieved. Furthermore, this work expands on the model developed and used in the 2021 PHM Society Data Challenge, which received second place.

convolutional neural networks↗
DOE OSTI2021

Inception Based Deep Convolutional Neural Network for Remaining Useful Life Estimation of Turbofan Engines

Accurate estimation of the remaining useful life (RUL) is a key component of condition based maintenance (CBM) and prognosis and health management (PHM). Data-based models for the estimation of RUL are of particular interest because expert knowledge of systems is not always available and physical modeling is often not feasible. In this paper, a deep convolutional neural network (CNN) architecture is investigated for its ability to estimate the RUL of turbofan engines. The input to the model is a window of time series data collected from the engine under test. Inputting raw sensor data allows features to be learned instead of manually determined. To incorporate the ability to detect features of differing lengths, inception modules are used in the neural network architecture. The model is trained and tested using the new Commercial Modular Aero-Propulsion System Simulation (N-CMAPSS) data set and high prognosis accuracy was achieved. The developed model was used in the 2021 PHM Society Data Challenge and received second place, further validating its ability to accurately estimate RUL.

DeVol, Nathaniel↗
NASA NTRS1990

Comparisons of thermochemical nonequilibrium viscous flowfield predictions for AFE vehicle

Numerical solutions for the Aeroassist Flight Experiment vehicle were obtained from three methods at a trajectory point corresponding to the maximum aerodynamic heating. The flow regime and vehicle's speed require a viscous model of laminar flow and finite-rate chemical and thermal modeling. The computational domain covers both forebody and base such that the shock layer and near wake flowfield are included. Because of differences in computational grids, methods of solution, and models of rate equations, the results are generally in poor agreement. Temperature and species concentrations are strongly affected by the physical model equations and associated parameters. The chemistry model based on 11 species is found to yield lower translational temperature profile near stagnation than those from a seven-species model. The vibrational temperature varies according to the modeling details. All solutions indicate that strong neutral and/or molecular dissociation and weak ionization take place at the forebody and vibrational freezing is present in the afterbody expansion region where the vibrational temperature is higher than the translational temperature. Some forms of shear layer emanating from the aerobrake skirt coalesce in the region of reversed flow behind the vehicle.

Tam, Luen T.↗
NASA NTRS1993

Asteroid collisions: Target size effects and resultant velocity distributions

To study the dynamic fragmentation of rock to simulate asteroid collisions, we use a 2-D, continuum damage numerical hydrocode which models two-body impacts. This hydrocode monitors stress wave propagation and interaction within the target body, and includes a physical model for the formation and growth of cracks in rock. With this algorithm we have successfully reproduced fragment size distributions and mean ejecta speeds from laboratory impact experiments using basalt, and weak and strong mortar as target materials. Using the hydrocode, we have determined that the energy needed to fracture a body has a much stronger dependence on target size than predicted from most scaling theories. In addition, velocity distributions obtained indicate that mean ejecta speeds resulting from large-body collisions do not exceed escape velocities.

Ryan, Eileen V.↗
NASA NTRS1998

Stratospheric Assimilation of Chemical Tracer Observations Using a Kalman Filter: Chi-Square Validated Results and Analysis of Variance and Correlation Dynamics - Pt. 2

A Kalman filter system designed for the assimilation of limb-sounding observations of stratospheric chemical tracers, which has four tunable covariance parameters, was developed in Part I (Menard et al. 1998) The assimilation results of CH4 observations from the Cryogenic Limb Array Etalon Sounder instrument (CLAES) and the Halogen Observation Experiment instrument (HALOE) on board of the Upper Atmosphere Research Satellite are described in this paper. A robust (chi)(sup 2) criterion, which provides a statistical validation of the forecast and observational error covariances, was used to estimate the tunable variance parameters of the system. In particular, an estimate of the model error variance was obtained. The effect of model error on the forecast error variance became critical after only three days of assimilation of CLAES observations, although it took 14 days of forecast to double the initial error variance. We further found that the model error due to numerical discretization as arising in the standard Kalman filter algorithm, is comparable in size to the physical model error due to wind and transport modeling errors together. Separate assimilations of CLAES and HALOE observations were compared to validate the state estimate away from the observed locations. A wave-breaking event that took place several thousands of kilometers away from the HALOE observation locations was well captured by the Kalman filter due to highly anisotropic forecast error correlations. The forecast error correlation in the assimilation of the CLAES observations was found to have a structure similar to that in pure forecast mode except for smaller length scales. Finally, we have conducted an analysis of the variance and correlation dynamics to determine their relative importance in chemical tracer assimilation problems. Results show that the optimality of a tracer assimilation system depends, for the most part, on having flow-dependent error correlation rather than on evolving the error variance.

