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Results for “Automatic Differentiation”

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.

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NASA NTRS1988

Interleaver design for trellis-coded differential 8-PSK modulation with non-coherent detection

The effect of finite interleaver size on bit error rate (BER) performance of coded 8-DPSK is determined by means of computer simulations. The losses evaluated in this way include the SNR degradation due to the timing and frequency errors of the symbol synchronizer and the automatic frequency control (AFC) of the receiver. BER measurements are presented using a conventional 2/3 rate convolutional 8-state trellis-code for typical Rayleigh and Rician fading channels. It is shown that for a Rician channel with a Rician parameter of 7 dB, a Doppler spread of 100 Hz and a data rate of 2400 bps, an interleaver with size 16 x 16 symbols performs nearly as well as a very large interleaver. It is also shown that for very fast Rayleigh channels, the BER-curves flatten out at large SNR.

Edbauer, Franz↗

NASA NTRS2001

Test Results for an Off-the-Shelf GPS/INS During Approach and Landing Testing of the X-40A

The X-37 is an unpiloted, reusable space vehicle that will be launched into space, orbit the Earth, reenter the atmosphere, and land autonomously. At the heart of the Guidance, Navigation and Control (GN&C) will be the Space Integrated GPS/INS (SIGI) system, an off the shelf navigation grade GPS/INS that has been enhanced for space and reentry environments. SIGI will provide both navigation and flight control data to the X-37's GN&C. The X-40A is an unpiloted experimental vehicle whose shape and performance are similar to the X-37's and was flown earlier this year to develop and test the approach and landing phase of X-37. On board the X-40A is the X-37's SIGI, which is riding along as an experiment. The X-40A SIGI experiment provided early characterization of SIGI operation and performance with differential GPS (Global Positioning System) during real world approach and landing. Characterization testing was geared toward assessment of reliability and performance of the system. The objectives were to demonstrate performance levels sufficient to meet the X-37 requirements for automatic, autonomous approach and landing, demonstrate reliability over repeated ground and flight tests, and reduce risk for integration of SIGI into the vehicle and support environment. This paper presents a summary of this testing and the results to date.

Childers, Dave↗

NASA NTRS1975

Use of numerically generated body-fitted coordinate systems for solution of the Navier-Stokes equations

A procedure for numerical solution of the time-dependent, two-dimensional incompressible Navier-Stokes equations that can treat the unsteady laminar flow about bodies of arbitrary shape, such as two-dimensional airfoils, multiple airfoils, and submerged hydrofoils, as naturally as it can deal with the flow about simple bodies. The solution is based on a method of automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multiconnected region containing any number of arbitrarily shaped bodies. The curvilinear coordinates are generated as the solution of two elliptical partial differential equations with Dirichlet boundary conditions, one coordinate being specified to be constant on each of the boundaries, and a distribution of the other being specified along the boundaries. The solution compares excellently with the Blasius boundary layer solution for the flow past a semiinfinite flat plate.

Thompson, J. F.↗

NASA NTRS1986

Fast algorithm for calculating chemical kinetics in turbulent reacting flow

This paper addresses the need for a fast batch chemistry solver to perform the kinetics part of a split operator formulation of turbulent reacting flows, with special attention focused on the solution of the ordinary differential equations governing a homogeneous gas-phase chemical reaction. For this purpose, a two-part predictor-corrector algorithm which incorporates an exponentially fitted trapezoidal method was developed. The algorithm performs filtering of ill-posed initial conditions, automatic step-size selection, and automatic selection of Jacobi-Newton or Newton-Raphson iteration for convergence to achieve maximum computational efficiency while observing a prescribed error tolerance. The new algorithm, termed CREK1D (combustion reaction kinetics, one-dimensional), compared favorably with the code LSODE when tested on two representative problems drawn from combustion kinetics, and is faster than LSODE.

Radhakrishnan, K.↗

NASA NTRS1995

A deterministic particle method for one-dimensional reaction-diffusion equations

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Mascagni, Michael↗

NASA NTRS1974

LC-oscillator with automatic stabilized amplitude via bias current control

A stable excitation supply for measurement transducers is described. It consists of a single-transistor oscillator with a coil connected to the collector and a capacitor connected from the collector to the emitter. The output of the oscillator is rectified and the rectified signal acts as one input to a differential amplifier; the other input being a reference potential. The output of the amplifier is connected at a point between the emitter of the transistor and ground. When the rectified signal is greater than the reference signal, the differential amplifier produces a signal of polarity to reduce bias current and, consequently, amplification.

