SEARCH · Engineering Papers

Results for “linearity”

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.

SourceResearch connectionFrom yearThrough year

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

At least 559 records · Page 31

All sources NASA NTRS DOE OSTI

NASA NTRS1984

A model of asynchronous iterative algorithms for solving large, sparse, linear systems

Solving large, sparse, linear systems of equations is one of the fundamental problems in large scale scientific and engineering computation. A model of a general class of asynchronous, iterative solution methods for linear systems is developed. In the model, the system is solved by creating several cooperating tasks that each compute a portion of the solution vector. This model is then analyzed to determine the expected intertask data transfer and task computational complexity as functions of the number of tasks. Based on the analysis, recommendations for task partitioning are made. These recommendations are a function of the sparseness of the linear system, its structure (i.e., randomly sparse or banded), and dimension.

Reed, D. A.↗

NASA NTRS1983

A linear analysis of the transition curve for the baroclinic annulus

A primitive equation linear model is shown to be capable of quantitatively predicting the neutral curve for a baroclinic annulus. Flows unstable to small nonaxisymmetric perturbations are assumed to lie on the nonaxisymmetric side of a transition curve, while the stable flows are on the axisymmetric side. The stability in the presence of perturbations is tested with linearized hydrostatic primitive equations. Attention is given to the fastest growing eigenmodes, demonstrating that the linear and nonlinear wave have similar structures at a particular point in the nonaxisymmetric regime. All the waves are similar to the Eddy wave except at the extreme to the transition curve, where the waves maintain little structure with height. The eddy kinetic energy is baroclinic with a potential energy suppresed by the large static stability of the basic state. Eddy dissipation is noted to be significant near all boundaries.

Miller, T. L.↗

NASA NTRS1983

Solution algorithms for non-linear singularly perturbed optimal control problems

The applicability and usefulness of several classical and other methods for solving the two-point boundary-value problem which arises in non-linear singularly perturbed optimal control are assessed. Specific algorithms of the Picard, Newton and averaging types are formally developed for this class of problem. The computational requirements associated with each algorithm are analysed and compared with the computational requirement of the method of matched asymptotic expansions. Approximate solutions to a linear and a non-linear problem are obtained by each method and compared.

Ardema, M. D.↗

NASA NTRS1983

Thermal oxidative degradation reactions of linear perfluoroalkyl ethers

Thermal and thermal oxidative stability studies were performed on linear perfluoroalkyl ether fluids. The effect on degradation by metal catalysts and degradation inhibitors is reported. The linear perfluoroalkyl ethers are inherently unstable at 316 C in an oxidizing atmosphere. The metal catalysts greatly increased the rate of degradation in oxidizing atmospheres. In the presence of these metals in an oxidizing atmosphere, the degradation inhibitors were highly effective in arresting degradation at 288 C. However, the inhibitors had only limited effectiveness at 316 C. The metals promote degradation by chain scission. Based on elemental analysis and oxygen consumption data, the linear perfluoroalkyl ether fluids have a structural arrangement based on difluoroformyl and tetrafluoroethylene oxide units, with the former predominating. Previously announced in STAR as N82-26468

Jones, W. R., Jr.↗

NASA NTRS1986

Design of Linear Quadratic Regulators and Kalman Filters

AESOP solves problems associated with design of controls and state estimators for linear time-invariant systems. Systems considered are modeled in state-variable form by set of linear differential and algebraic equations with constant coefficients. Two key problems solved by AESOP are linear quadratic regulator (LQR) design problem and steady-state Kalman filter design problem. AESOP is interactive. User solves design problems and analyzes solutions in single interactive session. Both numerical and graphical information available to user during the session.