Menard, Richard↗
NASA NTRS2002

2-D Magnetohydrodynamic Modeling of A Pulsed Plasma Thruster

Experiments are being performed on the NASA Marshall Space Flight Center (MSFC) MK-1 pulsed plasma thruster. Data produced from the experiments provide an opportunity to further understand the plasma dynamics in these thrusters via detailed computational modeling. The detailed and accurate understanding of the plasma dynamics in these devices holds the key towards extending their capabilities in a number of applications, including their applications as high power (greater than 1 MW) thrusters, and their use for producing high-velocity, uniform plasma jets for experimental purposes. For this study, the 2-D MHD modeling code, MACH2, is used to provide detailed interpretation of the experimental data. At the same time, a 0-D physics model of the plasma initial phase is developed to guide our 2-D modeling studies.

Thio, Y. C. Francis↗
NASA NTRS2002

An Experimental Study of a Pulsed Electromagnetic Plasma Accelerator

Experiments are being performed on the NASA Marshall Space Flight Center (MSFC) pulsed electromagnetic plasma accelerator (PEPA-0). Data produced from the experiments provide an opportunity to further understand the plasma dynamics in these thrusters via detailed computational modeling. The detailed and accurate understanding of the plasma dynamics in these devices holds the key towards extending their capabilities in a number of applications, including their applications as high power (greater than 1 MW) thrusters, and their use for producing high-velocity, uniform plasma jets for experimental purposes. For this study, the 2-D MHD modeling code, MACH2, is used to provide detailed interpretation of the experimental data. At the same time, a 0-D physics model of the plasma initial phase is developed to guide our 2-D modeling studies.

Thio, Y. C. Francis↗
DOE OSTI2018

Secondary neutron yields from thick-target GCR accelerator experiments - 25434

This work overviews recent experiments conducted at the NASA Space Radiation Laboratory which sought to experimentally verify model predictions of an optimal spacecraft shielding thickness and provide data which can be used to quantify uncertainties in the physics models within the standard particle transport codes which presently, in some places, poorly predict data and whose results can vary significantly from code to code. Now that the multi-year experiment campaign is complete, some of the overarching trends in the data can be studied; though this work only provides a cursory look at these overarching trends. A small set of the neutron yields measured in these experiments are showcased here. The experiment employed two thick targets along a beamline to emulate the walls of a spacecraft being bombarded by galactic cosmic rays. Time-of-flight techniques were used to characterize neutrons produced in the upstream target while a novel pulse height deconvolution methodology was developed and implemented to characterize neutrons produced in the downstream target. (authors)

43 PARTICLE ACCELERATORS↗
DOE OSTI2010

Radiative properties of astrophysical matter : a quest to reproduce astrophysical conditions on earth.