Hamlet, J. F.↗

NASA NTRS1979

Evaluating the reforested area for the municipality of Buri by automatic analysis of LANDSAT imagery

The author has identified the following significant results. The class of reforestation (Pinus, Eucalyptus, Araucaria) was defined using iterative image analysis (1-100) and LANDSAT MSS data. Estimates of class area by 1-100 were compared with data supplied by the forestry institute in Sao Paulo. LANDSAT channels 4 and 5 served to differentiate the Pinus, Eucalyptus, and Araucaria from the other trees. Channels 6 and 7 gave best results for differentiating between the classes. A good representative spectral response was obtained for Auraucaria on these two channels. The small relative differences obtained were +4.24% for Araucaria, -7.51% for Pinus, and -32.07% for Eucalyptus.

Dejesusparada, N.↗

NASA NTRS1974

Automatic numerical generation of body-fitted curvilinear coordinate system for field containing any number of arbitrary two-dimensional bodies

A method for automatic numerical generation of a general curvilinear coordinate system with coordinate lines coincident with all boundaries of a general multi-connected region containing any number of arbitrarily shaped bodies is presented. With this procedure the numerical solution of a partial differential system may be done on a fixed rectangular field with a square mesh with no interpolation required regardless of the shape of the physical boundaries, regardless of the spacing of the curvilinear coordinate lines in the physical field, and regardless of the movement of the coordinate system. Numerical solutions for the lifting and nonlifting potential flow about Joukowski and Karman-Trefftz airfoils using this coordinate system generation show excellent comparison with the analytic solutions. The application to fields with multiple bodies is illustrated by a potential flow solution for multiple airfoils.

Thompson, J. F.↗

NASA NTRS1993

Automated Surface Profilometer

Computer-controlled system saves time and labor. Electromechanical scanning system automatically measures deviation of sheets and plates from flatness. Quickly measures surface profile and detects bumps, bulges, and indentations as small as 0.001 in. in height or depth. X-y table moves specimen to programmed locations under digital linear variable differential transformer (LVDT) while computer records surface-height readings of LVDT. Resulting graphical display shows surface contour.

Chern, E. James↗

NASA NTRS1993

An automatic multigrid method for the solution of sparse linear systems

An automatic version of the multigrid method for the solution of linear systems arising from the discretization of elliptic PDE's is presented. This version is based on the structure of the algebraic system solely, and does not use the original partial differential operator. Numerical experiments show that for the Poisson equation the rate of convergence of our method is equal to that of classical multigrid methods. Moreover, the method is robust in the sense that its high rate of convergence is conserved for other classes of problems: non-symmetric, hyperbolic (even with closed characteristics) and problems on non-uniform grids. No double discretization or special treatment of sub-domains (e.g. boundaries) is needed. When supplemented with a vector extrapolation method, high rates of convergence are achieved also for anisotropic and discontinuous problems and also for indefinite Helmholtz equations. A new double discretization strategy is proposed for finite and spectral element schemes and is found better than known strategies.

Shapira, Yair↗

NASA NTRS1992

Self-learning fuzzy controllers based on temporal back propagation

This paper presents a generalized control strategy that enhances fuzzy controllers with self-learning capability for achieving prescribed control objectives in a near-optimal manner. This methodology, termed temporal back propagation, is model-insensitive in the sense that it can deal with plants that can be represented in a piecewise-differentiable format, such as difference equations, neural networks, GMDH structures, and fuzzy models. Regardless of the numbers of inputs and outputs of the plants under consideration, the proposed approach can either refine the fuzzy if-then rules if human experts, or automatically derive the fuzzy if-then rules obtained from human experts are not available. The inverted pendulum system is employed as a test-bed to demonstrate the effectiveness of the proposed control scheme and the robustness of the acquired fuzzy controller.

Jang, Jyh-Shing R.↗

NASA NTRS1951

A Simplified Instrument for Recording and Indicating Frequency and Intensity of Icing Conditions Encountered in Flight

An instrument for recording and indicating the frequency and intensity of aircraft icing conditions encountered in flight has been developed by the NACA Lewis Laboratory to obtain statistical icing data over world-wide air routes during routine airline operations. The operation of the instrument is based on the creation of a differential pressure between an ice-free total-pressure system and a total-pressure system in which small total-pressure holes vented to static pressure are allowed to plug with ice accretion. The simplicity of this operating principle permits automatic operation, and provides relative freedom from maintenance and operating problems. The complete unit weighing only 18 pounds records icing rate, airspeed, and altitude on photographic film and provides visual indications of icing intensity to the pilot.

