Search NASA⌕ Search

SEARCH · Search NASA

Results for “Approximate inverses”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Saturn's rings - Particle size distributions for thin layer model

A model incorporating limited interaction between the incident energy and particles in the ring is considered which appears to be consistent with the multiple scattering process in Saturn's rings. The model allows for the small physical thickness of the rings and can be used to relate Voyager 1 observations of 3.6- and 13-cm wavelength microwave scatter from the rings to the ring particle size distribution function for particles with radii ranging from 0.001 to 20 m. This limited-scatter model yields solutions for particle size distribution functions for eight regions in the rings, which exhibit approximately inverse-cubic power-law behavior.

Zebker, H. A.↗
NASA NTRS1985

A methodology for designing robust multivariable nonlinear feedback control systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: (1) Properties of the solution of certain optimal control problems; (2) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; (3) The Loop Operator Recovery (LOR) procedure, and (4) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.

Grunberg, D. B.↗
NASA NTRS1989

Digital restoration of multichannel images

The Wiener solution of a multichannel restoration scheme is presented. Using matrix diagonalization and block-Toeplitz to block-circulant approximation, the inversion of the multichannel, linear space-invariant imaging system becomes feasible by utilizing a fast iterative matrix inversion procedure. The restoration uses both the within-channel (spatial) and between-channel (spectral) correlation; hence, the restored result is a better estimate than that produced by independent channel restoration. Simulations are also presented.

Galatsanos, Nikolas P.↗
NASA NTRS1991

Polynomial Transformations For Discrete-Time Linear Systems

Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.

Baram, Yoram↗
NASA NTRS1990

Thermodynamic structure of the stratocumulus-capped boundary layer on 5 July 1987

The National Center for Atmospheric Research (NCAR) Electra flew a single aircraft mission on July 5 in comparatively uniform stratocumulus cloud (80 to 100 percent cloud coverage). The flight pattern, a series of north-south doglegs centered at (32N, -122W), included 15 full or partial soundings to examine layer vertical structure between altitudes of 150 and 5000 m. The air below the inversion was well-mixed in moist static energy, total water, and ozone. The inversion base measured by the aircraft ranged from 920 to 938 hPa, while the thickness of the cloud layer varied between 30 and 10 hPa. Maximum cloud liquid water contents approached 0.3 g kg(-1) (as measured by the Johnson-Williams and King probes). Comparison of soundings made in the same location show a strengthening of the inversion and increasing shear at cloud top over the observation period (16:50 to 00:22 UT). Typical windspeeds below the inversion were approximately 10 m s(-1) decreasing to 6 m s(-1) 8 hPa above cloud top. A thermodynamic budget for this case is in preparation; it will provide a comparison and contrast with the more complicated July 7 case.

Austin, Philip H.↗
NASA NTRS1991

Waves in Venus's middle and upper atmosphere - Implications of Pioneer Venus probe data above the clouds

This paper reevaluates Pioneer Venus probe data which show the presence of waves in Venus's middle and upper atmosphere. The data are extended to 138 km. Uncertainties in the temperature are typically about 0.1 times amplitude, supporting the reliability of large-amplitude oscillations approaching 40 K at 120 km. Growth rates above 100 km follow approximately the inverse square root of density and 'saturation' occurs. The waves then break at the 120 km level, providing a source for the 'friction' required in models to match the observed day-night temperature contrast in the lower thermosphere. The data correlated to an unexpected degree with temperatures from the Pioneer Venus orbiter atmospheric drag experiment. The observations lead to the suggestion that the thermospheric waves are solar-fixed, induced either by the major subsidence across the termination or as continuation upward of waves in the middle atmosphere.

