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NASA NTRS2005

A Tool for Requirements-Based Programming

Absent a general method for mathematically sound, automated transformation of customer requirements into a formal model of the desired system, developers must resort to either manual application of formal methods or to system testing (either manual or automated). While formal methods have afforded numerous successes, they present serious issues, e.g., costs to gear up to apply them (time, expensive staff), and scalability and reproducibility when standards in the field are not settled. The testing path cannot be walked to the ultimate goal, because exhaustive testing is infeasible for all but trivial systems. So system verification remains problematic. System or requirements validation is similarly problematic. The alternatives available today depend on either having a formal model or pursuing enough testing to enable the customer to be certain that system behavior meets requirements. The testing alternative for non-trivial systems always have some system behaviors unconfirmed and therefore is not the answer. To ensure that a formal model is equivalent to the customer s requirements necessitates that the customer somehow fully understands the formal model, which is not realistic. The predominant view that provably correct system development depends on having a formal model of the system leads to a desire for a mathematically sound method to automate the transformation of customer requirements into a formal model. Such a method, an augmentation of requirements-based programming, will be briefly described in this paper, and a prototype tool to support it will be described. The method and tool enable both requirements validation and system verification for the class of systems whose behavior can be described as scenarios. An application of the tool to a prototype automated ground control system for NASA mission is presented.

Rash, James L.↗
NASA NTRS2005

Evaluating the Effectiveness of the 2003-2004 NASA SCIence Files(trademark) Program

The NASA SCI Files is an Emmy award-winning series of instructional programs for grades 3-5. Produced by the NASA Center for Distance Learning, programs in the series are research-, inquiry-, standards-, teacher- and technology-based. Each NASA SCI Files program (1) integrates mathematics, science, and technology; (2) uses Problem-Based Learning (PBL) to enhance and enrich the teaching and learning of science; (3) emphasizes science as inquiry and the scientific method; (4) motivates students to become critical thinkers and active problem solvers; and (5) uses NASA research, facilities, and personnel to raise student awareness of careers and to exhibit the "real-world" application of mathematics, science, and technology. In April 2004, 1,500 randomly selected registered users of the NASA SCI Files were invited to complete a survey containing a series of questions. A total of 263 surveys were received. This report contains the quantitative and qualitative results of that survey.

Caton, Randall H.↗
NASA NTRS2005

Automated Image Registration Using Morphological Region of Interest Feature Extraction

With the recent explosion in the amount of remotely sensed imagery and the corresponding interest in temporal change detection and modeling, image registration has become increasingly important as a necessary first step in the integration of multi-temporal and multi-sensor data for applications such as the analysis of seasonal and annual global climate changes, as well as land use/cover changes. The task of image registration can be divided into two major components: (1) the extraction of control points or features from images; and (2) the search among the extracted features for the matching pairs that represent the same feature in the images to be matched. Manual control feature extraction can be subjective and extremely time consuming, and often results in few usable points. Automated feature extraction is a solution to this problem, where desired target features are invariant, and represent evenly distributed landmarks such as edges, corners and line intersections. In this paper, we develop a novel automated registration approach based on the following steps. First, a mathematical morphology (MM)-based method is used to obtain a scale-orientation morphological profile at each image pixel. Next, a spectral dissimilarity metric such as the spectral information divergence is applied for automated extraction of landmark chips, followed by an initial approximate matching. This initial condition is then refined using a hierarchical robust feature matching (RFM) procedure. Experimental results reveal that the proposed registration technique offers a robust solution in the presence of seasonal changes and other interfering factors. Keywords-Automated image registration, multi-temporal imagery, mathematical morphology, robust feature matching.

Plaza, Antonio↗
NASA NTRS2004

The New Approach to Self-Achievement (N.A.S.A.) Project 2004

The New Approach to Self-Achievement Program is designed to target rising seventh, eighth, and ninth grade students who require assistance in refining their mathematical skills, science awareness and knowledge, and test taking strategies. During the six week duration of the program, students are challenged in these areas through the application of robotic and aeronautic projects which encourage the students to practically apply their mathematical and science awareness accordingly. The first three weeks of my tenure were designated to assisting Mrs. Tammy Allen in the preparation of the 2004 NASA Project. As her assistant, I was held accountable for organizing, filing, preparing, analyzing, and completing the applications for the NASA Project. Additionally, I constructed the apposite databases which contained imperative information which aided in the selection of our participants. During the latter portion of those three weeks, Mrs. Allen, various staff members, and I, interviewed the numerous first-time applicants of the NASA Project. Furthermore, I was assigned to contact the accepted applicants of the program and provide all necessary information for the initiation of the child into the NASA Project. During the six week duration of the program, I will be working as a Project Leader at the Lorain Middle School site located in Lorain, Oh, with Mr. Fondriest Fountain. Mr. Fountain and I Will work with the eighth and ninth grade students in constructing robots, in which the students are told are made for NASA research which is being conducted on the surface of planet Mars. The robots, which are built from LEGOS and programmed through RoboLab computer software, are prepared to complete assigned Missions such as running obstacle courses; plowing and retrieving LEGOS; and scanning surfaces for intense regions of light.

