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Results for “algorithmic 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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

DDA realizations of attitude algorithms.

Digital differential analyzer (DDA) realization of the direction cosine, Euler angle, and quaternion algorithms. It is shown that, for any one of the three attitude algorithms, 27 DDAs are needed. This number is considerably smaller than those obtained by others for the cases of Euler angle and quaternion algorithms.

Yeh, Y.↗
NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗
NASA NTRS1988

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, Joel H.↗
NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗
NASA NTRS1981

Symbolic Solution of Linear Differential Equations

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Feinberg, R. B.↗
NASA NTRS1993

Analysis of the Command and Control Segment (CCS) attitude estimation algorithm

This paper categorizes the qualitative behavior of the Command and Control Segment (CCS) differential correction algorithm as applied to attitude estimation using simultaneous spin axis sun angle and Earth cord length measurements. The categories of interest are the domains of convergence, divergence, and their boundaries. Three series of plots are discussed that show the dependence of the estimation algorithm on the vehicle radius, the sun/Earth angle, and the spacecraft attitude. Common qualitative dynamics to all three series are tabulated and discussed. Out-of-limits conditions for the estimation algorithm are identified and discussed.

Stockwell, Catherine↗
NASA NTRSDate not supplied

Implementation of Combinatorial Optimization Techniques for Automated Fiber Placement Through Thickness Defect Stack-Up Minimization

The Computer Aided Process Planning (CAPP) module was developed to facilitate and accelerate the process planning workflow for Automated Fiber Placement (AFP). CAPP assists process planners in identifying optimal starting point locations and layup strategies for each ply of a laminate. Ply optimization operates on measurement and scoring of geometry-based defects such as gaps, overlaps, angle deviation, and steering. This paper expands on the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: (1) genetic algorithm, (2) differential evolution, (3) particle swarm, and (4) greedy search. The algorithms identify the optimal combination of ply-level layup strategies, by scoring potential laminates on defect stacking, using two different objective functions. A final optimization approach is also presented which trades some performance for a large gain in efficiency. These approaches are compared to a randomized combination using a complex tool surface in a virtual case study. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack up.

CAPP↗
NASA NTRS1989

Simultaneous quaternion estimation (QUEST) and bias determination

Tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function are presented. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and Earth-pointing reference attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. They converge to the same estimates at the same rate for inertially-fixed attitude, but the new algorithm converges more slowly than the differential correction for Earth-pointing attitude. The slower convergence of the new method for non-zero attitude rates is believed to be due to the use of an inadequate approximation for a partial derivative matrix. The new method requires about twice the computational effort of the differential correction. Improving the approximation for the partial derivative matrix in the new method is expected to improve its convergence at the cost of increased computational effort.

Markley, F. Landis↗
NASA NTRS1972

DAA realizations of attitude algorithms

The attitude algorithms applied to strapdown inertial platforms are discussed. A review of six attitude transformation algorithms and the realizations of these algorithms by digital differential analyzers are presented. The number of digital differential analyzers for each algorithm is either smaller than or equal to that obtained by others.

Hung, J. C.↗
NASA NTRS1973

The numerical solution of ordinary differential equations by the Taylor series method

A programming implementation of the Taylor series method is presented for solving ordinary differential equations. The compiler is written in PL/1, and the target language is FORTRAN IV. The reduction of a differential system to rational form is described along with the procedures required for automatic numerical integration. The Taylor method is compared with two other methods for a number of differential equations. Algorithms using the Taylor method to find the zeroes of a given differential equation and to evaluate partial derivatives are presented. An annotated listing of the PL/1 program which performs the reduction and code generation is given. Listings of the FORTRAN routines used by the Taylor series method are included along with a compilation of all the recurrence formulas used to generate the Taylor coefficients for non-rational functions.

Silver, A. H.↗
NASA NTRS1993

Line-of-sight determination in real-time simulations

This paper describes the selection of a method for determining line-of-sight in real-time simulations for the NASA Ames Vertical Motion Simulator (VMS) facility. Five different combinations of terrain representation and line-of-sight determination algorithms were tested. A gridpost terrain format, in conjunction with a Digital Differential Analyzer algorithm, was found to best meet the simulation criteria of high speed, low storage requirements, and accuracy.

Kull, Frederick G., Jr.↗
NASA NTRS1996

A Multilevel Algorithm for the Solution of Second Order Elliptic Differential Equations on Sparse Grids

A multilevel algorithm is presented that solves general second order elliptic partial differential equations on adaptive sparse grids. The multilevel algorithm consists of several V-cycles. Suitable discretizations provide that the discrete equation system can be solved in an efficient way. Numerical experiments show a convergence rate of order Omicron(1) for the multilevel algorithm.

Pflaum, Christoph↗
NASA NTRS1990

Attitude determination and parameter estimation using vector observations - Application

This paper presents tests of a new method for the simultaneous estimation of spacecraft attitude and sensor biases, based on a quaternion estimation algorithm minimizing Wahba's loss function. The new method is compared with a conventional batch least-squares differential correction algorithm. The estimates are based on data from strapdown gyros and star trackers, simulated with varying levels of Gaussian noise for both inertially-fixed and earth-pointing attitudes. Both algorithms solve for the spacecraft attitude and the gyro drift rate biases. In the majority of tests performed, the two methods converge to the same estimates in the same number of iterations, but the new algorithm requires about 60 percent more computational effort. Some cases were found in which the new method converges in fewer iterations than the differential correction, and some for which the differential correction requires fewer iterations.

Markley, F. Landis↗