Experiments in terrestrial laboratories can be used to evaluate the physical models that interpret astronomical observations. The properties of matter in astrophysical objects are essential components of these models, but terrestrial laboratories struggle to reproduce the extreme conditions that often exist. Megajoule-class DOE/NNSA facilities such as the National Ignition Facility and Z can create unprecedented amounts of matter at extreme conditions, providing new capabilities to test astrophysical models with high accuracy. Experiments at these large facilities are challenging, and access is very competitive. However, the cylindrically-symmetric Z source emits radiation in all directions, enabling multiple physics experiments to be driven with a single Z discharge. This helps ameliorate access limitations. This article describes research efforts under way at Sandia National Laboratories Z facility investigating radiation transport through stellar interior matter, population kinetics of atoms exposed to the intense radiation emitted by accretion powered objects, and spectral line formation in white dwarf (WD) photospheres. Opacity quantifies the absorption of radiation by matter and strongly influences stellar structure and evolution, since radiation dominates energy transport deep inside stars. Opacity models have become highly sophisticated, but laboratory tests at the conditions existing inside stars have not been possible - until now. Z research is presently focused on measuring iron absorption at conditions relevant to the base of the solar convection zone, where the electron temperature and density are 190 eV and 9 x 10{sup 22} e/cc, respectively. Creating these conditions in a sample that is sufficiently large, long-lived, and uniform is extraordinarily challenging. A source of radiation that streams through the relatively-large samples can produce volumetric heating and thus, uniform conditions, but to achieve high temperatures a strong source is required. Z dynamic hohlraums provide such a megajoule-class source. Initial Z experiments measured transmission through iron samples ionized to the same charge states that exist at the solar convection zone base. The resulting data made it possible to test challenging aspects of the opacity calculations such as the ionization balance and the completeness and accuracy of the atomic energy level description. However, the density was too low to provide a definitive test of the physics at the solar convection zone base. Recent experiments have reached higher densities, and opacity model tests for stellar interiors now appear within reach. Accretion powered objects, including active galactic nuclei, x-ray binaries, and black hole accretion disks, are the most luminous objects in the universe. Astrophysical models for these objects rely largely on comparing spectroscopic predictions with observations. A dilemma arises because the spectra originate from plasmas that are bathed in the enormous photon flux from the accretion disk and photoionization dominates the atomic ionization and energy level populations. Thus, constraining astrophysical models depends on accurate atomic models for photoionized plasmas. Unfortunately, to date the ionization in almost all laboratory experiments is collision-dominated and very few tests of photoionized plasma atomic kinetics exist. Megajoule class high-energy-density facilities can help because they generate higher x-ray fluence over larger spatial scales and longer times. Expanded iron foils and pre-filled neon gas cells have been used in experiments at Z to study photoionized atomic kinetics in two elements commonly observed in astrophysical objects. In these experiments, low density samples are exposed to a measured intense x-ray spectrum, emergent emission or absorption spectra are recorded, and the results are compared to predictions made with spectral synthesis codes used by astrophysicists. Initial experiments focused on testing models used to interpret spectra from the 'warm absorber,' a plasma observed in the vicinity of some active galactic nuclei. In future experiments, spectra from plasmas exposed to higher radiation intensities will be measured, possibly leading to improved understanding of the plasma in the immediate vicinity of the accretion disk. WDs are the oldest stars and can serve as cosmic clocks, since the universe must be at least as old as the objects within it. Astrophysicists determine WD ages using stellar models combined with effective temperature (T{sub eff}) and mass inferred from spectral observations of WD photospheres. Many line profiles in the observed spectra are dominated by Stark broadening, a process sensitive to the photosphere density and related to the total mass through the stellar model. Accurate Stark broadening theory is, therefore, critical to the precise determination of the WD properties and the inferred ages.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2019

Spectral Variability of Remotely Sensed Target Materials: Causes, Models, and Strategies for Mitigation and Robust Exploitation

Here, the purpose of this survey is to examine the major causes of spectral variability in target materials, survey some associated physical models, and discuss how hyper spectral analyses can be made more robust to this variability. Although there are many kinds of hyperspectral-image exploitation algorithms (e.g., classification, clustering, and unmixing) and virtually all of them are affected by spectral variability, we will concentrate on the problem of target detection and, more specifically, the detection, identification, and location of particular materials of interest.

42 ENGINEERING↗
DOE OSTI2011

An investigation of some models and approximations used in calculating fuel assemblies of a high-temperature gas-cooled reactor of the GT-MHR type

The paper describes basic neutron-physics models developed in the Division of Advanced Nuclear Power Systems of the Institute of Nuclear Reactors, Russian Research Center Kurchatov Institute, as design models intended for calculating the characteristics of block fuel assemblies of a high-temperature gas-cooled reactor GT-MHR, namely, models for calculating burnup of fuel and isotopes of burnable neutron absorbers and calculating fuel assemblies at fixed points with respect to burnup with preparation of the neutron constants in a preassigned number of energy groups for full-scale design of a reactor. A model problem for investigation of calculated approximations is proposed. The outcome of this investigation is a developed stage-by-stage procedure of preparing group homogeneous cross sections of a fuel assembly and its parts that has been introduced into the practice of design calculations of a GT-MHR reactor.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2013

Empirical and physics based mathematical models of uranium hydride decomposition kinetics with quantified uncertainties.

