Search NASA⌕ Search

SEARCH · Search NASA

Results for “SYMBOLS - COMBUSTION - NACA”

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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Comparison of symbolic and numerical integration methods for an assumed-stress hybrid shell element

Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favor of hybrid elements is that numerical integration to generate element matrices can be entirely avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom and the significant time savings achieved is demonstrated through an example.

Rengarajan, Govind↗
NASA NTRS1995

The analysis of control trajectories using symbolic and database computing

This final report comprises the formal semi-annual status reports for this grant for the periods June 30-December 31, 1993, January 1-June 30, 1994, and June 1-December 31, 1994. The research supported by this grant is broadly concerned with the symbolic computation, mixed numeric-symbolic computation, and database computation of trajectories of dynamical systems, especially control systems. A review of work during the report period covers: trajectories and approximating series, the Cayley algebra of trees, actions of differential operators, geometrically stable integration algorithms, hybrid systems, trajectory stores, PTool, and other activities. A list of publications written during the report period is attached.

Grossman, Robert↗
NASA NTRS2001

From the Origins of Life to Intelligence: The Emergence of Symbolic Constructs

Intelligence cannot be understood - and cannot be 'artificially recreated' - without also understanding how it fits as a phenomenon in the evolution of matter. I say 'matter' instead of 'life' because my thesis is that the distinction between matter, with its associated interactions, and life, is simply in the complexity of these interactions and in the number of 'symbolic levels' that are defined by these interactions. Most of us think of symbols only in the context of language. This is understandable, since it is at this level where it is easiest to draw a distinction between natural objects and their 'names', i.e., the different sets of 'abstract' objects that can be manipulated to produce models of the 'real' world. Of course sets of abstract objects can also acquire names and be manipulated at higher and higher conceptual levels. When we use the words 'philosophy' or 'the Declaration of Independence' we use abstract constructs that will only make sense in other specific abstract contexts. Additional information is contained in the original extended abstract.

Colombano, Silvano P.↗
NASA NTRS2007

Symbolic LTL Compilation for Model Checking: Extended Abstract

In Linear Temporal Logic (LTL) model checking, we check LTL formulas representing desired behaviors against a formal model of the system designed to exhibit these behaviors. To accomplish this task, the LTL formulas must be translated into automata [21]. We focus on LTL compilation by investigating LTL satisfiability checking via a reduction to model checking. Having shown that symbolic LTL compilation algorithms are superior to explicit automata construction algorithms for this task [16], we concentrate here on seeking a better symbolic algorithm.We present experimental data comparing algorithmic variations such as normal forms, encoding methods, and variable ordering and examine their effects on performance metrics including processing time and scalability. Safety critical systems, such as air traffic control, life support systems, hazardous environment controls, and automotive control systems, pervade our daily lives, yet testing and simulation alone cannot adequately verify their reliability [3]. Model checking is a promising approach to formal verification for safety critical systems which involves creating a formal mathematical model of the system and translating desired safety properties into a formal specification for this model. The complement of the specification is then checked against the system model. When the model does not satisfy the specification, model-checking tools accompany this negative answer with a counterexample, which points to an inconsistency between the system and the desired behaviors and aids debugging efforts.

Rozier, Kristin Y.↗
NASA NTRS2008

Hand-Held Ultrasonic Instrument for Reading Matrix Symbols

A hand-held instrument that would include an ultrasonic camera has been proposed as an efficient means of reading matrix symbols. The proposed instrument could be operated without mechanical raster scanning. All electronic functions from excitation of ultrasonic pulses through final digital processing for decoding matrix symbols would be performed by dedicated circuitry within the single, compact instrument housing.

Schramm, Harry F.↗
NASA NTRS2010

Efficient Bit-to-Symbol Likelihood Mappings

This innovation is an efficient algorithm designed to perform bit-to-symbol and symbol-to-bit likelihood mappings that represent a significant portion of the complexity of an error-correction code decoder for high-order constellations. Recent implementation of the algorithm in hardware has yielded an 8- percent reduction in overall area relative to the prior design.

