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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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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Application of the generalized Galerkin method to the computation of fluid flows.

The purpose of this paper is to show that most existing methods for the calculation of fluid flows can be interpreted as special applications of a single mathematical formalism. This formalism, called the generalized Galerkin method, then provides a single conceptual framework for comparing various methods in terms of convergence and accuracy. The method is presented in sufficient mathematical detail to permit its interpretation as a projection in function space. In order to demonstrate the basic thesis, finite difference, finite element, strip integral, and classical integral methods of boundary layer theory are developed by application of the method.

Murphy, J. D.↗
NASA NTRS1971

New techniques for the analysis of manual control systems

Studies are summarized on the application of advanced analytical and computational methods to the development of mathematical models of human controllers in multiaxis manual control systems. Specific accomplishments include the following: (1) The development of analytical and computer methods for the measurement of random parameters in linear models of human operators. (2) Discrete models of human operator behavior in a multiple display situation were developed. (3) Sensitivity techniques were developed which make possible the identification of unknown sampling intervals in linear systems. (4) The adaptive behavior of human operators following particular classes of vehicle failures was studied and a model structure proposed.

Bekey, G. A.↗
NASA NTRS2006

Experiences applying Formal Approaches in the Development of Swarm-Based Space Exploration Systems

NASA is researching advanced technologies for future exploration missions using intelligent swarms of robotic vehicles. One of these missions is the Autonomous Nan0 Technology Swarm (ANTS) mission that will explore the asteroid belt using 1,000 cooperative autonomous spacecraft. The emergent properties of intelligent swarms make it a potentially powerful concept, but at the same time more difficult to design and ensure that the proper behaviors will emerge. NASA is investigating formal methods and techniques for verification of such missions. The advantage of using formal methods is the ability to mathematically verify the behavior of a swarm, emergent or otherwise. Using the ANTS mission as a case study, we have evaluated multiple formal methods to determine their effectiveness in modeling and ensuring desired swarm behavior. This paper discusses the results of this evaluation and proposes an integrated formal method for ensuring correct behavior of future NASA intelligent swarms.

Rouff, Christopher A.↗
NASA NTRS1987

A hybrid perturbation Galerkin technique with applications to slender body theory

A two step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1989

A hybrid perturbation Galerkin technique with applications to slender body theory

A two-step hybrid perturbation-Galerkin method to solve a variety of applied mathematics problems which involve a small parameter is presented. The method consists of: (1) the use of a regular or singular perturbation method to determine the asymptotic expansion of the solution in terms of the small parameter; (2) construction of an approximate solution in the form of a sum of the perturbation coefficient functions multiplied by (unknown) amplitudes (gauge functions); and (3) the use of the classical Bubnov-Galerkin method to determine these amplitudes. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is applied to some singular perturbation problems in slender body theory. The results obtained from the hybrid method are compared with approximate solutions obtained by other methods, and the degree of applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗
NASA NTRS1989

Force-reflective teleoperated system with shared and compliant control capabilities

The force-reflecting teleoperator breadboard is described. It is the first system among available Research and Development systems with the following combined capabilities: (1) The master input device is not a replica of the slave arm. It is a general purpose device which can be applied to the control of different robot arms through proper mathematical transformations. (2) Force reflection generated in the master hand controller is referenced to forces and moments measured by a six DOF force-moment sensor at the base of the robot hand. (3) The system permits a smooth spectrum of operations between full manual, shared manual and automatic, and full automatic (called traded) control. (4) The system can be operated with variable compliance or stiffness in force-reflecting control. Some of the key points of the system are the data handling and computing architecture, the communication method, and the handling of mathematical transformations. The architecture is a fully synchronized pipeline. The communication method achieves optimal use of a parallel communication channel between the local and remote computing nodes. A time delay box is also implemented in this communication channel permitting experiments with up to 8 sec time delay. The mathematical transformations are computed faster than 1 msec so that control at each node can be operated at 1 kHz servo rate without interpolation. This results in an overall force-reflecting loop rate of 200 Hz.

Szakaly, Z.↗
NASA NTRSDate not supplied

Applying Formal Methods to Safety-Critical Systems

How do you know a proof is correct? Traditionally, mathematical proofs are socially verified – at least one human, following a set of implicit rules of natural language and logic, determines if the proof is believable. If the proof becomes overly tedious and/or is essential to some safety- or mission-critical application, it becomes necessary to determine the soundness to a higher standard. 'Formal methods' refer to mathematically rigorous techniques and tools that enable specification, design, and verification of hardware and software systems. The specification used in formal methods are statements in a mathematical logic while the formal verifications are deductions in that logic. Formal methods can be difficult or time/resource intensive, but offer a higher level of assurance than standard verification through testing or handwritten proofs. This talk will introduce formal methods, motivated by applications of interest to NASA, including uncrewed aircraft operations in the national airspace, urban air environments, and wildfire areas. The audience will be given a crash course in mechanically verified proofs in the Prototype Verification System (PVS), an interactive theorem prover.

