Search NASA⌕ Search

SEARCH · Search NASA

Results for “symbolic computation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

STAR - A computer language for hybrid AI applications

Constructing Artificial Intelligence application systems which rely on both symbolic and non-symbolic processing places heavy demands on the communication of data between dissimilar languages. This paper describes STAR (Simple Tool for Automated Reasoning), a computer language for the development of AI application systems which supports the transfer of data structures between a symbolic level and a non-symbolic level defined in languages such as FORTRAN, C and PASCAL. The organization of STAR is presented, followed by the description of an application involving STAR in the interpretation of airborne imaging spectrometer data.

Borchardt, G. C.↗
NASA NTRS1977

Observations on approximate integrations

A class of integration strategies is explored that fall in between the two extremes of symbolic integration and numerical quadrature, which are, respectively, aimed at the computer generation of answers in the form of exact expressions and numerical values. The theoretical advances in symbolic integration are discussed. Three major contexts of applications with attendant case studies, four possible types of strategies for approximate integration are examined. The feasibility and adequacy (or inadequancy) of MACSYMA for implementing these strategies are considered.

Ng, E. W.↗
NASA NTRS1986

Symbolic generation of elastic rotor blade equations using a FORTRAN processor and numerical study on dynamic inflow effects on the stability of helicopter rotors

The process of performing an automated stability analysis for an elastic-bladed helicopter rotor is discussed. A symbolic manipulation program, written in FORTRAN, is used to aid in the derivation of the governing equations of motion for the rotor. The blades undergo coupled bending and torsional deformations. Two-dimensional quasi-steady aerodynamics below stall are used. Although reversed flow effects are neglected, unsteady effects, modeled as dynamic inflow are included. Using a Lagrangian approach, the governing equations are derived in generalized coordinates using the symbolic program. The program generates the steady and perturbed equations and writes into subroutines to be called by numerical routines. The symbolic program can operate on both expressions and matrices. For the case of hovering flight, the blade and dynamic inflow equations are converted to equations in a multiblade coordinate system by rearranging the coefficients of the equations. For the case of forward flight, the multiblade equations are obtained through the symbolic program. The final multiblade equations are capable of accommodating any number of elastic blade modes. The computer implementation of this procedure consists of three stages: (1) the symbolic derivation of equations; (2) the coding of the equations into subroutines; and (3) the numerical study after identifying mass, damping, and stiffness coefficients. Damping results are presented in hover and in forward flight with and without dynamic inflow effects for various rotor blade models, including rigid blade lag-flap, elastic flap-lag, flap-lag-torsion, and quasi-static torsion. Results from dynamic inflow effects which are obtained from a lift deficiency function for a quasi-static inflow model in hover are also presented.

Reddy, T. S. R.↗
NASA NTRS1976

The formulation of simulation models of aeronautical systems

Recent developments in formula-manipulation compilers have led to a significant reduction in the time spent in formulating models of complex multi-degrees-of-freedom dynamical systems. MACSYMA, a computer system that can be used to perform symbolic manipulations in an interactive mode, is applied to the problem of formulating models of aeronautical systems for simulation studies. An example demonstrates that once the procedure is established, the formulation and modification of the models can be reduced to a series of routine computer operations.

Howard, J. C.↗
NASA NTRS1982

Performance of concatenated Reed-Solomon/Viterbi channel coding

The concatenated Reed-Solomon (RS)/Viterbi coding system is reviewed. The performance of the system is analyzed and results are derived with a new simple approach. A functional model for the input RS symbol error probability is presented. Based on this new functional model, we compute the performance of a concatenated system in terms of RS word error probability, output RS symbol error probability, bit error probability due to decoding failure, and bit error probability due to decoding error. Finally we analyze the effects of the noisy carrier reference and the slow fading on the system performance.

Divsalar, D.↗
NASA NTRS1970

Syntax-directed documentation for PL360

PL360 is a phrase-structured programming language which provides the facilities of a symbolic machine language for the IBM 360 computers. An automatic process, syntax-directed documentation, is described which acquires programming documentation through the syntactical analysis of a program, followed by the interrogation of the originating programmer. This documentation can be dispensed through reports of file query replies when other programmers later need to know the program structure and its details. A key principle of the programming documentation process is that it is managed solely on the basis of the syntax of programs.