Moision, Bruce E.↗
NASA NTRS2011

Symbolically Modeling Concurrent MCAPI Executions

Improper use of Inter-Process Communication (IPC) within concurrent systems often creates data races which can lead to bugs that are challenging to discover. Techniques that use Satisfiability Modulo Theories (SMT) problems to symbolically model possible executions of concurrent software have recently been proposed for use in the formal verification of software. In this work we describe a new technique for modeling executions of concurrent software that use a message passing API called MCAPI. Our technique uses an execution trace to create an SMT problem that symbolically models all possible concurrent executions and follows the same sequence of conditional branch outcomes as the provided execution trace. We check if there exists a satisfying assignment to the SMT problem with respect to specific safety properties. If such an assignment exists, it provides the conditions that lead to the violation of the property. We show how our method models behaviors of MCAPI applications that are ignored in previously published techniques.

Fischer, Topher↗
NASA NTRS2011

A Multi-Encoding Approach for LTL Symbolic Satisfiability Checking

Formal behavioral specifications written early in the system-design process and communicated across all design phases have been shown to increase the efficiency, consistency, and quality of the system under development. To prevent introducing design or verification errors, it is crucial to test specifications for satisfiability. Our focus here is on specifications expressed in linear temporal logic (LTL). We introduce a novel encoding of symbolic transition-based Buchi automata and a novel, "sloppy," transition encoding, both of which result in improved scalability. We also define novel BDD variable orders based on tree decomposition of formula parse trees. We describe and extensively test a new multi-encoding approach utilizing these novel encoding techniques to create 30 encoding variations. We show that our novel encodings translate to significant, sometimes exponential, improvement over the current standard encoding for symbolic LTL satisfiability checking.

Rozier, Kristin Y.↗
NASA NTRS2005

Hidden Identification on Parts: Magnetic Machine-Readable Matrix Symbols

All NASA parts have identification, usually expressed in terms of part number, serial number, and the like. In most cases, this identification is permanently marked directly on the part for tracking throughout its life cycle. NASA has developed a method for reading the matrix symbol through up to 15 mils (25 m) of paint (5 or 6 layers). This method of part identification involves coating selected patches on the objects with magnetic materials in matrix symbol patterns and reading the patterns by use of magneto-optical imaging equipment.

Schramm, Harry F.↗
NASA NTRS2012

Symbolic Execution Enhanced System Testing

We describe a testing technique that uses information computed by symbolic execution of a program unit to guide the generation of inputs to the system containing the unit, in such a way that the unit's, and hence the system's, coverage is increased. The symbolic execution computes unit constraints at run-time, along program paths obtained by system simulations. We use machine learning techniques treatment learning and function fitting to approximate the system input constraints that will lead to the satisfaction of the unit constraints. Execution of system input predictions either uncovers new code regions in the unit under analysis or provides information that can be used to improve the approximation. We have implemented the technique and we have demonstrated its effectiveness on several examples, including one from the aerospace domain.

Davies, Misty D.↗
NASA NTRSDate not supplied

Bingo: A Customizable Framework for Symbolic Regression with Genetic Programming

In this paper, we introduce Bingo, a flexible and customizable yet performant Python framework for symbolic regression with genetic programming. Bingo maintains a modular code structure for simple abstraction and easily swappable components. Fitness functions, selection methods, and constant optimization methods allow for easy problem-specific customization. Bingo also maintains several features for increased efficiency such as parallelism, equation simplification, and a C++ backend. We compare Bingo’s performance to other genetic programming for symbolic regression (GPSR) methods to show that it is both competitive and flexible.

David Randall↗
NASA NTRSDate not supplied

Bayesian Model Selection for Reducing Bloat and Overfitting in Genetic Programming for Symbolic Regression

When performing symbolic regression using genetic programming, overfitting and bloat can negatively impact generalizability and interpretability of the resulting equations as well as increase computation times. A Bayesian fitness metric is introduced and its impact on bloat and overfitting during population evolution is studied and compared to common alternatives in the literature. The proposed approach was found to be more robust to noise and data sparsity in numerical experiments, guiding evolution to a level of complexity appropriate to the dataset. Further evolution of the population resulted not in overfitting or bloat, but rather in slight simplifications in model form. The ability to identify an equation of complexity appropriate to the scale of noise in the training data was also demonstrated. In general, the Bayesian model selection algorithm was shown to be an effective means of regularization which resulted in less bloat and overfitting when any amount of noise was present in the training data.

Uncertainty quantification↗