Formal Methods↗
NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗
NASA NTRS1990

Extension of transonic flow computational concepts in the analysis of cavitated bearings

An analogy between the mathematical modeling of transonic potential flow and the flow in a cavitating bearing is described. Based on the similarities, characteristics of the cavitated region and jump conditions across the film reformation and rupture fronts are developed using the method of weak solutions. The mathematical analogy is extended by utilizing a few computational concepts of transonic flow to numerically model the cavitating bearing. Methods of shock fitting and shock capturing are discussed. Various procedures used in transonic flow computations are adapted to bearing cavitation applications, for example, type differencing, grid transformation, an approximate factorization technique, and Newton's iteration method. These concepts have proved to be successful and have vastly improved the efficiency of numerical modeling of cavitated bearings.

Vijayaraghavan, D.↗
NASA NTRS2016

Nonlinear Unsteady Aerodynamic Modeling Using Wind Tunnel and Computational Data

Extensions to conventional aircraft aerodynamic models are required to adequately predict responses when nonlinear unsteady flight regimes are encountered, especially at high incidence angles and under maneuvering conditions. For a number of reasons, such as loss of control, both military and civilian aircraft may extend beyond normal and benign aerodynamic flight conditions. In addition, military applications may require controlled flight beyond the normal envelope, and civilian flight may require adequate recovery or prevention methods from these adverse conditions. These requirements have led to the development of more general aerodynamic modeling methods and provided impetus for researchers to improve both techniques and the degree of collaboration between analytical and experimental research efforts. In addition to more general mathematical model structures, dynamic test methods have been designed to provide sufficient information to allow model identification. This paper summarizes research to develop a modeling methodology appropriate for modeling aircraft aerodynamics that include nonlinear unsteady behaviors using both experimental and computational test methods. This work was done at Langley Research Center, primarily under the NASA Aviation Safety Program, to address aircraft loss of control, prevention, and recovery aerodynamics.

Murphy, Patrick C.↗
NASA NTRS1983

Formulas for Precise Transverse Mercator Projection

Transverse mercator projection, surface of Earth or other spheroid is mapped onto cylinder tangent at meridian of longitude. New method performs mapping by means of mathematical series in which higher order terms correct for deviation from exact sphericity. New method yields precise geodetic maps.

Wallis, D. E.↗
NASA NTRS1990

Using data with models - Ill-posed problems

An attempt is made to show that the combination of data with models leads to a sequence of conventionally ill-posed problems which can be treated in a systematic and practical way by control-theory techniques. The illustrative approach is to exploit the very great mathematical simplifications which result when the methods of finite dimensional vector spaces are used, thus reducing a lot of difficult mathematics to classical least squares. The immediate motivation for this study comes from ocean acoustic tomography.

Wunsch, C.↗
NASA NTRS2008

Estimation of Supersonic Stage Separation Aerodynamics of Winged-Body Launch Vehicles Using Response Surface Methods

A collection of statistical and mathematical techniques referred to as response surface methodology was used to estimate the longitudinal stage separation aerodynamic characteristics of a generic, bimese, winged multi-stage launch vehicle configuration using data obtained on small-scale models at supersonic speeds in the NASA Langley Research Center Unitary Plan Wind Tunnel. The simulated Mach 3 staging was dominated by multiple shock wave interactions between the orbiter and booster vehicles throughout the relative spatial locations of interest. This motivated a partitioning of the overall inference space into several contiguous regions within which the separation aerodynamics were presumed to be well-behaved and estimable using cuboidal and spherical central composite designs capable of fitting full second-order response functions. The primary goal was to approximate the underlying overall aerodynamic response surfaces of the booster vehicle in belly-to-belly proximity to the orbiter vehicle using relatively simple, lower-order polynomial functions that were piecewise-continuous across the full independent variable ranges of interest. The quality of fit and prediction capabilities of the empirical models were assessed in detail, and the issue of subspace boundary discontinuities was addressed. The potential benefits of augmenting the central composite designs to full third order using computer-generated D-optimality criteria were also evaluated. The usefulness of central composite designs, the subspace sizing, and the practicality of fitting low-order response functions over a partitioned inference space dominated by highly nonlinear and possibly discontinuous shock-induced aerodynamics are discussed.