Lehtinen, B.↗

NASA NTRS1984

Overview of magnetic bearing control and linearization approaches for annular magnetically suspended devices

An overview of magnetic bearing control and linearization approaches which have been considered for annular magnetically suspended devices is presented. These devices include the Annular Momentum Control Device and the Annular Suspension and Pointing System. Two approaches were investigated for controlling the magnetic actuator. One approach involves controlling the upper and lower electromagnets differentially about a bias flux. The bias flux can either be supplied by permanent magnets in the magnetic circuit or by bias currents. In the other approach, either the upper electromagnet or the lower electromagnet is controlled depending on the direction of force required. One advantage of the bias flux is that for small gap perturbations about a fixed operating point, the force-current characteristic is linear. Linearization approaches investigated for individual element control include an analog solution of the nonlinear electromagnet force equation and a microprocessor-based table lookup method.

Groom, N. J.↗

NASA NTRS1985

The Use of Linear Feature Detection to Investigate Thematic Mapper Data Performance and Processing

The geometric and radiometric characteristics of thematic mapper data through analysis of linear features in the data are investigated. The particular aspects considered are: (1) thematic mapper ground IFUV; (2) radiometric contrast between linear features and background; (3) precision of system geometric correction; (4) band-to-band registration; and (5) potential utility of TM data for linear feature detection especially as compared to MSS data. It is shown that TM data may be used to estimate TM pixel size illustrate band: band mis-registration.

Gurney, C. M.↗

NASA NTRS1984

A high-accuracy optical linear algebra processor for finite element applications

Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.

Casasent, D.↗

NASA NTRS1985

A method for high order linear system reduction and nonlinear system simplification

Least-squares-type algorithms for reducing the order of linear systems in the frequency domain and simplifying nonlinear systems in time domain are developed and demonstrated. The possible model structures are represented as nodes in a tree, and costs along the branches are assigned using the repeated-Gram-Schmidt orthogonalization procedure of Desrochers and Saridis (1980), permitting identification of the optimal n-term model by searching the tree to depth n, with no need for parameter identification. The efficiency and flexibility of the algorithms is shown in applications to the eighth-order linear system studied by Hsia (1972), a three-state eight-nonlinear-term aircraft-dynamics problem, and the related linear-controller problem (Garrard and Jordan, 1977).

Desrochers, A. A.↗

NASA NTRS1983

Linear approximations of nonlinear systems

A method for designing an automatic flight controller for short and vertical takeoff aircraft is presently being developed at NASA Ames Research Center. This technique involves transformations of nonlinear systems to controllable linear systems and takes into account the nonlinearities of the aircraft. In general, the transformations cannot always be given in closed form. Using partial differential equations, an approximate linear system, called the modified tangent model, was recently introduced. A linear transformation of this tangent model to Brunovsky canonical form can be constructed, and from this an approximation of an exact transformation for the nonlinear system can be found. It is shown that a canonical expansion in Lie brackets about the point x(0) yields the same modified tangent model.

Hunt, L. R.↗

NASA NTRS1985

Variability simulations with a steady, linearized primitive equations model

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

Kinter, J. L., III↗

NASA NTRS1985

Linearity optimization in a class of analog phase modulators

This paper examines the ultimate modulating linearity attainable with a phase modulation technique based on the linear addition of quadrature phase carrier signals which have been multiplied by precisely defined nonlinear transformations of the modulating signal. Optimum gain coefficients are derived and plotted to permit implementation of analog phase modulators capable of exceptionally good linearity of phase deviations as large as 5 radians.

Hearn, C. P.↗

NASA NTRS1986

A method for linearizing a nonlinear system with six state variables and three control variables

A nonlinear system governed by x = f(x,u) with six state variables and three control variables is considered in this project. A set of transformations from (x,u) - space to (z,v) - space is defined such that the linear tangent model is independent of the operating point in the z-space. Therefore, it is possible to design a control law satisfying all operating points in the transformed space. An algorithm to construct the above transformations and to obtain the associated linearized system is described in this report. This method is applied to a rigid body using pole placement for the control law. Results are verified by numerical simulation. Closed loop poles in x-space using traditional local linearization are compared with those pole placements in the z-space.

