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At least 649 records · Page 36

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NASA NTRS1981

Some aspects of algorithm performance and modeling in transient thermal analysis of structures

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms with variable time steps, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite-element models of the configurations are described. These problems include a Space Shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system, and a model of the Space Shuttle Orbiter wing. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are 'stiff' (typical of many practical problems such as insulated metal structures).

Adelman, H. M.↗

NASA NTRS1981

Comparison between variable and fixed dwell-time PN acquisition algorithms

Pseudo noise (PN) spread spectrum systems require a very accurate alignment between the PN code epochs at the transmitter and receiver. This synchronism is typically established through a two-step algorithm, including a coarse synchronization procedure and a fine synchronization procedure. A standard approach for the coarse synchronization is a sequential search over all code phases. The measurement of the power in the filtered signal is used to either accept or reject the code phase under test as the phase of the received PN code. This acquisition strategy, called a single dwell-time system, has been analyzed by Holmes and Chen (1977). A synopsis of the field of sequential analysis as it applies to the PN acquisition problem is provided. From this, the implementation of the variable dwell time algorithm as a sequential probability ratio test is developed. The performance of this algorithm is compared to the optimum detection algorithm and to the fixed dwell-time system.

Braun, W. R.↗

NASA NTRS1983

SETI Pulse Detection Algorithm: Analysis of False-alarm Rates

Some earlier work by the Search for Extraterrestrial Intelligence (SETI) Science Working Group (SWG) on the derivation of spectrum analyzer thresholds for a pulse detection algorithm based on an analysis of false alarm rates is extended. The algorithm previously analyzed was intended to detect a finite sequence of i periodically spaced pulses that did not necessarily occupy the entire observation interval. This algorithm would recognize the presence of such a signal only if all i-received pulse powers exceeded a threshold T(i): these thresholds were selected to achieve a desired false alarm rate, independent of i. To simplify the analysis, it was assumed that the pulses were synchronous with the spectrum sample times. This analysis extends the earlier effort to include infinite and/or asynchronous pulse trains. Furthermore, to decrease the possibility of missing an extraterrestrial intelligence signal, the algorithm was modified to detect a pulse train even if some of the received pulse powers fall below the threshold. The analysis employs geometrical arguments that make it conceptually easy to incorporate boundary conditions imposed on the derivation of the false alarm rates. While the exact results can be somewhat complex, simple closed form approximations are derived that produce a negligible loss of accuracy.

Levitt, B. K.↗

NASA NTRS1983

A robust Feasible Directions algorithm for design synthesis

A nonlinear optimization algorithm is developed which combines the best features of the Method of Feasible Directions and the Generalized Reduced Gradient Method. This algorithm utilizes the direction-finding sub-problem from the Method of Feasible Directions to find a search direction which is equivalent to that of the Generalized Reduced Gradient Method, but does not require the addition of a large number of slack variables associated with inequality constraints. This method provides a core-efficient algorithm for the solution of optimization problems with a large number of inequality constraints. Further optimization efficiency is derived by introducing the concept of infrequent gradient calculations. In addition, it is found that the sensitivity of the optimum design to changes in the problem parameters can be obtained using this method without the need for second derivatives or Lagrange multipliers. A numerical example is given in order to demonstrate the efficiency of the algorithm and the sensitivity analysis.

Vanderplaats, G. N.↗

NASA NTRS1983

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

Baker, A. J.↗

NASA NTRS1984

A comparison of two position estimate algorithms that use ILS localizer and DME information. Simulation and flight test results

Simulation and flight tests were conducted to compare the accuracy of two algorithms designed to compute a position estimate with an airborne navigation computer. Both algorithms used ILS localizer and DME radio signals to compute a position difference vector to be used as an input to the navigation computer position estimate filter. The results of these tests show that the position estimate accuracy and response to artificially induced errors are improved when the position estimate is computed by an algorithm that geometrically combines DME and ILS localizer information to form a single component of error rather than by an algorithm that produces two independent components of error, one from a DMD input and the other from the ILS localizer input.

Knox, C. E.↗

NASA NTRS1984

Fast algorithms for combustion kinetics calculations: A comparison

To identify the fastest algorithm currently available for the numerical integration of chemical kinetic rate equations, several algorithms were examined. Findings to date are summarized. The algorithms examined include two general-purpose codes EPISODE and LSODE and three special-purpose (for chemical kinetic calculations) codes CHEMEQ, CRK1D, and GCKP84. In addition, an explicit Runge-Kutta-Merson differential equation solver (IMSL Routine DASCRU) is used to illustrate the problems associated with integrating chemical kinetic rate equations by a classical method. Algorithms were applied to two test problems drawn from combustion kinetics. These problems included all three combustion regimes: induction, heat release and equilibration. Variations of the temperature and species mole fraction are given with time for test problems 1 and 2, respectively. Both test problems were integrated over a time interval of 1 ms in order to obtain near-equilibration of all species and temperature. Of the codes examined in this study, only CREK1D and GCDP84 were written explicitly for integrating exothermic, non-isothermal combustion rate equations. These therefore have built-in procedures for calculating the temperature.