Metal particle beds have recently become a major technique for hydrogen storage. In order to extract hydrogen from such beds, it is crucial to understand the decomposition kinetics of the metal hydride. We are interested in obtaining a a better understanding of the uranium hydride (UH3) decomposition kinetics. We first developed an empirical model by fitting data compiled from different experimental studies in the literature and quantified the uncertainty resulting from the scattered data. We found that the decomposition time range predicted by the obtained kinetics was in a good agreement with published experimental results. Secondly, we developed a physics based mathematical model to simulate the rate of hydrogen diffusion in a hydride particle during the decomposition. We used this model to simulate the decomposition of the particles for temperatures ranging from 300K to 1000K while propagating parametric uncertainty and evaluated the kinetics from the results. We compared the kinetics parameters derived from the empirical and physics based models and found that the uncertainty in the kinetics predicted by the physics based model covers the scattered experimental data. Finally, we used the physics-based kinetics parameters to simulate the effects of boundary resistances and powder morphological changes during decomposition in a continuum level model. We found that the species change within the bed occurring during the decomposition accelerates the hydrogen flow by increasing the bed permeability, while the pressure buildup and the thermal barrier forming at the wall significantly impede the hydrogen extraction.

08 HYDROGEN↗
DOE OSTI2024

3D high-fidelity automated neutronics guided optimization of fusion blanket designs

The compact Fusion Pilot Plant (FPP) is defined in the recent National Academies of Sciences, Engineering, and Medicine report as the next step of fusion energy demonstration with a $50$ MWe peak net electricity production, $Q_e$ greater than $1$, and at least $3$ hours of continuous operation. This fusion pilot plant will be a test bed enabling materials, designs, and fuel management assessment, and it will represent an engineering challenge because of its high-fusion power and compact design targets. Previous reactor data is limited to experiments operating in different design space ranges. Therefore, design iterations and assessments should rely on high-fidelity first-principle theoretical and computational models. The high-fidelity integrated modeling of the plasma is a fundamental part of fusion energy research. However, the whole device modeling is often neglected, utilizing low-fidelity, system-level analysis. Recently, the need for high-fidelity multi-physics modeling was recognized, resulting in a selection of integrated tools. Further, autonomous design optimization requires a streamlined framework that perturbs the design point, reruns the analysis, and examines the outputs. However, high-fidelity analysis requires complex geometry specification that is difficult to perturb. This work presents the parametric CAD generation tool TRACER and a new neutronic workflow. TRACER allows the perturbation of the geometry representation, creating geometry files ready for further analysis. The streamlined neutronic workflow allows efficient and accurate calculations. The two new tools coupled together were used to perform a 3D high-fidelity multi-objective, multi-input optimization of an "ARC Class" compact tokamak design. The workflow was driven by an optimization driver for full automation.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1987

The effect of decay of the amplitude of oscillation on random process models for QPO X-ray stars

Random process models provide a useful mathematical framework for analysis of the quasi-periodic oscillations (QPO) recently discovered in the X-ray emission from certain luminous Galactic X-ray stars. In this paper, consideration is given to the effects of the power spectrum of the decay of the amplitude of oscillation that is expected in some physical models for the QPO phenomena. The resulting changes in the power spectrum depend on the ratio of the decay time of the amplitude of oscillation to the lifetime of the shot envelope. For values of this ratio less than about 10, it is found that incoherent QPO peaks in the power spectrum are significantly reduced in height and total power and are broadened in width, making them more difficult to detect. Coherent terms in the power spectrum, if present, are reduced in height and total power, but their width is unaffected. The red noise component remains unchanged. The present results are applied to the beat-frequency modulated accretion model in order to set constraints on the physical properties of the boundary layer between the inner edge of the accretion disk and the neutron star magnetosphere.

