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NASA NTRS1988

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 NTRS1988

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗

NASA NTRS1988

Application of the Thurston bifurcation solution strategy to problems with modal interaction

The solution of bifurcation problems with closely-spaced critical points is achieved by first separating the singular part of the equation system encountered during a Newton iteration and carrying the Taylor expansion of the reduced system out to higher order. This separation is accomplished by transforming the equation system into an equivalent system in which some of the original unknowns are replaced with an equal number of modal amplitude coefficients. This method was used to continue the analysis of two significant example problems well past multiple fiburcation points, allowing a detailed examination of postbuckling behavior in the presence of modal interaction.

Rankin, C. C.↗

NASA NTRS1988

Solution of structural analysis problems on a parallel computer

The problems of a blade-stiffened panel with a hole subjected to compression, and a deployable space mast subjected to tip loads, are treated through the application of FEM to model generation followed by the solution of a linear system of equations. Direct and iterative approaches to the solution of the linear systems are solved in turn; for the panel problems using varying numbers of processors, the incomplete Cholesky-conjugate gradient method was the fastest iterative method on all but two instances in which the number of processors was large.

Storaasli, Olaf↗

NASA NTRS1987

Solutions to the linear camera calibration problem

The general linear camera calibration problem is formulated and several classification schemes for various subcases of this problem are developed. For each subcase, simple solutions are found that satisfy all necessary constraints. The results improve those already in the literature with respect to simplicity, efficiency, and coverage. However, the classification scheme is not exhaustive.

Grosky, William I.↗

NASA NTRS1988

Exact image theory for the slab problem

Exact image theory, recently introduced for the exact solution of problems involving homogeneous half spaces and microstrip-like geometries, is developed here for the problem of homogeneous slab of isotropic dielectric and/or magnetic material in free space. Expressions for image sources, creating the exact reflected and transmitted fields, are given and their numerical evaluation is demonstrated. Nonradiating modes, guided by the slab and responsible for the loss of convergence of the image functions, are considered and extracted. The theory can be applied, for example, in an analysis of finite ground planes in microstrip antenna structures.

Lindell, I. V.↗

NASA NTRS1988

Singular perturbation analysis of the atmospheric orbital plane change problem

A three-state model is presented for the aeroassisted orbital plane change problem. A further model order reduction to a single state model is examined using singular perturbation theory. The optimal solution for this single state model compares favorably with the exact numerical solution using a four-state model; however, a separate boundary layer solution is required to satisfy the terminal constraint on altitude. This, in general, involves the solution of a two-point boundary value problem, but for a two-state model. An approximation is introduced to obtain an analytical control solution for lift and bank angle. Included are numerical simulation results of a guidance law derived from this analysis, along with comparison to earlier work by other researchers.

Calise, A. J.↗

NASA NTRS1988

Chebyshev minimax problems for skip trajectories

The dimensionless equations of motion for hypersonic flight in the upper layer of the atmosphere are presented. The necessary conditions for the Chebyshev minimax problems are provided. Some important properties concerning the peak heating rate, the peak dynamic pressure and the peak altitude drop for a skip trajectory are discussed. As application of the theory, the problem of minimizing the peak altitude drop is solved. The numerical results support the theory that the nearly-grazing trajectory is useful in reducing the peak heating rate and the peak dynamic pressure.

Vinh, N. X.↗

NASA NTRS1988

Radiometric calibration of IR Fourier transform spectrometers - Solution to a problem with the High-Resolution Interferometer Sounder

A calibrated Fourier transform spectrometer, known as the High-Resolution Interferometer Sounder (HIS), has been flown on the NASA U-2 research aircraft to measure the infrared emission spectrum of the earth. The primary use - atmospheric temperature and humidity sounding - requires high radiometric precision and accuracy (of the order of 0.1 and 1 C, respectively). To meet these requirements, the HIS instruments, the HIS instrument performs inflight radiometric calibration, using observations of hot and cold blackbody reference sources as the basis for two-point calibrations at each wavenumber. Initially, laboratory tests revealed a calibration problem with brightness temperature errors as large as 15 C between 600 and 900/cm. The symptom of the problem, which occurred in one of the three spectral bands of HIS, was a source-dependent phase response. Minor changes to the calibration equations completely eliminated the anomalous errors. The new analysis properly accounts for the situation in which the phase response for radiance from the instrument itself differs from that for radiance from an external source. The mechanism responsible for the dual phase response of the HIS instrument is identified as emission from the interferometer beam splitter.

Revercomb, Henry E.↗

NASA NTRS1988

Reliable use of determinants to solve nonlinear structural eigenvalue problems efficiently

The analytical derivation, numerical implementation, and performance of a multiple-determinant parabolic interpolation method (MDPIM) for use in solving transcendental eigenvalue (critical buckling or undamped free vibration) problems in structural mechanics are presented. The overall bounding, eigenvalue-separation, qualified parabolic interpolation, accuracy-confirmation, and convergence-recovery stages of the MDPIM are described in detail, and the numbers of iterations required to solve sample plane-frame problems using the MDPIM are compared with those for a conventional bisection method and for the Newtonian method of Simpson (1984) in extensive tables. The MDPIM is shown to use 31 percent less computation time than bisection when accuracy of 0.0001 is required, but 62 percent less when accuracy of 10 to the -8th is required; the time savings over the Newtonian method are about 10 percent.

Williams, F. W.↗

NASA NTRS1988

Adaptive remeshing for transient problems with moving bodies

The combination of adaptive remeshing techniques, flow solvers for transient problems with moving grids, and integrators for rigid body motion is presented. The resulting scheme allows the economic simulation of fully coupled fluid-rigid body interaction problems of arbitrary geometric complexity. Several results are given to demonstrate the capabilities developed.