Radhakrishnan, K.↗

NASA NTRS1984

User's manual for a fuel-conservative descent planning algorithm implemented on a small programmable calculator

A simplified flight management descent algorithm was developed and programmed on a small programmable calculator. It was designed to aid the pilot in planning and executing a fuel conservative descent to arrive at a metering fix at a time designated by the air traffic control system. The algorithm may also be used for planning fuel conservative descents when time is not a consideration. The descent path was calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard temperature effects. An explanation and examples of how the algorithm is used, as well as a detailed flow chart and listing of the algorithm are contained.

Vicroy, D. D.↗

NASA NTRS1984

Investigation and appreciation of optimal output feedback. Volume 1: A convergent algorithm for the stochastic infinite-time discrete optimal output feedback problem

The stochastic, infinite time, discrete output feedback problem for time invariant linear systems is examined. Two sets of sufficient conditions for the existence of a stable, globally optimal solution are presented. An expression for the total change in the cost function due to a change in the feedback gain is obtained. This expression is used to show that a sequence of gains can be obtained by an algorithm, so that the corresponding cost sequence is monotonically decreasing and the corresponding sequence of the cost gradient converges to zero. The algorithm is guaranteed to obtain a critical point of the cost function. The computational steps necessary to implement the algorithm on a computer are presented. The results are applied to a digital outer loop flight control problem. The numerical results for this 13th order problem indicate a rate of convergence considerably faster than two other algorithms used for comparison.

Halyo, N.↗

NASA NTRS1983

Simulation of the Galileo spacecraft axial - Delta-V algorithm

Preliminary results are presented from the analysis of the Galileo spacecraft axial delta-V algorithm. The Galileo spacecraft is a dual spin interplanetary spacecraft which will study the four Galilean moons of Jupiter as well as the Jovian environment and atmosphere. In order to achieve orbit about Jupiter and accurately deliver the probe to the planet's upper atmosphere, the Galileo spacecraft must be capable of performing many trajectory corrections or delta-V maneuvers. Twelve 10 Newton thrusters and one 400 Newton engine are utilized for this purpose. There are many maneuver modes and control algorithms available to the spacecraft. In this paper only the analysis of the axial delta-V algorithm will be discussed. The analysis consists of two parts: an analytic study and a simulation study. The analytic results are based on rigid body dynamics, while the simulation includes the first order effect of the flexible magnetometer boom and nutation damper. The simulation utilizes a program developed at JPL which allows flexible body effects to be simulated by modeling a collection of rigid bodies attached together by hinges, springs and dampers. In this preliminary study of the Galileo only two rigid bodies were used in the simulation, but many more can and will be used in the final tests. In this analysis, the algorithm appears to be working correctly and the analytic and simulation results agree very well.

Longuski, J. M.↗

NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm

A new hybrid-stress finite element algorithm, suitable for analyses of large, quasistatic, inelastic deformations, is presented. The algorithm is base upon a generalization of de Veubeke's complementary energy principle. The principal variables in the formulation are the nominal stress rate and spin, and thg resulting finite element equations are discrete versions of the equations of compatibility and angular momentum balance. The algorithm produces true rates, time derivatives, as opposed to 'increments'. There results a complete separation of the boundary value problem (for stress rate and velocity) and the initial value problem (for total stress and deformation); hence, their numerical treatments are essentially independent. After a fairly comprehensive discussion of the numerical treatment of the boundary value problem, we launch into a detailed examination of the numerical treatment of the initial value problem, covering the topics of efficiency, stability and objectivity. The paper is closed with a set of examples, finite homogeneous deformation problems, which serve to bring out important aspects of the algorithm.

Reed, K. W.↗

NASA NTRS1984

Acoustooptic linear algebra processors - Architectures, algorithms, and applications

Architectures, algorithms, and applications for systolic processors are described with attention to the realization of parallel algorithms on various optical systolic array processors. Systolic processors for matrices with special structure and matrices of general structure, and the realization of matrix-vector, matrix-matrix, and triple-matrix products and such architectures are described. Parallel algorithms for direct and indirect solutions to systems of linear algebraic equations and their implementation on optical systolic processors are detailed with attention to the pipelining and flow of data and operations. Parallel algorithms and their optical realization for LU and QR matrix decomposition are specifically detailed. These represent the fundamental operations necessary in the implementation of least squares, eigenvalue, and SVD solutions. Specific applications (e.g., the solution of partial differential equations, adaptive noise cancellation, and optimal control) are described to typify the use of matrix processors in modern advanced signal processing.