Shibazaki, N.↗
DOE OSTI2019

The simulation of the sensitivity of the Antarctic Impulsive Transient Antenna (ANITA) to Askaryan radiation from cosmogenic neutrinos interacting in the Antarctic Ice

A Monte Carlo simulation program for the radio detection of Ultra High Energy (UHE) neutrino interactions in the Antarctic ice as viewed by the Antarctic Impulsive Transient Antenna (ANITA) is described in this article. The program, icemc, provides an input spectrum of UHE neutrinos, the parametrization of the Askaryan radiation generated by their interaction in the ice, and the propagation of the radiation through ice and air to a simulated model of the third and fourth ANITA flights. Lastly, this paper provides an overview of the icemc simulation, descriptions of the physics models used and of the ANITA electronics processing chain, data/simulation comparisons to validate the predicted performance, and a summary of the impact of published results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

A search for the higgs boson and a search for dark-matter particle with jets and missing transverse energy at collider detector at Fermilab

Finding the standard model Higgs boson and discovering beyond-standard model physics phenomena have been the most important goals for the high-energy physics in the last decades. In this thesis, we present two such searches. First is the search for the low mass standard model Higgs boson produced in association with a vector boson; second is the rst search for a dark-matter candidate (D) produced in association with a top quark (t) in particle colliders. We search in events with energetic jets and large missing transverse energy { a signature characterized by complicated backgrounds { in data collected by the CDF detector with proton-antiproton collisions at p s = 1:96 TeV. We discuss the techniques that have been developed for background modeling, for discriminating signal from background, and for reducing background resulting from detector e ects. In the Higgs search, we report the 95% con dence level upper limits on the pro- duction cross section across masses of 90 to 150 GeV/c2. The expected limits are improved by an average of 14% relative to the previous analysis. The Large Hadron Collider experiments reported a Higgs-like particle with mass of 125 GeV/c2 by study- ing the data collected in year 2011/12. At a Higgs boson mass of 125 GeV/c2, our observed (expected) limit is 3.06 (3.33) times the standard model prediction, corre- sponding to one of the most sensitive searches to date in this nal state. In the dark matter search, we nd the data are consistent with the standard model prediction, thus set 95% con dence level upper limits on the cross section of the process p p ! t + D as a function of the mass of the dark-matter candidate. The xviii upper limits are approximately 0.5 pb for a dark-matter particle with masses in the range of 0 􀀀 150 GeV/c2.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2013

