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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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NASA NTRS1983

An efficient computational method for characterizing the effects of random surface errors on the average power pattern of reflectors

Based on the works of Ruze (1966) and Vu (1969), a novel mathematical model has been developed to determine efficiently the average power pattern degradations caused by random surface errors. In this model, both nonuniform root mean square (rms) surface errors and nonuniform illumination functions are employed. In addition, the model incorporates the dependence on F/D in the construction of the solution. The mathematical foundation of the model rests on the assumption that in each prescribed annular region of the antenna, the geometrical rms surface value is known. It is shown that closed-form expressions can then be derived, which result in a very efficient computational method for the average power pattern. Detailed parametric studies are performed with these expressions to determine the effects of different random errors and illumination tapers on parameters such as gain loss and sidelobe levels. The results clearly demonstrate that as sidelobe levels decrease, their dependence on the surface rms/wavelength becomes much stronger and, for a specified tolerance level, a considerably smaller rms/wavelength is required to maintain the low sidelobes within the required bounds.

Rahmat-Samii, Y.↗

NASA NTRS1986

Mathematical correlation of modal parameter identification methods via system realization theory

A unified approach is introduced using system realization theory to derive and correlate modal parameter identification methods for flexible structures. Several different time-domain and frequency-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research towards the unification of the many possible approaches for modal parameter identification.

Juang, J. N.↗

NASA NTRS1985

Books and monographs on finite element technology

The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

Noor, A. K.↗

NASA NTRS1986

Effects of noise on modal parameters identified by the Eigensystem Realization Algorithm

The basic concept of the Eigensystem Realization Algorithm for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators, such as the singular values of the data matrix and modal amplitude coherence, is provided, based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo Simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1986

Effects of noise on ERA-identified modal parameters

The basic concept of the Eigensystem Realization Algorithm (ERA) for modal parameter identification and model reduction is extended to minimize the distortion of the identified parameters caused by noise. The mathematical foundation for the properties of accuracy indicators such as the singular values of the data matrix and modal amplitude coherence is provided based on knowledge of the noise characteristics. These indicators quantitatively discriminate noise from system information and are used to reduce the realized system model to a better approximation of the true model. Monte Carlo simulations are included to support the analytical studies.

Juang, J.-N.↗

NASA NTRS1984

Shape design sensitivity analysis of built-up structures

Selection of the best shape of a fillet in a tension bar such that no yielding occurs has long attracted the attention of engineers. Dimensions and notations for the bar and fillet are shown. With symmetry, only the upper half of the bar is considered. The optimal design problem is to find a boundary shape to minimize the total area of the fillet such that no yielding occurs. The classical boundary value problem is reduced to a variational or energy related problem which not only has excellent properties of existence and uniqueness but also provides the mathematical foundation for finite element analysis. The variational formulation may be viewed as the principle of virtual work and the finite element method as a application of the Galerkin method to the variational equation for approximate solution of the boundary value problem.

Choi, K. K.↗

NASA NTRS1987

Expert system development for commonality analysis in space programs

This report is a combination of foundational mathematics and software design. A mathematical model of the Commonality Analysis problem was developed and some important properties discovered. The complexity of the problem is described herein and techniques, both deterministic and heuristic, for reducing that complexity are presented. Weaknesses are pointed out in the existing software (System Commonality Analysis Tool) and several improvements are recommended. It is recommended that: (1) an expert system for guiding the design of new databases be developed; (2) a distributed knowledge base be created and maintained for the purpose of encoding the commonality relationships between design items in commonality databases; (3) a software module be produced which automatically generates commonality alternative sets from commonality databases using the knowledge associated with those databases; and (4) a more complete commonality analysis module be written which is capable of generating any type of feasible solution.

Yeager, Dorian P.↗

NASA NTRS1988

Efficient spacecraft formationkeeping with consideration of ballistic coefficient control

The extent to which drag can be used to enhance retrieval and servicing of platforms in the Space Staion environment is investigated for the case when separations on the order of several hundred or even thousands of kilometers occur over extended, but predefined, periods of time. The nature of the problem is formulated, the analytical tools used are described, and the mathematical foundation of the analysis is presented. Results are reported for the cases of formation flying cycles without ballistic coefficient control, formation flying with controlled relative decay, and the effects of varying solar activity.

Mathews, Michael↗

NASA NTRS1987

Mathematical correlation of modal-parameter-identification methods via system-realization theory

A unified approach is introduced using system-realization theory to derive and correlate modal-parameter-identification methods for flexible structures. Several different time-domain methods are analyzed and treated. A basic mathematical foundation is presented which provides insight into the field of modal-parameter identification for comparison and evaluation. The relation among various existing methods is established and discussed. This report serves as a starting point to stimulate additional research toward the unification of the many possible approaches for modal-parameter identification.