ICE FORMATION↗

NASA NTRS1976

Aeroelastic analysis for helicopter rotor blades with time-variable, non-linear structural twist and multiple structural redundancy: Mathematical derivation and program user's manual

The differential equations of motion for the lateral and torsional deformations of a nonlinearly twisted rotor blade in steady flight conditions together with those additional aeroelastic features germane to composite bearingless rotors are derived. The differential equations are formulated in terms of uncoupled (zero pitch and twist) vibratory modes with exact coupling effects due to finite, time variable blade pitch and, to second order, twist. Also presented are derivations of the fully coupled inertia and aerodynamic load distributions, automatic pitch change coupling effects, structural redundancy characteristics of the composite bearingless rotor flexbeam - torque tube system in bending and torsion, and a description of the linearized equations appropriate for eigensolution analyses. Three appendixes are included presenting material appropriate to the digital computer program implementation of the analysis, program G400.

Bielawa, R. L.↗

NASA NTRS1991

Computerized reduction of elementary reaction sets for combustion modeling

If the entire set of elementary reactions is to be solved in the modeling of chemistry in computational fluid dynamics, a set of stiff ordinary differential equations must be integrated. Some of the reactions take place at very high rates, requiring short time steps, while others take place more slowly and make little progress in the short time step integration. The goal is to develop a procedure to automatically obtain sets of finite rate equations, consistent with a partial equilibrium assumptions, from an elementary set appropriate to local conditions. The possibility of computerized reaction reduction was demonstrated. However, the ability to use the reduced reaction set depends on the ability of the CFD approach in incorporate partial equilibrium calculations into the computer code. Therefore, the results should be tested on a code with partial equilibrium capability.

Wikstrom, Carl V.↗

NASA NTRS1994

1988-1991 photometry of the chromospherically active double-lined binary system HD 163621 = V835 Herculis

Photometry in V and B with a 16-inch automatic telescope from 1988 to 1991 confirms the synchronous rotation suspected earlier and reveals variability up to 0.1M in the B bandpass at one epoch. Five spots formed with lifetimes ranging from 0.15 to 0.77 years. As with other rapid rotators, the differential rotation coefficient (k = 0.03) is significantly smaller than that of the Sun (k = 0.19).

Hall, Douglas↗

NASA NTRS1972

On the dependence of information display quality requirements upon human characteristics and pilot/automatics relations

Present information display concepts for pilot landing guidance are outlined considering manual control as well as substitution of man by fully competent automatics. Display improvements are achieved by compressing the distributed indicators into an accumulative display and thus reducing information scanning. Complete integration of quantitative indications, outer loop information, and real world display in a pictorial information channel geometry constitutes an interface with human ability to differentiate and integrate for optimal manual control of the aircraft.

Wilckens, V.↗

NASA NTRS1980

Generation of boundary and boundary-layer fitting grids

The details of extended physical processes, such as the gas dynamic flow over an airfoil, the reactive flow through a combustor, or the electric field in a multi-contact transistor, are understood by solving the differential equations of a mathematical model of the process. The accuracy of finite difference methods for the numerical solution of the equations is increased if the underlying mesh fits the region boundaries and is closely spaced in regions where the solution is rapidly varying. Automatic methods for producing a satisfactorily adjusted mesh were developed for one dimensional problems. In one simple, effective scheme of this kind the unknown function and the distribution of mesh modes are found simultaneously, the nodes being placed so that they correspond to points uniformly spaced on the solution curve. In a two dimensional generalization, the nodes correspond to points equally spaced on the solution surface in two directions that are as nearly orthogonal as possible. Examples of such meshes are shown.

Ablow, C. M.↗

NASA NTRS2011

Radiation-Tolerant, SpaceWire-Compatible Switching Fabric

Current and future near-Earth and deep space exploration programs and space defense programs require the development of robust intra-spacecraft serial data transfer electronics that must be reconfigurable, fault-tolerant, and have the ability to operate effectively for long periods of time in harsh environmental conditions. Existing data transfer systems based on state-of-the-art serial data transfer protocols or passive backplanes are slow, power-hungry, and poorly reconfigurable. They provide limited expandability and poor tolerance to radiation effects and total ionizing dose (TID) in particular, which presents harmful threats to modern submicron electronics. This novel approach is based on a standard library of differential cells tolerant to TID, and patented, multi-level serial interface architecture that ensures the reliable operation of serial interconnects without application of a data-strobe or other encoding techniques. This proprietary, high-speed differential interface presents a lowpower solution fully compatible with the SpaceWire (SW) protocol. It replaces a dual data-strobe link with two identical independent data channels, thus improving the system s tolerance to harsh environments through additional double redundancy. Each channel incorporates an automatic line integrity control circuitry that delivers error signals in case of broken or shorted lines.

Katzman, Vladimir↗