Erickson, Gary E.↗
NASA NTRS2001

The CE/SE Method: a CFD Framework for the Challenges of the New Millennium

The space-time conservation element and solution element (CE/SE) method, which was originated and is continuously being developed at NASA Glenn Research Center, is a high-resolution, genuinely multidimensional and unstructured-mesh compatible numerical method for solving conservation laws. Since its inception in 1991, the CE/SE method has been used to obtain highly accurate numerical solutions for 1D, 2D and 3D flow problems involving shocks, contact discontinuities, acoustic waves, vortices, shock/acoustic waves/vortices interactions, shock/boundary layers interactions and chemical reactions. Without the aid of preconditioning or other special techniques, it has been applied to both steady and unsteady flows with speeds ranging from Mach number = 0.00288 to 10. In addition, the method has unique features that allow for (i) the use of very simple non-reflecting boundary conditions, and (ii) a unified wall boundary treatment for viscous and inviscid flows. The CE/SE method was developed with the conviction that, with a solid foundation in physics, a robust, coherent and accurate numerical framework can be built without involving overly complex mathematics. As a result, the method was constructed using a set of design principles that facilitate simplicity, robustness and accuracy. The most important among them are: (i) enforcing both local and global flux conservation in space and time, with flux evaluation at an interface being an integral part of the solution procedure and requiring no interpolation or extrapolation; (ii) unifying space and time and treating them as a single entity; and (iii) requiring that a numerical scheme be built from a nondissipative core scheme such that the numerical dissipation can be effectively controlled and, as a result, will not overwhelm the physical dissipation. Part I of the workshop will be devoted to a discussion of these principles along with a description of how the ID, 2D and 3D CE/SE schemes are constructed. In Part II, various applications of the CE/SE method, particularly those involving chemical reactions and acoustics, will be presented. The workshop will be concluded with a sketch of the future research directions.

Chang, Sin-Chung↗
NASA NTRS1995

Program Helps Generate Boundary-Element Mathematical Models

Composite Model Generation-Boundary Element Method (COM-GEN-BEM) computer program significantly reduces time and effort needed to construct boundary-element mathematical models of continuous-fiber composite materials at micro-mechanical (constituent) scale. Generates boundary-element models compatible with BEST-CMS boundary-element code for anlaysis of micromechanics of composite material. Written in PATRAN Command Language (PCL).

Goldberg, R. K.↗
NASA NTRS1999

A Methodology for Investigating Adaptive Postural Control

Our research on postural control and human-environment interactions provides an appropriate scientific foundation for understanding the skill of mass handling by astronauts in weightless conditions (e.g., extravehicular activity or EVA). We conducted an investigation of such skills in NASA's principal mass-handling simulator, the Precision Air-Bearing Floor, at the Johnson Space Center. We have studied skilled movement-body within a multidisciplinary context that draws on concepts and methods from biological and behavioral sciences (e.g., psychology, kinesiology and neurophysiology) as well as bioengineering. Our multidisciplinary research has led to the development of measures, for manual interactions between individuals and the substantial environment, that plausibly are observable by human sensory systems. We consider these methods to be the most important general contribution of our EVA investigation. We describe our perspective as control theoretic because it draws more on fundamental concepts about control systems in engineering than it does on working constructs from the subdisciplines of biomechanics and motor control in the bio-behavioral sciences. At the same time, we have attempted to identify the theoretical underpinnings of control-systems engineering that are most relevant to control by human beings. We believe that these underpinnings are implicit in the assumptions that cut across diverse methods in control-systems engineering, especially the various methods associated with "nonlinear control", "fuzzy control," and "adaptive control" in engineering. Our methods are based on these theoretical foundations rather than on the mathematical formalisms that are associated with particular methods in control-systems engineering. The most important aspects of the human-environment interaction in our investigation of mass handling are the functional consequences that body configuration and stability have for the pick up of information or the achievement of overt goals. It follows that an essential characteristic of postural behavior is the effective maintenance of the orientation and stability of the sensory and motor "platforms" (e.g., head or shoulders) over variations in the human, the environment and the task. This general skill suggests that individuals should be sensitive to the functional consequences of body configuration and stability. In other words, individuals should perceive the relation between configuration, stability, and performance so that they can adaptively control their interaction with the surroundings. Human-environment interactions constitute robust systems in that individuals can maintain the stability of such interactions over uncertainty about and variations in the dynamics of the interaction. Robust interactions allow individuals to adopt orientations and configurations that are not optimal with respect to purely energetic criteria. Individuals can tolerate variation in postural states, and such variation can serve an important function in adaptive systems. Postural variability generates stimulation which is "textured" by the dynamics of the human-environment system. The texture or structure in stimulation provides information about variation in dynamics, and such information can be sufficient to guide adaption in control strategies. Our method were designed to measure informative patterns of movement variability.

McDonald, P. V.↗
NASA NTRS2002

TIES for Dummies 3rd Edition (Technology Identification, Evaluation, and Selection) Basic how to's to implement the TIES method

The TIES method is a forecasting environment whereby the decision-maker has the ability to easily assess and trade-off the impact of various technologies without sophisticated and time-consuming mathematical formulations. TIES provides a methodical approach where technically feasible alternatives can be identified with accuracy and speed to reduce design cycle time, and subsequently, life cycle costs, and was achieved through the use of various probabilistic methods, such as Response Surface Methodology and Monte Carlo Simulations. Furthermore, structured and systematic techniques are utilized from other fields to identify possible concepts and evaluation criteria by which comparisons can be made. This objective is achieved by employing the use of Morphological Matrices and Multi-Attribute Decision Making techniques. Through the execution of each step, a family of design alternatives for a given set of customer requirements can be identified and assessed subjectively or objectively. This methodology allows for more information (knowledge) to be brought into the earlier phases of the design process and will have direct implications on the affordability of the system. The increased knowledge allows for optimum allocation of company resources and quantitative justification for program decisions. Finally, the TIES method provided novel results and quantitative justification to facilitate decision making in the early stages of design so as to produce affordable and quality products.

Kirby, Michelle R.↗