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NASA NTRS1983

Design and implementation of a multigrid code for the Euler equations

The steady-state equations of inviscid fluid flow, the Euler equations, are a nonlinear nonelliptic system of equations admitting solutions with discontinuities (for example, shocks). The efficient numerical solution of these equations poses a strenuous challenge to multigrid methods. A multigrid code has been developed for the numerical solution of the Euler equations. In this paper some of the factors that had to be taken into account in the design and development of the code are reviewed. These factors include the importance of choosing an appropriate difference scheme, the usefulness of local mode analysis as a design tool, and the crucial question of how to treat the nonlinearity. Sample calculations of transonic flow about airfoils will be presented. No claim is made that the particular algorithm presented is optimal.

Jespersen, D. C.↗

NASA NTRS1987

Optimal checkpointing of real-time tasks

Analytical models for the design and evaluation of checkpointing of real-time tasks are developed. First, the execution of a real-time task is modeled under a common assumption of perfect coverage of on-line detection mechanisms (which is termed a basic model). Then, the model is generalized (to an extended model) to include more realistic cases, i.e., imperfect coverages of on-line detection mechanisms and acceptance tests. Finally, an optimal placement of checkpoints is determined to minimize the mean task execution time while the probability of an unreliable result (or lack of confidence) is kept below a specified level. In the basic model, it is shown that equidistant intercheckpoint intervals are optimal, whereas this is not necessarily true in the extended model. An algorithm for calculating the optimal number of checkpoints and intercheckpoint intervals is presented with some numerical examples for the extended model.

Shin, Kang G.↗

NASA NTRS1987

Far-field mission planning for nap-of-the-earth flight

In the face of numerically superior hostile forces, deployment of individual vehicles to the right place, at the right time, and the ability to plan missions with less conservatism, will become significant force multipliers. Far-field mission planning is one of the enabling technologies that will facilitate force coordination through management of mission timeline, vehicle survivability and fuel constraints. On-board replanning is required to deal responsively with departures from nominal plan execution that result from imperfect knowledge of and temporal variability in the mission environment. The far-field planning problem is posed as a constrained optimization problem and algorithms and structural organization are proposed for the solution.

Deutsch, Owen L.↗

NASA NTRS1989

OPTICON: Pro-Matlab software for large order controlled structure design

A software package for large order controlled structure design is described and demonstrated. The primary program, called OPTICAN, uses both Pro-Matlab M-file routines and selected compiled FORTRAN routines linked into the Pro-Matlab structure. The program accepts structural model information in the form of state-space matrices and performs three basic design functions on the model: (1) open loop analyses; (2) closed loop reduced order controller synthesis; and (3) closed loop stability and performance assessment. The current controller synthesis methods which were implemented in this software are based on the Generalized Linear Quadratic Gaussian theory of Bernstein. In particular, a reduced order Optimal Projection synthesis algorithm based on a homotopy solution method was successfully applied to an experimental truss structure using a 58-state dynamic model. These results are presented and discussed. Current plans to expand the practical size of the design model to several hundred states and the intention to interface Pro-Matlab to a supercomputing environment are discussed.

Peterson, Lee D.↗

NASA NTRS1989

Multiprocessor performance modeling with ADAS

A graph managing strategy referred to as the Algorithm to Architecture Mapping Model (ATAMM) appears useful for the time-optimized execution of application algorithm graphs in embedded multiprocessors and for the performance prediction of graph designs. This paper reports the modeling of ATAMM in the Architecture Design and Assessment System (ADAS) to make an independent verification of ATAMM's performance prediction capability and to provide a user framework for the evaluation of arbitrary algorithm graphs. Following an overview of ATAMM and its major functional rules are descriptions of the ADAS model of ATAMM, methods to enter an arbitrary graph into the model, and techniques to analyze the simulation results. The performance of a 7-node graph example is evaluated using the ADAS model and verifies the ATAMM concept by substantiating previously published performance results.