Seiff, Alvin↗
NASA NTRS1995

Real-time design with peer tasks

We introduce a real-time design methodology for large scale, distributed, parallel architecture, real-time systems (LDPARTS), as an alternative to those methods using rate or dead-line monotonic analysis. In our method the fundamental units of prioritization, work items, are domain specific objects with timing requirements (deadlines) found in user's specification. A work item consists of a collection of tasks of equal priority. Current scheduling theories are applied with artifact deadlines introduced by the designer whereas our method schedules work items to meet user's specification deadlines (sometimes called end-to-end deadlines). Our method supports these scheduling properties. Work item scheduling is based on domain specific importance instead of task level urgency and still meets as many user specification deadlines as can be met by scheduling tasks with respect to urgency. Second, the minimum (closest) on-line deadline that can be guaranteed for a work item of highest importance, scheduled at run time, is approximately the inverse of the throughput, measured in work items per second. Third, throughput is not degraded during overload and instead of resorting to task shedding during overload, the designer can specify which work items to shed. We prove these properties in a mathematical model.

Goforth, Andre↗
NASA NTRS1961

Applications of Power Spectral Analysis Methods to Maneuver Loads Obtained on Jet Fighter Airplanes During Service Operations

Power spectral densities of normal load factor have been obtained for two service operational training flights of a Republic F-84G airplane and three service operational training flights of a North American F-86A airplane in order to indicate the load-factor frequency content and possible uses of power spectral methods in analyzing maneuver load data. It was determined that the maneuvering load-factor time histories appeared to be described by a truncated normal distribution. The power spectral densities obtained were relatively level at frequencies below 0.03 cycle per second and varied inversely with approximately the cube of the frequency at the higher frequencies. In general, the frequency content was very low above 0.2 cycle per second. The load-factor peak distributions were estimated fairly well from the spectrum analysis. In addition, peak load data obtained during service operations of fighter-type airplanes with flight time totaling about 24,000 hours were examined and appeared to agree reasonably well with the type of equations obtained from spectrum peak-load distributions.

Mayer, John P.↗
NASA NTRS2004

Molecular Oxygen Mixing Ratio and Its Seasonal Variability in the Martian Atmosphere

The mixing ratio of molecular oxygen and other species that do not condense at martian ambient conditions will vary as the mass of atmosphere oscillates over a martian year due to alternate condensation and vaporization of carbon dioxide at the poles. This variation can be estimated utilizing measurements of mixing ratio made in-situ together with multi-year measurements of atmospheric pressure, both available from the Viking landers starting in 1976. The concentration of non-condensables, on average, will be approximately an inverse function of the atmospheric pressure.

England, Christopher↗
NASA NTRS2005

Calculation of H2-He Flow with Nonequilibrium Ionization and Radiation: an Interim Report

The nonequilibrium ionization process in hydrogen-helium mixture behind a strong shock wave is studied numerically using the detailed ionization rate model developed recently by Park which accounts for emission and absorption of Lyman lines. The study finds that, once the avalanche ionization is started, the Lyman line is self-absorbed. The intensity variation of the radiation at 5145 Angstroms found by Leibowitz in a shock tube experiment can be numerically reproduced by assuming that ionization behind the shock wave prior to the onset of avalanche ionization is 1.3%. Because 1.3% initial ionization is highly unlikely, Leibowitz s experimental data is deemed questionable. By varying the initial electron density value in the calculation, the calculated ionization equilibration time is shown to increase approximately as inverse square-root of the initial electron density value. The true ionization equilibration time is most likely much longer than the value found by Leibowitz.

Furudate, Michiko↗
NASA NTRS1993

Transversal filter for parabolic phase equalization

An equalizer (10) for removing parabolic phase distortion from an analog signal (3), utilizing a pair of series connected transversal filters. The parabolic phase distortion is cancelled by generating an inverse parabolic approximation using a sinusoidal phase control filter (18). The signal (3) is then passed through an amplitude control filter (21) to remove magnitude ripple components.

