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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 NTRS1973

Real-time optimal guidance for orbital maneuvering.

A new formulation for soft-constraint trajectory optimization is presented as a real-time optimal feedback guidance method for multiburn orbital maneuvers. Control is always chosen to minimize burn time plus a quadratic penalty for end condition errors, weighted so that early in the mission (when controllability is greatest) terminal errors are held negligible. Eventually, as controllability diminishes, the method partially relaxes but effectively still compensates perturbations in whatever subspace remains controllable. Although the soft-constraint concept is well-known in optimal control, the present formulation is novel in addressing the loss of controllability inherent in multiple burn orbital maneuvers. Moreover the necessary conditions usually obtained from a Bolza formulation are modified in this case so that the fully hard constraint formulation is a numerically well behaved subcase. As a result convergence properties have been greatly improved.

Cohen, A. O.↗
NASA NTRS1999

Some Continuum Aspects of Data Assimilation

A long-sought goal in data assimilation is to build more fully the time dimension into the data assimilation process. Truly four-dimensional data assimilation requires evolving second-moment information, namely the estimation error covariance, along with the state estimate itself. The continuum evolution equations for the estimation error covariance constitute a system of partial differential equations in six space dimensions, forced by a model error covariance and by the observations themselves. The high dimensionality of this system poses a difficult computational problem. Numerous methods have been proposed for approximate, discrete solution of this system of equations. Four-dimensional variational schemes solve these equations indirectly, while schemes based on Kalman filtering solve the equations more directly, usually on a small subspace of the full six-dimensional space. In both cases, most proposed solution methods are not derived from the continuum covariance evolution equations themselves. Instead, most methods simply inherit the discretization used for evolving the state estimate, either in the form of a discrete tangent linear model or, in the case of ensemble schemes, in the form of a fully nonlinear discrete model. In this lecture we show that solutions of the continuum covariance evolution equations possess simple properties that are not readily satisfied upon discretization of the equations. we give numerical examples illustrating that "inherited" discretizations sometimes fail to produce meaningfully accurate solutions. Finally, we suggest alternative discretization methods that may yield more faithful approximate solutions of the continuum problem.

Cohn, Stephen E.↗
NASA NTRS1985

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are useed to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1986

Spline-based Rayleigh-Ritz methods for the approximation of the natural modes of vibration for flexible beams with tip bodies

Rayleigh-Ritz methods for the approximation of the natural modes for a class of vibration problems involving flexible beams with tip bodies using subspaces of piecewise polynomial spline functions are developed. An abstract operator-theoretic formulation of the eigenvalue problem is derived and spectral properties investigated. The existing theory for spline-based Rayleigh-Ritz methods applied to elliptic differential operators and the approximation properties of interpolatory splines are used to argue convergence and establish rates of convergence. An example and numerical results are discussed.

Rosen, I. G.↗
NASA NTRS1992

Implementation details of the coupled QMR algorithm

The original quasi-minimal residual method (QMR) relies on the three-term look-ahead Lanczos process, to generate basis vectors for the underlying Krylov subspaces. However, empirical observations indicate that, in finite precision arithmetic, three-term vector recurrences are less robust than mathematically equivalent coupled two-term recurrences. Therefore, we recently proposed a new implementation of the QMR method based on a coupled two-term look-ahead Lanczos procedure. In this paper, we describe implementation details of this coupled QMR algorithm, and we present results of numerical experiments.

Freund, Roland W.↗
NASA NTRS2017

Subspace-based Background Subtraction Applied to Aeroacoustic Wind Tunnel Testing

A subspace-based form of background subtraction is presented and applied to aeroacoustic wind tunnel data. A variant of this method has seen use in other fields such as climatology and medical imaging. The technique is based on an eigenvalue decomposition of the background noise cross-spectral matrix. Simulated results indicate similar performance to conventional background subtraction when the subtracted spectra are weaker than the true contaminating background levels. Superior performance is observed when the subtracted spectra are stronger than the true contaminating background levels, and when background data do not match between measurements. Experimental results show limited success in recovering signal behavior for data in which conventional background subtraction fails. The results also demonstrate the subspace subtraction technique's ability to maintain a physical coherence relationship in the modified cross-spectral matrix. Deconvolution results from microphone phased array data indicate that array integration methods are largely insensitive to subtraction type, and that background subtraction with appropriate background data is an effective alternative to diagonal removal.