Hayes, Paul J.↗

NASA NTRS1990

A Unified Statistical Rain-Attenuation Model for Communication Link Fade Predictions and Optimal Stochastic Fade Control Design Using a Location-Dependent Rain-Statistic Database

A static and dynamic rain-attenuation model is presented which describes the statistics of attenuation on an arbitrarily specified satellite link for any location for which there are long-term rainfall statistics. The model may be used in the design of the optimal stochastic control algorithms to mitigate the effects of attenuation and maintain link reliability. A rain-statistics data base is compiled, which makes it possible to apply the model to any location in the continental U.S. with a resolution of 0-5 degrees in latitude and longitude. The model predictions are compared with experimental observations, showing good agreement.

Manning, Robert M.↗

NASA NTRS1991

On the theory of the synthesis of offset dual-shaped reflectors - Case examples

In an earlier paper by Galindo-Israel et al. (1987), the geometrical optics (GO) principles, constraints, and requirements of the dual- and single-offset-shaped reflector synthesis problem were collected and developed into a set of nonlinear first-order PDEs. An extension of the methods by which solutions to the PDEs can be obtained is presented, together with several case examples. These examples are independently analyzed by GO and physical optics diffraction methods. The starting point for the integration over each reflector can be taken on the outer rim, at the center, or at an intermediate point-the intermediate starting point being the more general case. The utility of the speed of this synthesis method is demonstrated. For example, the program utilized completes a synthesis in less than 45 s on a 386/20 personal computer and within a fraction of a second on a mainframe Cray. This makes practical the incorporation of the synthesis into a search algorithm that can optimize one or more parameters of the reflector system. As an example, the optimization of the mapping equations for low cross polarization is discussed.

Galindo-Israel, Victor↗

NASA NTRS1991

Hidden Markov model analysis of force/torque information in telemanipulation

A model for the prediction and analysis of sensor information recorded during robotic performance of telemanipulation tasks is presented. The model uses the hidden Markov model to describe the task structure, the operator's or intelligent controller's goal structure, and the sensor signals. A methodology for constructing the model parameters based on engineering knowledge of the task is described. It is concluded that the model and its optimal state estimation algorithm, the Viterbi algorithm, are very succesful at the task of segmenting the data record into phases corresponding to subgoals of the task. The model provides a rich modeling structure within a statistical framework, which enables it to represent complex systems and be robust to real-world sensory signals.

Hannaford, Blake↗

NASA NTRS1992

Improved interpretation of satellite altimeter data using genetic algorithms

Genetic algorithms (GA) are optimization techniques that are based on the mechanics of evolution and natural selection. They take advantage of the power of cumulative selection, in which successive incremental improvements in a solution structure become the basis for continued development. A GA is an iterative procedure that maintains a 'population' of 'organisms' (candidate solutions). Through successive 'generations' (iterations) the population as a whole improves in simulation of Darwin's 'survival of the fittest'. GA's have been shown to be successful where noise significantly reduces the ability of other search techniques to work effectively. Satellite altimetry provides useful information about oceanographic phenomena. It provides rapid global coverage of the oceans and is not as severely hampered by cloud cover as infrared imagery. Despite these and other benefits, several factors lead to significant difficulty in interpretation. The GA approach to the improved interpretation of satellite data involves the representation of the ocean surface model as a string of parameters or coefficients from the model. The GA searches in parallel, a population of such representations (organisms) to obtain the individual that is best suited to 'survive', that is, the fittest as measured with respect to some 'fitness' function. The fittest organism is the one that best represents the ocean surface model with respect to the altimeter data.

Messa, Kenneth↗

NASA NTRS1992

Aerocapture and aeromaneuvering at Mars

This paper presents the results of a guidance analysis study for aerocapture and aeromaneuvering at Mars. A 4-state, near-optimal, hybrid guidance algorithm is derived for applications throughout the paper. It is based on the critical assumption that Loh's function remains constant between successive guidance updates. Besides the guidance algorithm, the paper presents a performance evaluation of guidance derived from estimated or 'navigated' spacecraft state, provided by an onboard navigation subsystem for real-time applications on Mars. For the performance evaluation, the spacecraft state is augmented by such parameters as the reference atmospheric density and scale-height, the banking angle and angle of attack for spacecraft control and the accelerometer measurement model errors. Finally, the paper examines also, the influence of random uncertainties in atmospheric density on aeroassisted maneuvers, by a Monte Carlo type of simulation.

