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NASA NTRS1992

Inference in fuzzy rule bases with conflicting evidence

Inference based on fuzzy 'If ... then' rules has played a very important role since when Zadeh proposed the Compositional Rule of Inference and, especially, since the first successful application presented by Mamdani. From the mid-1980's when the 'fuzzy boom' started in Japan, numerous industrial applications appeared, all using simplified techniques because of the high levels of computational complexity. Another feature is that antecedents in the rules are distributed densely in the input space, so the conclusion can be calculated by some weighted combination of the consequents of the matching (fired) rules. The CRI works in the following way: If R is a rule and A* is an observation, the conclusion is computed by B* = R o A* (o stands for the max-min composition). Algorithms implementing this idea directly have an exponential time complexity (maybe the problem is NP-hard) as the rules are relations in X x Y, a k1 x k2 dimensional space, if X is k1, Y is k2 dimensional. The simplified techniques usually decompose the relation into k1 projections in X(sub i) and measure in some way the degree of similarity between observation and antecedent by some parameter of the overlapping. These parameters are aggregated to a single value in (0,1) which is applied as a resulting weight for the given rule. The projections of rules in dimensions Y(sub i) are weighted by these aggregated values and then they are combined in order to obtain a resulting conclusion separately in every dimension. This method is unapplicable with sparse bases as there is no guarantee that an arbitrary observation matches with any of the antecedents. Then, the degree of similarity is 0 and all consequents are weighted by 0. Some considerations for such a situation are summarized in the next sections.

Koczy, Laszlo T.↗
NASA NTRS1990

Spatial variations in the suprathermal ion distributions during substorms in the plasma sheet

The preinjection and postinjection suprathermal energy spectra of the ion species H(+), O(+), He(+), and He(++) in two events in which substorm-associated particle injections were observed in both the near-earth plasma sheet and farther down the tail were determined using data obtained by the Suprathermal Energetic Ion Charge Analyzer on AMPTE IRM and the Charge Energy Mass Spectrometer on AMPTE CCE. Similar spectral changes were observed in both locations. In both cases, the spectra became harder with injection. Postinjection, the flux decreased exponentially with radial distance. The gradients observed for all ion species were very similar.

Kistler, L. M.↗
NASA NTRS2016

Elevated Aerosol Layers and Their Radiative Impact over Kanpur During Monsoon Onset Period

Accurate information about aerosol vertical distribution is needed to reduce uncertainties in aerosol radiative forcing and its effect on atmospheric dynamics. The present study deals with synergistic analyses of aerosol vertical distribution and aerosol optical depth (AOD) with meteorological variables using multisatellite and ground-based remote sensors over Kanpur in central Indo-Gangetic Plain (IGP). Micro-Pulse Lidar Network-derived aerosol vertical extinction (sigma) profiles are analyzed to quantify the interannual and daytime variations during monsoon onset period (May-June) for 2009-2011. The mean aerosol profile is broadly categorized into two layers viz., a surface layer (SL) extending up to 1.5 km (where sigma decreased exponentially with height) and an elevated aerosol layer (EAL) extending between 1.5 and 5.5 km. The increase in total columnar aerosol loading is associated with relatively higher increase in contribution from EAL loading than that from SL. The mean contributions of EALs are about 60%, 51%, and 50% to total columnar AOD during 2009, 2010, and 2011, respectively. We observe distinct parabolic EALs during early morning and late evening but uniformly mixed EALs during midday. The interannual and daytime variations of EALs are mainly influenced by long-range transport and convective capacity of the local emissions, respectively. Radiative flux analysis shows that clear-sky incoming solar radiation at surface is reduced with increase in AOD, which indicates significant cooling at surface. Collocated analysis of atmospheric temperature and aerosol loading reveals that increase in AOD not only resulted in surface dimming but also reduced the temperature (approximately 2-3 C) of lower troposphere (below 3 km altitude). Radiative transfer simulations indicate that the reduction of incoming solar radiation at surface is mainly due to increased absorption by EALs (with increase in total AOD). The observed cooling in lower troposphere in high aerosol loading scenario could be understood as a dynamical feedback of EAL-induced stratification of lower troposphere. Further, the observed radiative effect of EALs increases the stability of the lower troposphere, which could modulate the large-scale atmospheric dynamics during monsoon onset period. These findings encourage follow-up studies on the implication of EALs to the Indian summer monsoon dynamics using numerical models.