Kelly, Larry R.↗
NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗
NASA NTRS2007

Reconfigurable Control with Neural Network Augmentation for a Modified F-15 Aircraft

This paper describes the performance of a simplified dynamic inversion controller with neural network supplementation. This 6 DOF (Degree-of-Freedom) simulation study focuses on the results with and without adaptation of neural networks using a simulation of the NASA modified F-15 which has canards. One area of interest is the performance of a simulated surface failure while attempting to minimize the inertial cross coupling effect of a [B] matrix failure (a control derivative anomaly associated with a jammed or missing control surface). Another area of interest and presented is simulated aerodynamic failures ([A] matrix) such as a canard failure. The controller uses explicit models to produce desired angular rate commands. The dynamic inversion calculates the necessary surface commands to achieve the desired rates. The simplified dynamic inversion uses approximate short period and roll axis dynamics. Initial results indicated that the transient response for a [B] matrix failure using a Neural Network (NN) improved the control behavior when compared to not using a neural network for a given failure, However, further evaluation of the controller was comparable, with objections io the cross coupling effects (after changes were made to the controller). This paper describes the methods employed to reduce the cross coupling effect and maintain adequate tracking errors. The IA] matrix failure results show that control of the aircraft without adaptation is more difficult [leas damped) than with active neural networks, Simulation results show Neural Network augmentation of the controller improves performance in terms of backing error and cross coupling reduction and improved performance with aerodynamic-type failures.

Burken, John J.↗
NASA NTRS1985

Approximation methods for the solution of inverse problems in lake and sea sediment core analysis

A theoretical model employing one-dimensional (depth) transport equations to describe vertical redistribution of ocean-floor and lake-floor sediment (particulates, volcanic ash, microtektites, or radioactive tracers) by episodic and nonepisodic events including bioturbation is developed analytically and demonstrated. The principles underlying the model are explained; the model equations are derived; the inverse problem of identifying the depth-dependent bioturbation coefficient is addressed; two approximation theorems are presented; and numerical results for two sample problems are presented graphically. It is suggested that compatification, porosity effects, and depth-dependent sedimentation be taken into account when formulating future models.

Banks, H. T.↗
NASA NTRS1978

Analytical inversions in remote sensing of particle size distributions. I - Multispectral extinctions in the anomalous diffraction approximation. II Angular and spectral scattering in diffraction approximations

Consideration is given to analytical inversions in the remote sensing of particle size distributions, noting multispectral extinctions in anomalous diffraction approximation and angular and spectral scattering in diffraction approximation. A closed-form analytical inverse solution is derived in order to reconstruct the size distribution of atmospheric aerosols. The anomalous diffraction approximation to Mie's solution is used to describe the particles. Experimental data yield the geometrical area of aerosol polydispersion. Size distribution is thus found from a set of multispectral extinction measurements. In terms of the angular and spectral scattering of light in a narrow forward cone, it is shown that an analytical inverse solution may also be found for the Fraunhofer approximation to the Kirchhoff diffraction, and for an improved expression of this approximation due to Penndorf (1962) and Shifrin-Punina (1968).

Fymat, A. L.↗
NASA NTRS1992

Large-scale sparse singular value computations

Four numerical methods for computing the singular value decomposition (SVD) of large sparse matrices on a multiprocessor architecture are presented. Lanczos and subspace iteration-based methods for determining several of the largest singular triplets (singular values and corresponding left and right-singular vectors) for sparse matrices arising from two practical applications: information retrieval and seismic reflection tomography are emphasized. The target architectures for implementations are the CRAY-2S/4-128 and Alliant FX/80. The sparse SVD problem is well motivated by recent information-retrieval techniques in which dominant singular values and their corresponding singular vectors of large sparse term-document matrices are desired, and by nonlinear inverse problems from seismic tomography applications which require approximate pseudo-inverses of large sparse Jacobian matrices.

Berry, Michael W.↗
NASA NTRS1981

Rapid inversion of limb radiance data using an emissivity growth approximation

The time-consuming nature of limb relaxation-type inversion algorithms is due primarily to the numerous integrations over an absorption band to obtain forward radiance values with which to compare measured values. A new method has been devised for the quick and accurate (0.5% error) calculation of single gas broadband (approximately 100 per cm) limb radiance. The method uses a precalculated data base consisting of homogeneous path emissivity vs mass path data for a wide range of temperature and pressure. A 50-km altitude range, 1-km resolution, constituent inversion employing this method requires under 1 sec of computational time when run on modern computer hardware. The method does not rely upon a priori statistical knowledge.

Gordley, L. L.↗