Lohner, Rainald↗

NASA NTRS1988

An analytic-geometric model of the effect of spherically distributed injection errors for Galileo and Ulysses spacecraft - The multi-stage problem

In previous work the problem of injecting the Galileo and Ulysses spacecraft from low earth orbit into their respective interplanetary trajectories has been discussed for the single stage (Centaur) vehicle. The central issue, in the event of spherically distributed injection errors, is what happens to the vehicle? The difficulties addressed in this paper involve the multi-stage problem since both Galileo and Ulysses will be utilizing the two-stage IUS system. Ulysses will also include a third stage: the PAM-S. The solution is expressed in terms of probabilities for total percentage of escape, orbit decay and reentry trajectories. Analytic solutions are found for Hill's Equations of Relative Motion (more recently called Clohessy-Wiltshire Equations) for multi-stage injections. These solutions are interpreted geometrically on the injection sphere. The analytic-geometric models compare well with numerical solutions, provide insight into the behavior of trajectories mapped on the injection sphere and simplify the numerical two-dimensional search for trajectory families.

Longuski, James M.↗

NASA NTRS1988

Development of three-dimensional code for the analysis of jet mixing problem. Part 1: Laminar solution

Future aircraft will eventually feature nonaxisymmetric or rectangular nozzles. Developing a three-dimensional code to stimulate the characteristics of the jet exhaust plume, issuing from nonaxisymmetric nozzles, in general, at different flight conditions, is very important. Two three-dimensional codes were developed to simulate the shock-cell structure of circular nozzles. These codes were developed to solve the parabolized and simplified Navier-Stokes equations respectively. Both codes are based on a method previously developed by Newsome et al. These codes are fully vectorized on the VPS 32 at NASA Langley Research Center. The axisymmetric underexpanded supersonic jet flow problem, exhausting into still air, was used as a test case for developing an efficient three-dimensional problems and preserving crossplane symmetry of the flow downstream of the jet exit.

Abdol-Hamid, Khaled S.↗

NASA NTRS1988

A technique for solving constraint satisfaction problems using Prolog's definite clause grammars

A new technique for solving constraint satisfaction problems using Prolog's definite clause grammars is presented. It exploits the fact that the grammar rule notation can be viewed as a state exchange notation. The novel feature of the technique is that it can perform informed as well as blind search. It provides the Prolog programmer with a new technique for application to a wide range of design, scheduling, and planning problems.

Nachtsheim, Philip R.↗

NASA NTRS1988

Engineering calculations for solving the orbital allotment problem

Four approaches for calculating downlink interferences for shaped-beam antennas are described. An investigation of alternative mixed-integer programming models for satellite synthesis is summarized. Plans for coordinating the various programs developed under this grant are outlined. Two procedures for ordering satellites to initialize the k-permutation algorithm are proposed. Results are presented for the k-permutation algorithms. Feasible solutions are found for 5 of the 6 problems considered. Finally, it is demonstrated that the k-permutation algorithm can be used to solve arc allotment problems.

Reilly, C.↗

NASA NTRS1988

Functional reasoning in diagnostic problem solving

This work is one facet of an integrated approach to diagnostic problem solving for aircraft and space systems currently under development. The authors are applying a method of modeling and reasoning about deep knowledge based on a functional viewpoint. The approach recognizes a level of device understanding which is intermediate between a compiled level of typical Expert Systems, and a deep level at which large-scale device behavior is derived from known properties of device structure and component behavior. At this intermediate functional level, a device is modeled in three steps. First, a component decomposition of the device is defined. Second, the functionality of each device/subdevice is abstractly identified. Third, the state sequences which implement each function are specified. Given a functional representation and a set of initial conditions, the functional reasoner acts as a consequence finder. The output of the consequence finder can be utilized in diagnostic problem solving. The paper also discussed ways in which this functional approach may find application in the aerospace field.

Sticklen, Jon↗

NASA NTRS1988

A Very Large Area Network (VLAN) knowledge-base applied to space communication problems

This paper first describes a hierarchical model for very large area networks (VLAN). Space communication problems whose solution could profit by the model are discussed and then an enhanced version of this model incorporating the knowledge needed for the missile detection-destruction problem is presented. A satellite network or VLAN is a network which includes at least one satellite. Due to the complexity, a compromise between fully centralized and fully distributed network management has been adopted. Network nodes are assigned to a physically localized group, called a partition. Partitions consist of groups of cell nodes with one cell node acting as the organizer or master, called the Group Master (GM). Coordinating the group masters is a Partition Master (PM). Knowledge is also distributed hierarchically existing in at least two nodes. Each satellite node has a back-up earth node. Knowledge must be distributed in such a way so as to minimize information loss when a node fails. Thus the model is hierarchical both physically and informationally.

Zander, Carol S.↗

NASA NTRS1988

An investigation of transitional management problems for the NSTS at NASA

This quarterly report summarizes the ideas and concepts developed by the University of Houston team with the collaboration and support of the Management Integration Offices of NASA. In addition it is hoped that this report will help to stimulate the healthy problem solving process already present at NASA. This is the second report in the fourth year of the research contract. The main aim of the work is to assist the National Space Transportation System (NSTS) in finding ways and means of moving into a truly operational era in the sense of routine timely production of flights. The reader who seeks an understanding of the concepts presented is encouraged to read the reports of the last three years. The overall strategy of this effort is to: (1) search the literature for applications of transition management and other related issues, (2) conduct investigations into the experiences of the industries with the transition management, and (3) to adapt the information found in (1) and (2) above into a form useful to NASA while at the same time applying industrial engineering and engineering management expertise to problems and issues as they emerge.

Hunsucker, John↗