aerosol vertical distribution↗
NASA NTRS1992

The kinematics of buoyancy induced mixing

A model problem to study mixing driven by buoyancy flow fields due to a time dependent body force which consists of a steady and an oscillatory component is considered. Flow fields generated by a time dependent body force, which consists of a steady and an oscillatory component from vibrations or g-jitter, mix two fluids inside a cavity by stretching and folding the interface into various morphological patterns. These patterns show two basic structures depending on the dominant components of the body force. These structures are whirls and tendrils, corresponding to the dominance of either the steady or oscillatory component, respectively. A combination of these structures also occurs in the interaction region. In this region the effect of the steady component opposes the oscillatory component and the result is to smooth the interface, and prevent breakup of the interface. For the parametric range considered, two basic flow regimes occur: convective and chaotic. In the convective regime, the morphological patterns are topological. In the chaotic regime, mixing occurs by a repetitive sequence of bubble formation, necking, and breakup which spreads the concentration field throughout the cavity. The length stretch of the interface increases exponentially with time. The dynamical system characteristics show that in the convective regime, at a point in space, the flow field is oscillatory with elliptical phase space trajectories, and its power spectrum indicates that the flow field responds to the corresponding input frequency. Whereas, in the chaotic regime, the flow field is aperiodic, the phase space trajectories show irregular patterns, and the power spectrum shows a broadband distribution.

Duval, Walter M. B.↗
NASA NTRS2001

A Diagnostic Analysis of the Kennedy Space Center LDAR Network 2. Cross-Sensor Studies

Range dependencies in total (intracloud and cloud to ground) lightning observed by the Kennedy Space Center Lightning Detection and Ranging (LDAR) network are established through cross comparison with other lightning sensors. Using total lightning observed from space by the Lightning Imaging Sensor (LIS), MAR flash detection efficiency is shown to remain above 90% out to 90-100 km range, and to be below 25% at 200 km range. MAR VHF source location error distributions are also determined as a function of range and are found to be asymmetric with standard deviation increasing roughly as r 2 . Range normalization schemes for total VHF source density are tested and shown to yield significant improvements in correlation with National Lightning Detection Network (NLDN) ground flash density at hourly, daily, monthly, and climatological timescales (up to 50% over uncorrected source densities using an exponential-in-range correction factor with 40-50 km e-folding scale).

Boccippio, D. J.↗
NASA NTRS2019

The International Space Station (ISS) Port 1 (P1) External Active Thermal Control System (EATCS) Ammonia Leak

Ammonia is used in the Starboard 1 (S1) and Port 1 (P1) External Active Thermal Control System (EATCS) to cool the pressurized modules, and some of the external electrical power distribution hardware. Leaks that develop in these critical cooling systems that deplete in-line tanks can ultimately result in loss of cooling, which can have devastating impacts to the mission, science and crew onboard the ISS. A slow ammonia leak was initially observed from the P1 EATCS in 2011, but later in 2013 the leak rate began to accelerate. The ammonia inventory eventually began to decay exponentially, raising concerns that the inventory could drop to levels where the system would not be operational.The Robotic External Leak Locator (RELL) was built and launched to the ISS to detect and help locate ammonia leaks using the ISS Robotic Arm and remote ground operator control without constant crew involvement. RELL pinpointed the ammonia leak to the two flexible jumper hose assemblies connecting one of two fluid loops in one of the three deployable radiators to the P1 EATCS. The ammonia inside the two hose assemblies and that radiator fluid loop was isolated and vented to space in 2017. This stopped the leak and an Extravehicular Activity was conducted to remove the two hose assemblies so they could be returned to ground for further Test, Teardown and Evaluation (TT&E). The purpose of this presentation is to discuss this leakage scenario and the TT&E efforts.

Cowan, Darnell T.↗
NASA NTRS1986

Missing matter in the vicinity of the sun

The Poisson and Vlasov equations are solved numerically for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs, and K giants with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar mass/sq pc. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc.