Casasent, D.↗

NASA NTRS1984

Modeling algorithm execution time on processor arrays

An approach to modelling the execution time of algorithms on parallel arrays is presented. This time is expressed as a function of the number of processors and system parameters. The resulting model has been applied to a parallel implementation of the conjugate-gradient algorithm on NASA's FEM. Results of experiments performed to compare the model predictions against actual behavior show that the floating-point arithmetic, communication, and synchronization components of the parallel algorithm execution time were correctly modelled. The results also show that the overhead caused by the interaction of the system software and the actual parallel hardware must be reflected in the model parameters. The model has been used to predict the performance of the conjugate gradient algorithm on a given problem as the number of processors and machine characteristics varied.

Adams, L. M.↗

NASA NTRS1985

Linearization of digital derived rate algorithm for use in linear stability analysis

The digital derived rate (DDR) algorithm is used to calculate the rate of rotation of the Centaur upper-stage rocket. The DDR is highly nonlinear algorithm, and classical linear stability analysis of the spacecraft cannot be performed without linearization. The performance of this rate algorithm is characterized by a gain and phase curve that drop off at the same frequency. This characteristic is desirable for many applications. A linearization technique for the DDR algorithm is investigated. The linearization method is described. Examples of the results of the linearization technique are illustrated, and the effects of linearization are described. A linear digital filter may be used as a substitute for performing classical linear stability analyses, while the DDR itself may be used in time response analysis.

Graham, R. E.↗

NASA NTRS1984

Comparison of atmospheric correction algorithms for the Coastal Zone Color Scanner

Before Nimbus-7 Costal Zone Color Scanner (CZC) data can be used to distinguish between coastal water types, methods must be developed for the removal of spatial variations in aerosol path radiance. These can dominate radiance measurements made by the satellite. An assessment is presently made of the ability of four different algorithms to quantitatively remove haze effects; each was adapted for the extraction of the required scene-dependent parameters during an initial pass through the data set The CZCS correction algorithms considered are (1) the Gordon (1981, 1983) algorithm; (2) the Smith and Wilson (1981) iterative algorityhm; (3) the pseudooptical depth method; and (4) the residual component algorithm.

Tanis, F. J.↗

NASA NTRS1984

Stability and accuracy analysis of some fully-discrete algorithms for the one-dimensional second-order wave equation

The present investigation is concerned with some basic results for a predictor-multicorrector algorithm applied to the one-dimensional wave equation, giving particular attention to so-called 2-pass explicit schemes in which both lumped and coupled mass matrices are employed. In an assessment of the accuracy and stability properties of the algorithms, use is made of the one-dimensional, second-order wave equation. The maximum stable time step of the lumped right-hand-side mass, 2-pass explicit algorithm is twice that of the 1-pass explicit algorithm. Improved accuracy is obtained by employing higher-order, or consistent, right-hand-side, mass.

Hughes, T. J. R.↗

NASA NTRS1983

A high-speed implementation of the random decrement algorithm

The algorithm is useful for measuring net system damping levels in stochastic processes and for the development of equivalent linearized system response models. The algorithm works by summing together all subrecords which occur after predefined threshold level is crossed. The random decrement signature is normally developed by scanning stored data and adding subrecords together. The high speed implementation of the random decrement algorithm exploits the digital character of sampled data and uses fixed record lengths of 2(n) samples to greatly speed up the process. The contributions to the random decrement signature of each data point was calculated only once and in the same sequence as the data were taken. A hardware implementation of the algorithm using random logic is diagrammed and the process is shown to be limited only by the record size and the threshold crossing frequency of the sampled data. With a hardware cycle time of 200 ns and 1024 point signature, a threshold crossing frequency of 5000 Hertz can be processed and a stably averaged signature presented in real time.

Kiraly, L. J.↗

NASA NTRS1984

Region-based modeling algorithms for remotely-sensed data

Five algorithms being developed for performing region-based modeling operations on classified remotely-sensed images are described. The first algorithm converts images from standard grid structure into topological grid structure, while the remaining algorithms act upon topologically grid-structured images to perform region-based relabelling, overlaying, distance searching, and neighborhood scanning operations. The use of precomputed topological information, through the use of topological grid structure, makes region-based algorithms highly accessible to earth scientists.

Goldberg, M.↗