deconvolution↗
NASA NTRS1978

On approximating hereditary dynamics by systems of ordinary differential equations

The paper deals with methods of obtaining approximate solutions to linear retarded functional differential equations (hereditary systems). The basic notion is to project the infinite dimensional space of initial functions for the hereditary system onto a finite dimensional subspace. Within this framework, two particular schemes are discussed. The first uses well-known piecewise constant approximations, while the second is a new method based on piecewise linear approximating functions. Numerical results are given.

Cliff, E. M.↗
NASA NTRS1989

Robust eigenstructure assignment by a projection method - Applications using multiple optimization criteria

A methodology for robust eigenstructure assignment for multivariable feedback systems is presented. The algorithm is based upon a pole placement technique using projections onto subspaces of admissible eigenvectors. New ideas are introduced to generate target (desired) sets of unitary eigenvectors and determine optimal feasible eigenvectors in a least-square sense. Useful connections are established between the pole-placement by independent modal space control and the method introduced in this paper. A multicriterion optimization algorithm is also presented, which takes efficient advantage of the present eigenstructure assignment method. These developments show significant improvement over an earlier version of this algorithm in both computational cost and accuracy. This optimization process appears to be numerically robust and suitable for high-dimensional multicriterion optimizations; it is especially attractive for computer-aided design of control systems.

Rew, D. W.↗
NASA NTRS1999

Multidisciplinary Design Technology Development: A Comparative Investigation of Integrated Aerospace Vehicle Design Tools

This research effort is a joint program between the Departments of Aerospace and Mechanical Engineering and the Computer Science and Engineering Department at the University of Notre Dame. The purpose of the project was to develop a framework and systematic methodology to facilitate the application of Multidisciplinary Design Optimization (MDO) to a diverse class of system design problems. For all practical aerospace systems, the design of a systems is a complex sequence of events which integrates the activities of a variety of discipline "experts" and their associated "tools". The development, archiving and exchange of information between these individual experts is central to the design task and it is this information which provides the basis for these experts to make coordinated design decisions (i.e., compromises and trade-offs) - resulting in the final product design. Grant efforts focused on developing and evaluating frameworks for effective design coordination within a MDO environment. Central to these research efforts was the concept that the individual discipline "expert", using the most appropriate "tools" available and the most complete description of the system should be empowered to have the greatest impact on the design decisions and final design. This means that the overall process must be highly interactive and efficiently conducted if the resulting design is to be developed in a manner consistent with cost and time requirements. The methods developed as part of this research effort include; extensions to a sensitivity based Concurrent Subspace Optimization (CSSO) NMO algorithm; the development of a neural network response surface based CSSO-MDO algorithm; and the integration of distributed computing and process scheduling into the MDO environment. This report overviews research efforts in each of these focus. A complete bibliography of research produced with support of this grant is attached.

Renaud, John E.↗
NASA NTRS1998

Multidisciplinary Design Technology Development: A Comparative Investigation of Integrated Aerospace Vehicle Design Tools

This research effort is a joint program between the Departments of Aerospace and Mechanical Engineering and the Computer Science and Engineering Department at the University of Notre Dame. Three Principal Investigators; Drs. Renaud, Brockman and Batill directed this effort. During the four and a half year grant period, six Aerospace and Mechanical Engineering Ph.D. students and one Masters student received full or partial support, while four Computer Science and Engineering Ph.D. students and one Masters student were supported. During each of the summers up to four undergraduate students were involved in related research activities. The purpose of the project was to develop a framework and systematic methodology to facilitate the application of Multidisciplinary Design Optimization (N4DO) to a diverse class of system design problems. For all practical aerospace systems, the design of a systems is a complex sequence of events which integrates the activities of a variety of discipline "experts" and their associated "tools". The development, archiving and exchange of information between these individual experts is central to the design task and it is this information which provides the basis for these experts to make coordinated design decisions (i.e., compromises and trade-offs) - resulting in the final product design. Grant efforts focused on developing and evaluating frameworks for effective design coordination within a MDO environment. Central to these research efforts was the concept that the individual discipline "expert", using the most appropriate "tools" available and the most complete description of the system should be empowered to have the greatest impact on the design decisions and final design. This means that the overall process must be highly interactive and efficiently conducted if the resulting design is to be developed in a manner consistent with cost and time requirements. The methods developed as part of this research effort include; extensions to a sensitivity based Concurrent Subspace Optimization (CSSO) MDO algorithm; the development of a neural network response surface based CSSO-MDO algorithm; and the integration of distributed computing and process scheduling into the MDO environment. This report overviews research efforts in each of these focus. A complete bibliography of research produced with support of this grant is attached.