Vijayaraghavan, A.↗

NASA NTRS1994

Computer code for controller partitioning with IFPC application: A user's manual

A user's manual for the computer code for partitioning a centralized controller into decentralized subcontrollers with applicability to Integrated Flight/Propulsion Control (IFPC) is presented. Partitioning of a centralized controller into two subcontrollers is described and the algorithm on which the code is based is discussed. The algorithm uses parameter optimization of a cost function which is described. The major data structures and functions are described. Specific instructions are given. The user is led through an example of an IFCP application.

Schmidt, Phillip H.↗

NASA NTRS1993

Space Reclamation for Uncoordinated Checkpointing in Message-Passing Systems

Checkpointing and rollback recovery are techniques that can provide efficient recovery from transient process failures. In a message-passing system, the rollback of a message sender may cause the rollback of the corresponding receiver, and the system needs to roll back to a consistent set of checkpoints called recovery line. If the processes are allowed to take uncoordinated checkpoints, the above rollback propagation may result in the domino effect which prevents recovery line progression. Traditionally, only obsolete checkpoints before the global recovery line can be discarded, and the necessary and sufficient condition for identifying all garbage checkpoints has remained an open problem. A necessary and sufficient condition for achieving optimal garbage collection is derived and it is proved that the number of useful checkpoints is bounded by N(N+1)/2, where N is the number of processes. The approach is based on the maximum-sized antichain model of consistent global checkpoints and the technique of recovery line transformation and decomposition. It is also shown that, for systems requiring message logging to record in-transit messages, the same approach can be used to achieve optimal message log reclamation. As a final topic, a unifying framework is described by considering checkpoint coordination and exploiting piecewise determinism as mechanisms for bounding rollback propagation, and the applicability of the optimal garbage collection algorithm to domino-free recovery protocols is demonstrated.

Wang, Yi-Min↗

NASA NTRS1994

Nonlinear control of magnetic bearings

In this paper we present a variety of nonlinear controllers for the magnetic bearing that ensure both stability and robustness. We utilize techniques of discontinuous control to design novel control laws for the magnetic bearing. We present in particular sliding mode controllers, time optimal controllers, winding algorithm based controllers, nested switching controllers, fractional controllers, and synchronous switching controllers for the magnetic bearing. We show existence of solutions to systems governed by discontinuous control laws, and prove stability and robustness of the chosen control laws in a rigorous setting. We design sliding mode observers for the magnetic bearing and prove the convergence of the state estimates to their true values. We present simulation results of the performance of the magnetic bearing subject to the aforementioned control laws, and conclude with comments on design.

Pradeep, A. K.↗

NASA NTRS1995

Separation analysis, a tool for analyzing multigrid algorithms

The separation of vectors by multigrid (MG) algorithms is applied to the study of convergence and to the prediction of the performance of MG algorithms. The separation operator for a two level cycle algorithm is derived. It is used to analyze the efficiency of the cycle when mixing of eigenvectors occurs. In particular cases the separation analysis reduces to Fourier type analysis. The separation operator of a two level cycle for a Schridubger eigenvalue problem, is derived and analyzed in a Fourier basis. Separation analysis gives information on how to choose performance relaxations and inter-level transfers. Separation analysis is a tool for analyzing and designing algorithms, and for optimizing their performance.

Costiner, Sorin↗

NASA NTRS1995

Use of nonlinear identification in robust attitude and attitude rate estimation for SAMPEX