Dynamics and Control of a Disordered System in Space

In this paper, we present some ideas regarding the modeling, dynamics and control aspects of granular spacecraft. Granular spacecraft are complex multibody systems composed of a spatially disordered distribution of a large number of elements, for instance a cloud of N grains in orbit, with N greater than 10(exp 3). These grains can be large (Cubesat-size) or small (mm-size), and can be active, i.e., a fully equipped vehicle capable sensing their own position and attitude, and enabled with propulsion means, or entirely passive. The ultimate objective would be to study the behavior of the single grains and of large ensembles of grains in orbit and to identify ways to guide and control the shape of a cloud composed of these grains so that it can perform a useful function in space, for instance, as an element of an optical imaging system for astrophysical applications. This concept, in which the aperture does not need to be continuous and monolithic, would increase the aperture size several times compared to large NASA observatories such as ATLAST, allowing for a true Terrestrial Planet Imager that would be able to resolve exo-planet details and do meaningful spectroscopy on distant world. In the paper, we address the modeling and autonomous operation of a distributed assembly (the cloud) of large numbers of highly miniaturized space-borne elements (the grains). A multi-scale, multi-physics model is proposed of the dynamics of the cloud in orbit, as well as a control law for cloud shape maintenance, and preliminary simulation studies yield an estimate of the computational effort, indicating a scale factor of approximately N(exp 1.4) as a function of the number of grains. A granular spacecraft can be defined as a collection of a large number of space-borne elements (in the 1000s) designed and controlled such that a desirable collective behavior emerges, either from the interactions among neighboring grains, and/or between the grains and the environment. In this paper, each grain is considered to be a highly miniaturized spacecraft which has limited size and mass, hence it has limited actuation, limited propulsive capability, limited power, limited sensing, limited communication, limited computational resources, limited range of motion, limited lifetime, and may be expendable. The modeling and dynamics of clouds of vehicles is more challenging than with conventional vehicles because we are faced with a probabilistic vehicle composed of a large number of physically disconnected vehicles. First, different scales of motion occur simultaneously in a cloud: translations and rotations of the cloud as a whole (macro-dynamics), relative rotation and translation of one cloud member with respect to another (meso-dynamics), and individual cloud member dynamics (micro-dynamics). Second, the control design needs to be tolerant of the system complexity, of the system architecture (centralized vs. decentralized large scale system control) as well as robust to un-modeled dynamics and noise sources. Figure 1, top left, shows the kinematic parameters of a 1000 element cloud in orbit. The motion of the system is described with respect to a local vertical-local horizontal (LV-LH) orbiting reference frame (x,y,z)=F(sub ORF) of origin O(sub ORF) which rotates with mean motion omega and orbital semi-major axis R(sub 0). The orbital geometry at the initial time is defined in terms of its six orbital elements, and the orbital dynamics equation for point O(sub ORF) is propagated forward in time under the influence of the gravitational field of the primary and other external perturbations, described below. The origin of this frame coincides with the initial position of the center of mass of the system, and the coordinate axes are z along the local vertical, x toward the flight direction, and y in the orbit normal direction. The assumptions we used to model the dynamics are as follows: 1) The inertial frame is fixed at Earth's center. 2) The orbiting Frame ORF follows Keplerian orbit. 3) the cloud system dynamics is referred to ORF. 4) the attitude of each grain uses the principal body frame as body fixed frame. 5) the atmosphere is assumed to be rigidly rotating with the Earth. Regarding the grains forming the cloud: 1) each grain is modeled as a rigid body; 2) a simple attitude estimator provides attitude estimates, 3) a simple guidance logic commands the position and attitude of each grain, 4) a simple local feedback controller based on PD control of local states is used to stabilize the attitude of the vehicle. Regarding the cloud: 1) the cloud as a whole is modeled as an equivalent rigid body in orbit, and 2) an associated graph establishes agent connectivity and enables coupling between modes of motion at the micro and macro scales; 3) a simple guidance and estimation logic is modeled to estimate and command the attitude of this equivalent rigid body; 4) a cloud shape maintenance controller is based on the dynamics of a stable virtual truss in the orbiting frame. Regarding the environmental perturbations acting on the cloud: 1) a non-spherical gravity field including JO (Earth's spherical field) zonal component, J2 (Earth's oblateness) and J3 zonal components is implemented; 2) atmospheric drag is modeled with an exponential model; 3) solar pressure is modeled assuming the Sun is inertially fixed; and 4) the Earth's magnetic field is model using an equivalent dipole model. The equations of motion are written in a referential system with respect to the origin of the orbiting frame and the state is propagated forward in time using an incremental predictor-corrector scheme. A representative cloud with varying number of grains is simulated to identify the limitations in computation time as the number of grains grows. We derive a control law to track a desired surface in the ORF (equivalently to maintain a reference cloud shape) by defining an error from a desired surface shape, and designing a control law that is exponentially stable and reduces the tracking error to zero. Figure 1 (top right) shows a comparison of various requirements for simulation of single spacecraft vs. granular spacecraft, indicating the high degree of complexity that needs to be taken into consideration. The ORF components of control force required by one of the grains is, for this particular case, in the micro-Newton range. However, no attempt has been made yet to reconfigure (or re-orient) the cloud configuration internally, for which forces in the milli-Newton level are expected, depending on the time required to do the reconfiguration. Figure 1, bottom, shows the computation time as a function of the number of grains, indicating an order N(exp 1.43) scaling on a 8 Gb, 1067 MHz RAM MacOSX computer with a 3.06 GHz Intel Core 2 Duo processor. With this metric, the same simulation for a system of N=1000 grains would take 5.4 hours, and 146 hours (i.e., 6 days) for a system with N=10,000 grains. Therefore, efficient ways to simulate this complex system, where not only the time scales of natural system dynamics, but also the sampling times of the Guidance, Navigation, and Control are included, remain to be explored. Additional details on the cloud modeling, dynamics, and control will be described in the paper.

simulation↗