Juang, Jer-Nan↗

NASA NTRS1988

Sparse distributed memory

Theoretical models of the human brain and proposed neural-network computers are developed analytically. Chapters are devoted to the mathematical foundations, background material from computer science, the theory of idealized neurons, neurons as address decoders, and the search of memory for the best match. Consideration is given to sparse memory, distributed storage, the storage and retrieval of sequences, the construction of distributed memory, and the organization of an autonomous learning system.

Kanerva, Pentti↗

NASA NTRS1989

Bending rate damping in elastic systems

Preliminary results of an investigation of the bending rate damping model for elastic structures are presented. A model for which the internal damping term is physically plausible and which can accomodate cantilevered boundary conditions is discussed. The model formulation and mathematical foundations are given, and numerical results are discussed.

Banks, H. T.↗

NASA NTRS1991

Imaging radar polarimetry - A review

The authors present a tutorial review of the broad sweep of topics relating to imaging radar polarimetry, ranging from mathematical foundations to hardware and from implementation approaches to signal processing and calibration. The authors examine current developments in sensor technology and implementation for recording polarimetric measurements, and describe techniques and areas of application for this form of remotely sensed data. Those aspects of ground signal processing and calibration peculiar to the polarimetric signals are addressed. Several of the currently operating instruments and some of the implementations planned for future use are discussed.

Zebker, Howard A.↗

NASA NTRS1992

The solution of coupled Schroedinger equations using an extrapolation method

In this paper, extrapolation to the limit in a finite-difference method is applied to solve a system of coupled Schroedinger equations. This combination results in a method that only requires knowledge of the potential energy functions for the system. This numerical procedure has several distinct advantages over the more conventional methods. Namely, initial guesses for the term values are not needed; assumptions need be made about the behavior of the wavefunctions, such as the slope or magnitude in the nonclassical region; and the algorithm is easy to implement, has a firm mathematical foundation, and provides error estimates. Moreover, the method is less sensitive to round-off error than other methods since a small number of mesh points is used and it can be implemented on small computers. A comparison of the method with another numerical method shows results agreeing within 1 part in 10 exp 4.

Goorvitch, D.↗

NASA NTRS1987

Validation of CFD for aircraft design: A Boeing view

Information is given in viewgraph form on computational fluid dynamics (CFD) for aircraft design. Topics covered include CFD validation for advanced systems, cavity flow, transonic flow, separated flow, boundary layer interaction, hypersonic flow, heat transfer, zonal modeling, the mathematical foundation for Navier-Stokes simulation, hypersonic inlets, and the role of wind tunnel tests.

Vas, Irwin E.↗

NASA NTRS1992

Modeling the performance of the human (pilot) interaction in a synthetic flight domain: Information theoretic approach

Current advances in computing technology are devoid of formal methods that describe the theories of how information is shared between humans and machines. Specifically, in the domain of human-machine interaction, a common mathematical foundation is lacking. The aim of this paper is to propose a formal method of human-machine (H-M) interaction paradigm from the information view point. The methods presented are interpretation- and context-free and can be used both in experimental analysis as well as in modeling problems.

Ntuen, Celestine A.↗

NASA NTRS1993

A statistical analysis of mesoscale rainfall as a random cascade

The paper considers the random cascade theory for spatial rainfall. Particular attention was given to the following four areas: (1) the relationship of the random cascade theory of rainfall to the simple scaling and the hierarchical cluster-point-process theories, (2) the mathematical foundations for some of the formalisms commonly applied in the develpment of statistical cascade theory, (3) the empirical evidence for a random cascade theory of rainfall, and (4) the way of using data for making estimates of parameters and for making statistical inference within this theoretical framework. An analysis of space-time rainfall data is presented. Cascade simulations are carried out to provide a comparison with methods of analysis that are applied to the rainfall data.

Gupta, Vijay K.↗

NASA NTRS1995

A review of Reynolds stress models for turbulent shear flows

A detailed review of recent developments in Reynolds stress modeling for incompressible turbulent shear flows is provided. The mathematical foundations of both two-equation models and full second-order closures are explored in depth. It is shown how these models can be systematically derived for two-dimensional mean turbulent flows that are close to equilibrium. A variety of examples are provided to demonstrate how well properly calibrated versions of these models perform for such flows. However, substantial problems remain for the description of more complex turbulent flows where there are large departures from equilibrium. Recent efforts to extend Reynolds stress models to nonequilibrium turbulent flows are discussed briefly along with the major modeling issues relevant to practical naval hydrodynamics applications.

Speziale, Charles G.↗

NASA NTRS1995

Properties of a center/surround retinex. Part 1: Signal processing design

The last version of Edwin Land's retinex model for human vision's lightness and color constancy has been implemented. Previous research has established the mathematical foundations of Land's retinex but has not examined specific design issues and their effects on the properties of the retinex operation. Here we describe the signal processing design of the retinex. We find that the placement of the logarithmic function is important and produces best results when placed after the surround formation. We also find that best rendition is obtained for a 'canonical' gain-offset applied after the retinex operation.

Rahaman, Zia-Ur↗