A method is described for obtaining optimal attitude estimation/identification algorithms for spacecraft lacking attitude rate measurement devices (rate gyros), and then demonstrated using actual flight data from the Solar, Anomalous, and Magnetospheric Particle Explorer (SAMPEX) spacecraft. SAMPEX does not have on-board rate sensing, and relies on sun sensors and a three-axis magnetometer for attitude determination. The absence of rate data normally reduces both the total amount of data available and the sampling density (in time) by a substantial fraction. In addition, attitude data is occasionally unavailable (for example, during sun occultation). As a result, the sensitivity of the estimates to model uncertainty and to measurement noise increases. In order to maintain accuracy in the attitude estimates, there is an increased need for accurate models of the rotational dynamics. The Minimum Model Error(MME)/Least Square Correlation(LSC) algorithm accurately identifies an improved model for SAMPEX to be used during periods of complete data loss or extreme noise. The model correction is determined by estimating only one orbit(the identification pass) just prior to the assumed data loss(the prediction pass). The MME estimator correctly predicted the states during the identification phase, but more importantly determines the necessary model correction trajectory, d(t). The LSC algorithm is then used to find this trajectory's functional form, H(x(t)). The results show significant improvement of the new corrected model's attitude estimates as compared to the original uncorrected model's estimates. The possible functional form of the correction term is limited at this point in the study to functions strictly of the estimated states. The results, however, strongly suggest that functions based on the relative position of the satellite may also be possible candidates for future consideration.

Mook, D. Joseph↗

NASA NTRS1995

A globally efficient means of distributing UTC time and frequency through GPS

Time and frequency outputs comparable in quality to the best laboratories have been demonstrated on an integrated system suitable for field application on a global basis. The system measures the time difference between 1 pulse-per-second (pps) signals derived from local primary frequency standards and from a multi-channel GPS C/A receiver. The measured data is processed through optimal SA Filter algorithms that enhance both the stability and accuracy of GPS timing signals. Experiments were run simultaneously at four different sites. Even with large distances between sites, the overall results show a high degree of cross-correlation of the SA noise. With sufficiently long simultaneous measurement sequences, the data shows that determination of the difference in local frequency from an accepted remote standard to better than 1 x 10(exp -14) is possible. This method yields frequency accuracy, stability, and timing stability comparable to that obtained with more conventional common-view experiments. In addition, this approach provides UTC(USNO MC) in real time to an accuracy better than 20 ns without the problems normally associated with conventional common-view techniques. An experimental tracking loop was also set up to demonstrate the use of enhanced GPS for dissemination of UTC(USNO MC) over a wide geographic area. Properly disciplining a cesium standard with a multi-channel GPS receiver, with additional input from USNO, has been found to permit maintaining a timing precision of better than 10 ns between Palo Alto, CA and Washington, DC.

Kusters, John A.↗

NASA NTRS1993

Space station static and dynamic analyses using parallel methods

Algorithms for high-performance parallel computers are applied to perform static analyses of large-scale Space Station finite-element models (FEMs). Several parallel-vector algorithms under development at NASA Langley are assessed. Sparse matrix solvers were found to be more efficient than banded symmetric or iterative solvers for the static analysis of large-scale applications. In addition, new sparse and 'out-of-core' solvers were found superior to substructure (superelement) techniques which require significant additional cost and time to perform static condensation during global FEM matrix generation as well as the subsequent recovery and expansion. A method to extend the fast parallel static solution techniques to reduce the computation time for dynamic analysis is also described. The resulting static and dynamic algorithms offer design economy for preliminary multidisciplinary design optimization and FEM validation against test modes. The algorithms are being optimized for parallel computers to solve one-million degrees-of-freedom (DOF) FEMs. The high-performance computers at NASA afforded effective software development, testing, efficient and accurate solution with timely system response and graphical interpretation of results rarely found in industry. Based on the author's experience, similar cooperation between industry and government should be encouraged for similar large-scale projects in the future.

Gupta, V.↗

NASA NTRS1998

Toward a More Robust Pruning Procedure for MLP Networks

Choosing a proper neural network architecture is a problem of great practical importance. Smaller models mean not only simpler designs but also lower variance for parameter estimation and network prediction. The widespread utilization of neural networks in modeling highlights an issue in human factors. The procedure of building neural models should find an appropriate level of model complexity in a more or less automatic fashion to make it less prone to human subjectivity. In this paper we present a Singular Value Decomposition based node elimination technique and enhanced implementation of the Optimal Brain Surgeon algorithm. Combining both methods creates a powerful pruning engine that can be used for tuning feedforward connectionist models. The performance of the proposed method is demonstrated by adjusting the structure of a multi-input multi-output model used to calibrate a six-component wind tunnel strain gage.

Stepniewski, Slawomir W.↗