Bahcall, John N.↗
NASA NTRS2015

An Empirical State Error Covariance Matrix Orbit Determination Example

State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. First, consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. Then it follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix of the estimate will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully include all of the errors in the state estimate. The empirical error covariance matrix is determined from a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm. It is a formally correct, empirical state error covariance matrix obtained through use of the average form of the weighted measurement residual variance performance index rather than the usual total weighted residual form. Based on its formulation, this matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty and whether the source is anticipated or not. It is expected that the empirical error covariance matrix will give a better, statistical representation of the state error in poorly modeled systems or when sensor performance is suspect. In its most straight forward form, the technique only requires supplemental calculations to be added to existing batch estimation algorithms. In the current problem being studied a truth model making use of gravity with spherical, J2 and J4 terms plus a standard exponential type atmosphere with simple diurnal and random walk components is used. The ability of the empirical state error covariance matrix to account for errors is investigated under four scenarios during orbit estimation. These scenarios are: exact modeling under known measurement errors, exact modeling under corrupted measurement errors, inexact modeling under known measurement errors, and inexact modeling under corrupted measurement errors. For this problem a simple analog of a distributed space surveillance network is used. The sensors in this network make only range measurements and with simple normally distributed measurement errors. The sensors are assumed to have full horizon to horizon viewing at any azimuth. For definiteness, an orbit at the approximate altitude and inclination of the International Space Station is used for the study. The comparison analyses of the data involve only total vectors. No investigation of specific orbital elements is undertaken. The total vector analyses will look at the chisquare values of the error in the difference between the estimated state and the true modeled state using both the empirical and theoretical error covariance matrices for each of scenario.

Frisbee, Joseph H., Jr.↗
NASA NTRS1989

Superbubble blowout dynamics

Multiple supernovae and stellar winds from OB associations carve large holes filled with hot gas in the galactic disk. These superbubbles sweep up H I into cold, thin, dense shells and eventually grow large enough to blow completely out of the galactic H I disk. When superbubbles blow out of the disk, they vent hot gas and supernova energy into the galactic corona. In this paper ZEUS, a two-dimensional hydrodynamics code, is used to model the blowout of a superbubble from exponential and Gaussian models for the vertical density stratification. The results are compared to those from the Kompaneets (thin-shell) approximation. It is found that this approximation works very well, and that most of the mass of the shell remains in the plane, with 5 percent of it accelerating upward. The venting of the hot gas and the stability of the shell depends strongly on the model of the density distribution. It is suggested that the low galactic halo actually consists of a froth of merged superbubbles.

Mac Low, Mordecai-Mark↗
NASA NTRS2005

Real-Time System Verification by Kappa-Induction

We report the first formal verification of a reintegration protocol for a safety-critical, fault-tolerant, real-time distributed embedded system. A reintegration protocol increases system survivability by allowing a node that has suffered a fault to regain state consistent with the operational nodes. The protocol is verified in the Symbolic Analysis Laboratory (SAL), where bounded model checking and decision procedures are used to verify infinite-state systems by k-induction. The protocol and its environment are modeled as synchronizing timeout automata. Because k-induction is exponential with respect to k, we optimize the formal model to reduce the size of k. Also, the reintegrator's event-triggered behavior is conservatively modeled as time-triggered behavior to further reduce the size of k and to make it invariant to the number of nodes modeled. A corollary is that a clique avoidance property is satisfied.

Pike, Lee S.↗
NASA NTRS1986

Dark matter near the sun

The amount of dark matter in the disk of the Galaxy at the solar position is determined by comparing the observed distributions of tracer stars with the predictions obtained from different assumptions of how the unseen matter is distributed. The major uncertainties, observational and theoretical, are estimated. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the sun is about 0.1 solar mass/cu pc; the corresponding column density is about 30 solar masses/cu pc. This, so far unseen, material must be in a disk with an exponential scale height of less than 0.7 kpc. All the existing observations are consistent with the unseen disk material being in the form of stars not massive enough to burn hydrogen. It is suggested that the unseen material that is required to hold up the rotation curves of galaxies and to satisfy the virial theorem for clusters of galaxies might also be in the form of low-mass stars.