Mills, H. D.↗
NASA NTRS1977

Ray trajectories in a torus: An application of MACSYMA to a complex numerical computation

The study of ray trajectories of plasma waves in a torodial geometry using MACSYMA is an example of how symbolic, numerical, and graphical facilities can be used in concert to accomplish a complex computational goal. Computational features of this study which are of particular significance include: the derivation of code (i.e. writing functions to generate program fragments), the use of array functions to simplify the specification of a numerical iteration scheme, and the graphical presentation of the results. Mathematically, this study originates in the solution of a linear inhomogeneous partial differential equation in 3 dimensions by the method of characteristics. While it is possible to describe this equation compactly by using vector notation, and by specifying the spatial variation of the coefficients in terms of intermediate parameters, the transformation of the equation into a form amenable to solution is very tedious. A MACSYMA program is presented for obtaining description of the rf field structure excited by a waveguide located at the edge of a toroidal plasma confinement device.

Kulp, J. L.↗
NASA NTRS1994

Computationally efficient multibody simulations

Computationally efficient approaches to the solution of the dynamics of multibody systems are presented in this work. The computational efficiency is derived from both the algorithmic and implementational standpoint. Order(n) approaches provide a new formulation of the equations of motion eliminating the assembly and numerical inversion of a system mass matrix as required by conventional algorithms. Computational efficiency is also gained in the implementation phase by the symbolic processing and parallel implementation of these equations. Comparison of this algorithm with existing multibody simulation programs illustrates the increased computational efficiency.

Ramakrishnan, Jayant↗
NASA NTRS1992

Determination of aerodynamic sensitivity coefficients for wings in transonic flow

The quasianalytical approach is applied to the 3-D full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. The quasianalytical approach is believed to be reasonably accurate and computationally efficient for 3-D problems.

Carlson, Leland A.↗
NASA NTRS1971

Calculation of inviscid surface streamlines and heat transfer on shuttle type configurations. Part 2: Description of computer program

A description of the computer program used for heating rate calculation for blunt bodies in hypersonic flow is given. The main program and each subprogram are described by defining the pertinent symbols involved and presenting a detailed flow diagram and complete computer program listing. Input and output parameters are discussed in detail. Listings are given for the computation of heating rates on (1) a blunted 15 deg half-angle cone at 20 deg incidence and Mach 10.6, (2) a blunted 70 deg slab delta wing at 10 deg incidence and Mach 8, and (3) the HL-10 lifting body at 20 deg incidence and Mach 10. In addition, the computer program output for two streamlines on the blunted 15 deg half-angle cone is listed. For Part 1, see N71-36186.

Dejarnette, F. R.↗
NASA NTRS1988

A flexible computer aid for conceptual design based on constraint propagation and component-modeling

The Rubber Airplane program, which combines two symbolic processing techniques with a component-based database of design knowledge, is proposed as a computer aid for conceptual design. Using object-oriented programming, programs are organized around the objects and behavior to be simulated, and using constraint propagation, declarative statements designate mathematical relationships among all the equation variables. It is found that the additional level of organizational structure resulting from the arrangement of the design information in terms of design components provides greater flexibility and convenience.

Kolb, Mark A.↗
NASA NTRS1994

An initial investigation into methods of computing transonic aerodynamic sensitivity coefficients

The primary accomplishments of the project are as follows: (1) Using the transonic small perturbation equation as a flowfield model, the project demonstrated that the quasi-analytical method could be used to obtain aerodynamic sensitivity coefficients for airfoils at subsonic, transonic, and supersonic conditions for design variables such as Mach number, airfoil thickness, maximum camber, angle of attack, and location of maximum camber. It was established that the quasi-analytical approach was an accurate method for obtaining aerodynamic sensitivity derivatives for airfoils at transonic conditions and usually more efficient than the finite difference approach. (2) The usage of symbolic manipulation software to determine the appropriate expressions and computer coding associated with the quasi-analytical method for sensitivity derivatives was investigated. Using the three dimensional fully conservative full potential flowfield model, it was determined that symbolic manipulation along with a chain rule approach was extremely useful in developing a combined flowfield and quasi-analytical sensitivity derivative code capable of considering a large number of realistic design variables. (3) Using the three dimensional fully conservative full potential flowfield model, the quasi-analytical method was applied to swept wings (i.e. three dimensional) at transonic flow conditions. (4) The incremental iterative technique has been applied to the three dimensional transonic nonlinear small perturbation flowfield formulation, an equivalent plate deflection model, and the associated aerodynamic and structural discipline sensitivity equations; and coupled aeroelastic results for an aspect ratio three wing in transonic flow have been obtained.