Thomas, Candace J.↗
NASA NTRS2004

The Investigation Of Carbon Contamination And Sputtering Effects Of Xenon Ion Thrusters

The Electro-Physics Branch of the NASA Glenn Research Center investigates the effect of atomic oxygen, environmental durability of high performance power materials and surfaces, and low earth orbit. One of its current projects involves the analysis of ion thrusters. Ion thrusters are devices that initiate a beam of ions to a target area. The type of ion thruster that I have been working with this Summer of 2004 emits positively charged Xenon (Xe(+)) atoms through two grids, the screen grid and the accelerator grid, after it enters an ionization chamber. Insulators are used to mechanically hold and separate these two grids. A propellant isolator, an instrument that closely resembles insulators, is placed in front of the ionization chamber. Both the insulator and isolator are made with a ceramic compound and filled with insulating beads. The main difference between the two devices is that the propellant isolator allows gas to flow through, in this case, the gas is Xe(+) and the insulators do not. In order to avoid carbon deposits and other contaminating chemicals to settle on the insulators and propellant isolator, a metal shadow shield is placed around them. These shadow shields function as a protectant and can be shaped in numerous configurations. Part of my job responsibility this summer is to investigate the effectiveness of different shadow shields that are utilized on three different ion engines: the NSTAR (NASA Solar Electric Propulsion Technology Application Readiness), JIMO (Jupiter Icy Moons Orbiter), and NEXIS (Nuclear Electric Xenon Ion System). Using calculus and other mathematical tactics, I was asked to find the total flux of carbon contamination that was able to pass the protectant shadow shield. I familiarized myself with the software program, MathCad2004, to help perform some mathematical computations such as complex integration. Another method of studying the probability of contamination is by experimental simulation. After attaining the precise parameters of the actual shadow shields, I created replicas of three types of shadow shielding to be used to undergo testing. It will be placed in a machine that produces carbon atoms at a high temperature of 200 C. or beam is aimed at a targeted material. As a result of this collision, atoms and other particles are ejected out of the target surface. Another part of my internship consisted of research on sputter ejection, or the angle distribution of sputtered material. This research entailed finding the past results of sputter ejection investigation as well as creating another type of mock simulation. Other minor projects include calculating the path of Xe(+) gas through the insulating beads of the isolators and assisting my mentor in collecting data for his paper for the Joint Propulsion Conference & Exhibit to be held July 11-14,2004 in Fort Lauderdale, Florida.

Prak, Moline K.↗
NASA NTRS2004

Stirling Engine Dynamic System Modeling

The Thermo-Mechanical systems branch at the Glenn Research Center focuses a large amount time on Stirling engines. These engines will be used on missions where solar power is inefficient, especially in deep space. I work with Tim Regan and Ed Lewandowski who are currently developing and validating a mathematical model for the Stirling engines. This model incorporates all aspects of the system including, mechanical, electrical and thermodynamic components. Modeling is done through Simplorer, a program capable of running simulations of the model. Once created and then proven to be accurate, a model is used for developing new ideas for engine design. My largest specific project involves varying key parameters in the model and quantifying the results. This can all be done relatively trouble-free with the help of Simplorer. Once the model is complete, Simplorer will do all the necessary calculations. The more complicated part of this project is determining which parameters to vary. Finding key parameters depends on the potential for a value to be independently altered in the design. For example, a change in one dimension may lead to a proportional change to the rest of the model, and no real progress is made. Also, the ability for a changed value to have a substantial impact on the outputs of the system is important. Results will be condensed into graphs and tables with the purpose of better communication and understanding of the data. With the changing of these parameters, a more optimal design can be created without having to purchase or build any models. Also, hours and hours of results can be simulated in minutes. In the long run, using mathematical models can save time and money. Along with this project, I have many other smaller assignments throughout the summer. My main goal is to assist in the processes of model development, validation and testing.

Nakis, Christopher G.↗
NASA NTRS2005

Mission leverage education: NSU/NASA innovative undergraduate model

The BEST Lab (Center for Excellence in Science Education), the Center for Materials Research (CMR), and the Chemistry, Mathematics, Physics, and Computer Science (CS) Departments at Norfolk State University (NSU) joined forces to implement MiLEN(2) IUM - an innovative approach tu integrate current and emerging research into the undergraduate curricula and train students on NASA-related fields. An Earth Observing System (EOS) mission was simulated where students are educated and trained in many aspects of Remote Sensing: detector physics and spectroscopy; signal processing; data conditioning, analysis, visualization; and atmospheric science. This model and its continued impact is expected to significantly enhance the quality of the Mathematics, Science, Engineering and Technology (MSET or SMET) educational experience and to inspire students from historically underrepresented groups to pursue careers in NASA-related fields. MiLEN(2) IUM will be applicable to other higher education institutions that are willing to make the commitment to this endeavor in terms of faculty interest and space.