Renaud, John E.↗
NASA NTRS1990

Stability analysis of position and force control problems for robot arms

Stability issues involving the control of a robot arm under the influence of external forces are discussed. Several different scenarios are considered: position control with the external force as an unmodeled disturbance, compliant control for a bounded external force in some subspace, and compliant control for a force due to the interaction with an environment whose dynamical behavior can be modeled. In each of these cases, a stability analysis using the Lyapunov method is presented. An explanation of instability is put forth for the case in which the environment has flexibility and the gains are inappropriately chosen. When the environment is stiff in the force control subspace, robust stability can be achieved with the integral force feedback.

Wen, John T.↗
NASA NTRS1989

Model reduction and control of flexible structures using Krylov subspaces

Krylov vectors and the concept of parameter-matching are combined to develop a model reduction algorithm for a damped structural dynamics system. The reduced-order model obtained matches a certain number of low-frequency moments of the full-order system. The major application of the present method is to the control of flexible structures. It is shown that, in the control of flexible structures, there generally exist three types of control energy spillover, namely, the control spillover, the observation spillover, and dynamic spillover. The formulation based on Krylov subspaces can eliminate the control and the observation spillover, while leaving only the dynamic spillover to be considered. Two examples are used to illustrate the efficacy of the Krylov method.

Craig, Roy R., Jr.↗
NASA NTRS1983

Restoration of multichannel microwave radiometric images

A constrained iterative image restoration method is applied to multichannel diffraction-limited imagery. This method is based on the Gerchberg-Papoulis algorithm utilizing incomplete information and partial constraints. The procedure is described using the orthogonal projection operators which project onto two prescribed subspaces iteratively. Some of its properties and limitations are also presented. The selection of appropriate constraints was emphasized in a practical application. Multichannel microwave images, each having different spatial resolution, were restored to a common highest resolution to demonstrate the effectiveness of the method. Both noise-free and noisy images were used in this investigation.

Chin, R. T.↗
NASA NTRS1990

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.↗
NASA NTRS1988

Block-Krylov component synthesis method for structural model reduction

A new analytical method is presented for generating component shape vectors, or Ritz vectors, for use in component synthesis. Based on the concept of a block-Krylov subspace, easily derived recurrence relations generate blocks of Ritz vectors for each component. The subspace spanned by the Ritz vectors is called a block-Krylov subspace. The synthesis uses the new Ritz vectors rather than component normal modes to reduce the order of large, finite-element component models. An advantage of the Ritz vectors is that they involve significantly less computation than component normal modes. Both 'free-interface' and 'fixed-interface' component models are derived. They yield block-Krylov formulations paralleling the concepts of free-interface and fixed-interface component modal synthesis. Additionally, block-Krylov reduced-order component models are shown to have special disturbability/observability properties. Consequently, the method is attractive in active structural control applications, such as large space structures. The new fixed-interface methodology is demonstrated by a numerical example. The accuracy is found to be comparable to that of fixed-interface component modal synthesis.

Craig, Roy R., Jr.↗
NASA NTRS1990

Analysis of spectral projectors in one-dimensional domains

A class of projection operators with values in a subspace of polynomials is analyzed. These projection operators are related to the Hilbert spaces involved in the numerical analysis of spectral methods. They are, in the first part of the paper, the standard Sobolev spaces and, in the second part, some weighted Sobolev spaces, the weight of which is related to the orthoronality relation satisfied by the Chebyshev polynomials. These results are used to study the approximation of a model fourth-order problem.

Maday, Y.↗