Carlson, Leland A.↗
NASA NTRS1992

Determination of aerodynamic sensitivity coefficients based on the three-dimensional full potential equation

The quasi-analytical approach is applied to the three-dimensional full potential equation to compute wing aerodynamic sensitivity coefficients in the transonic regime. Symbolic manipulation is used to reduce the effort associated with obtaining the sensitivity equations, and the large sensitivity system is solved using 'state of the art' routines. Results are compared to those obtained by the direct finite difference approach and both methods are evaluated to determine their computational accuracy and efficiency. The quasi-analytical approach is shown to be accurate and efficient for large aerodynamic systems.

Elbanna, Hesham M.↗
NASA NTRS1978

Effect of noisy phase reference on coherent detection of unbalanced QPSK signals

A phase error in the reference signal used in coherent detection of PSK signals causes a degradation in performance; this effect on bit error probability has been much discussed in the literature for BPSK and balanced QPSK systems. For unbalanced QPSK (UQPSK) systems, where the power and data rates in the two channels are unequal, and where the channel data symbols might also be different, the problem of computing the error probability is more complex, and only approximate solutions have been previously given. In this paper, exact expressions are derived for the conditional probability of error for the I and Q channels as a function of the channel power and data rate ratio. This is done for all combinations of Manchester and NRZ signalling schemes, and it is shown that in some cases the low data rate channel can be more seriously affected by a phase offset. Numerical results are also given for the average probability of error, assuming a biphase Costas loop is used for carrier synchronization.

Osborne, H. C.↗
NASA NTRS1962

Aerodynamic Heating and Deceleration During Entry into Planetary Atmospheres

Dr. Chapman's lecture examines the physics behind spacecraft entry into planetary atmospheres. He explains how scientists determine if a planet has an atmosphere and how scientists can compute deceleration when the atmospheric conditions are unknown. Symbols and equations used for calculations for aerodynamic heating and deceleration are provided. He also explains heat transfer in bodies approaching an atmosphere, deceleration, and the use of ablation in protecting spacecraft from high temperatures during atmospheric entry.

Chapman, Dean R.↗
NASA NTRS2014

Statistical Symbolic Execution with Informed Sampling

Symbolic execution techniques have been proposed recently for the probabilistic analysis of programs. These techniques seek to quantify the likelihood of reaching program events of interest, e.g., assert violations. They have many promising applications but have scalability issues due to high computational demand. To address this challenge, we propose a statistical symbolic execution technique that performs Monte Carlo sampling of the symbolic program paths and uses the obtained information for Bayesian estimation and hypothesis testing with respect to the probability of reaching the target events. To speed up the convergence of the statistical analysis, we propose Informed Sampling, an iterative symbolic execution that first explores the paths that have high statistical significance, prunes them from the state space and guides the execution towards less likely paths. The technique combines Bayesian estimation with a partial exact analysis for the pruned paths leading to provably improved convergence of the statistical analysis. We have implemented statistical symbolic execution with in- formed sampling in the Symbolic PathFinder tool. We show experimentally that the informed sampling obtains more precise results and converges faster than a purely statistical analysis and may also be more efficient than an exact symbolic analysis. When the latter does not terminate symbolic execution with informed sampling can give meaningful results under the same time and memory limits.

Reliability↗
NASA NTRS1990

An investigation of constraint-based component-modeling for knowledge representation in computer-aided conceptual design

Originally, computer programs for engineering design focused on detailed geometric design. Later, computer programs for algorithmically performing the preliminary design of specific well-defined classes of objects became commonplace. However, due to the need for extreme flexibility, it appears unlikely that conventional programming techniques will prove fruitful in developing computer aids for engineering conceptual design. The use of symbolic processing techniques, such as object-oriented programming and constraint propagation, facilitate such flexibility. Object-oriented programming allows programs to be organized around the objects and behavior to be simulated, rather than around fixed sequences of function- and subroutine-calls. Constraint propagation allows declarative statements to be understood as designating multi-directional mathematical relationships among all the variables of an equation, rather than as unidirectional assignments to the variable on the left-hand side of the equation, as in conventional computer programs. The research has concentrated on applying these two techniques to the development of a general-purpose computer aid for engineering conceptual design. Object-oriented programming techniques are utilized to implement a user-extensible database of design components. The mathematical relationships which model both geometry and physics of these components are managed via constraint propagation. In addition, to this component-based hierarchy, special-purpose data structures are provided for describing component interactions and supporting state-dependent parameters. In order to investigate the utility of this approach, a number of sample design problems from the field of aerospace engineering were implemented using the prototype design tool, Rubber Airplane. The additional level of organizational structure obtained by representing design knowledge in terms of components is observed to provide greater convenience to the program user, and to result in a database of engineering information which is easier both to maintain and to extend.

Kolb, Mark A.↗