Hsia, W. S.↗

NASA NTRS1986

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Gibson, J. S.↗

NASA NTRS1985

Effects of a high mean stress on the high cycle fatigue life of PWA 1480 and correlation of data by linear elastic fracture mechanics

High-cycle fatigue tests using 5-mm-diameter smooth specimens were performed on the single crystal alloy PWA 1480 (001 axis) at 70F (room temperature) in air and at 100F (538C) in vacuum (10 to the -6 power torr). Tests were conducted at zero mean stress as well as at high tensile mean stress. The results indicate that, although a tensile mean stress, in general, reduces life, the reduction in fatigue strength, for a given mean stress at a life of one million cycles, is much less than what is predicted by the usual linear Goodman plot. Further, the material appears to be significantly more resistant to mean stress effects at 1000F than at 70F. Metallographic examinations of failed specimens indicate that failures in all cases are initiated from micropores of sizes of the order of 30 to 40 microns. Since the macroscopic stress-strain response in all cases was observed to be linear elastic, linear elastic fracture mechanics (LEFM) analyses were carried out to determine the crack growth curves of the material assuming that crack initiation from a micropore (a sub o = 40 microns) occurs very early in life. The results indicate that the calculated crack growth rates at an R (defined as the ratio between minimum stress to maximum stress) value of zero are approximately the same at 70F as at 1000F. However, the calculated crack growth rates at other R ratios, both positive and negative, tend to be higher at 70F than at 1000F. Calculated threshold effects at large R values tend to be independent of temperature in the temperature regime studied. They are relatively constant with increasing R ratio up to a value of about 0.6, beyond which the calculated threshold stress intensity factor range decreases rapidly with increasing R ratios.

Majumdar, S.↗

NASA NTRS1986

Identification of linearized equations of motion for the fixed wing configuration of the rotor systems research aircraft

The purpose of this report is to establish linear, decoupled models of rigid body motion for the fixed wing configuration of the Rotor Systems Research Aircraft (RSRA). Longitudinal and lateral control surface fixed linear models were created from aircraft time histories using current system identification techniques. Models were obtained from computer simulation at 160 KCAS and 200 KCAS, and from flight data at 160 KCAS. Comparisons were performed to examine modeling accuracy, variation of dynamics with airspeed and correlation of simulation and flight data results. The results showed that the longitudinal and lateral linear models accurately predicted RSRA dynamics. The flight data results showed that no significant handling qualities problems were present in the RSRA fixed wing aircraft at the flight speed tested.

Balough, D. L.↗

NASA NTRS1986

Multispectral linear array multiband selection device

An apparatus for detecting multiple spectral bands, individually or concurrently, using linear detector arrays is described. The system employs a beamsplitter to divide the optical source into two or more optical beams which are directed at the linear detector arrays. Filter trays are positioned in the focal planes of the optical beams so that the beams pass through the filter trays prior to impinging upon the detector arrays. Multiple filters are placed on the filter trays. Linear actuators positioned adjacent the filter trays translate the trays across the focal planes of the optical beams so that individual filters are positioned in the path of beams such that those frequencies of the beams that fall within the spectral ranges of the individual bandpass filter through which it passes may be detected by the detector arrays for further examination and analysis.

Richard, H. L.↗

NASA NTRS1986

Descriptive Linear modeling of steady-state visual evoked response

A study is being conducted to explore use of the steady state visual-evoke electrocortical response as an indicator of cognitive task loading. Application of linear descriptive modeling to steady state Visual Evoked Response (VER) data is summarized. Two aspects of linear modeling are reviewed: (1) unwrapping the phase-shift portion of the frequency response, and (2) parsimonious characterization of task-loading effects in terms of changes in model parameters. Model-based phase unwrapping appears to be most reliable in applications, such as manual control, where theoretical models are available. Linear descriptive modeling of the VER has not yet been shown to provide consistent and readily interpretable results.

Levison, W. H.↗