Bahcall, J. N.↗
NASA NTRS1992

An analytic model of the neutral cloud evolution in the earth's atmosphere

An analytic model for the expansion of a chemically reacting gas in the upper atmosphere is discussed. The spatial-temporal distribution of released particles in the initial regime is described on the basis of self-similar solutions of Euler's equations. In the case of transition to the diffusion regime an approximate solution of the kinetic equation with the collision integral in the form of BGK is performed. Gravitation and the atmospheric inhomogeneity are taken into account, The diffusion regime is described by an analytic solution of the diffusion equation in an exponential atmosphere taking account of possible losses of the gas due to chemical reactions. Some peculiarities of the expansion of various gases as well as the possibility of applying the model for describing ionospheric 'holes' are discussed.

Bruskin, L. G.↗
NASA NTRS1972

X-ray study of solar plage regions and a small flare.

The O VII and Ne IX resonance line and 5 keV continuum emission of a small solar flare are interpreted on the basis of a model in which the emission measure of the region is an exponentially decreasing function of temperature. Good agreement with all three sets of data is obtained - a result not possible on the basis of an isothermal approximation. The change in the emission of the flare over a two minute interval appears to be consistent with a simple cooling of the region. Computation of the contribution function versus temperature for each emission indicates that each predominantly comes from a physically separate volume within the feature. The emission measure distribution for the flare is distinctly flatter than that of five plage regions which tend to have similar slopes and which are in turn flatter than the general corona.

Acton, L. W.↗
NASA NTRS1996

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

Ku, Jerry C.↗
NASA NTRS2011

Widespread Nanoflare Variability Detected with Hinode/XRT in a Solar Active Region

It is generally agreed that small impulsive energy bursts called nanoflares are responsible for at least some of the Sun s hot corona, but whether they are the explanation for most of the multi-million degree plasma has been a matter of ongoing debate. We here present evidence that nanoflares are widespread in an active region observed by the X-Ray Telescope on-board the Hinode mission. The distributions of intensity fluctuations have small but important asymmetries, whether taken from individual pixels, multi-pixel subregions, or the entire active region. Negative fluctuations (corresponding to reduced intensity) are greater in number but weaker in amplitude, so that the median fluctuation is negative compared to a mean of zero. Using Monte Carlo simulations, we show that only part of this asymmetry can be explained by Poisson photon statistics. The remainder is explainable with a tendency for exponentially decreasing intensity, such as would be expected from a cooling plasma produced, e.g., from a nanoflare. We suggest that nanoflares are a universal heating process within active regions.

Reale, Fabio↗
NASA NTRS1991

Neutral hydrogen in the outer Galaxy

The H I 21 cm emission-line survey data of Stark et al. (1991) have been used to study the distribution of H I in the outer Galaxy and to improve understanding of the various systematic problems which influence all studies of Galactic H I. For n(H) greater than 0.01/cu cm, the distributions are similar to those found by Burton and te Lintel Hekkert (1986) but are 'better behaved' at substantially lower values of n(H). The z distribution of gas in the H I layer is best described as complicated. The behavior of the gaseous matter is consistent with the observed distribution of H I found in external spiral galaxies. In the directions of the maximum warp the average distance of the gas away from the Galactic plane reaches about 4 kpc at R about 24 kpc, while the flaring of the layer as measured by z(rms) increases to about 3 kpc. In directions where the warp layers particularly well measured, the Galaxy is followed to R about 30 kpc. The surface density of the atomic gas decreases exponentially.

Diplas, Athanassios↗
NASA NTRS1987

Balloon-borne observations of the development and vertical structure of the Antarctic ozone hole in 1986

The vertical distribution of ozone measured at McMurdo Station, Antarctica using balloon-borne sensors on 33 occasions during November 6, 1986 - August 25, 1986 is described. These observations suggest a highly structured cavity confined to the 12-20 km altitude region. In the 17-19 km altitude range, the ozone volume mixing ratio declined from about 2 ppm at the end of August to about 0.5 ppm by mid-October. The average decay in this region can be described as exponential with a half life of about 25 days. While total ozone, as obtained from profile integration, declined only about 35 percent, the integrated ozone between 14 and 18 km declined more than 70 percent. Vertical ozone profiles in the vortex revealed unusual structure with major features from 1 to 5 km thick which had suffered ozone depletions as great as 90 percent.

Hofmann, D. J.↗
NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