Chaudhury, S. Raj↗
NASA NTRS2006

Thermal Imaging Applied to Cryocrystallography: Cryocooling and Beam Heating (Part I)

Thermal imaging provides a non-invasive method to study both the cryocooling process and the heating due to the X-ray beam interaction with a sample. The method has been used successfully to image cryocooling in a number of experimental situations, i.e. cooling as a function of sample volume and as a function of cryostream orientation. Although there are experimental limitations to the method, it has proved a powerful technique to aid cryocrystallography development. Due to the rapid spatial temperature information provided about the sample it is also a powerful tool in the testing of mathematical models. Recently thermal imaging has been used to measure the temperature distribution on both a model and typical crystal samples illuminated with an X-ray beam produced by an undulator. A brief overview of thermal imaging and previous results will be presented. In addition, a detailed description of the calibration and experimental aspects of the beam heating measurements will be described. This will complement the following talk on the mathematical modeling and analysis of the results.

Snell, Edward↗
NASA NTRS2006

Non-Uniform Thickness Electroactive Device

An electroactive device comprises at least two layers of material, wherein at least one layer is an electroactive material and wherein at least one layer is of non-uniform thickness. The device can be produced in various sizes, ranging from large structural actuators to microscale or nanoscale devices. The applied voltage to the device in combination with the non-uniform thickness of at least one of the layers (electroactive and/or non-electroactive) controls the contour of the actuated device. The effective electric field is a mathematical function of the local layer thickness. Therefore, the local strain and the local bending/ torsion curvature are also a mathematical function of the local thickness. Hence the thinnest portion of the actuator offers the largest bending and/or torsion response. Tailoring of the layer thicknesses can enable complex motions to be achieved.

Su, Ji↗
NASA NTRS1997

Convergence Analysis of a Cascade Architecture Neural Network

In this paper, we present a mathematical foundation, including a convergence analysis, for cascading architecture neural networks. From this, a mathematical foundation for the casade correlation learning algorithm can also be found. Furthermore, it becomes apparent that the cascade correlation scheme is a special case of an efficient hardware learning algorithm called Cascade Error Projection.

Neural Network↗
NASA NTRS1996

Optimality of Empirical Z-R Relations

This paper attempts to justify mathematically the two empirical approaches to the problem of deriving Z-R relations from (Z,R) measurements, namely the power-law regression and the probability matching method (PMM). The basic mathematical assumptions that apply in each case are explicitly identified.

rainfall estimation radar reflectivity Z-R relatio↗
NASA NTRS1995

Terminal Dynamics Approach to Discrete Event Systems

This paper presents and discusses a mathematical formalism for simulation of discrete event dynamic (DED)-a special type of 'man-made' systems to serve specific purposes of information processing. The main objective of this work is to demonstrate that the mathematical formalism for DED can be based upon a terminal model of Newtonian dynamics which allows one to relax Lipschitz conditions at some discrete points.!.

discrete event systems↗
NASA NTRS2007

A Method for Calculating the Probability of Successfully Completing a Rocket Propulsion Ground Test

Propulsion ground test facilities face the daily challenge of scheduling multiple customers into limited facility space and successfully completing their propulsion test projects. Over the last decade NASA s propulsion test facilities have performed hundreds of tests, collected thousands of seconds of test data, and exceeded the capabilities of numerous test facility and test article components. A logistic regression mathematical modeling technique has been developed to predict the probability of successfully completing a rocket propulsion test. A logistic regression model is a mathematical modeling approach that can be used to describe the relationship of several independent predictor variables X(sub 1), X(sub 2),.., X(sub k) to a binary or dichotomous dependent variable Y, where Y can only be one of two possible outcomes, in this case Success or Failure of accomplishing a full duration test. The use of logistic regression modeling is not new; however, modeling propulsion ground test facilities using logistic regression is both a new and unique application of the statistical technique. Results from this type of model provide project managers with insight and confidence into the effectiveness of rocket propulsion ground testing.

Messer, Bradley↗
NASA NTRS2007

Robust Fuzzy Controllers Using FPGAs

Electro-mechanical device controllers typically come in one of three forms, proportional (P), Proportional Derivative (PD), and Proportional Integral Derivative (PID). Two methods of control are discussed in this paper; they are (1) the classical technique that requires an in-depth mathematical use of poles and zeros, and (2) the fuzzy logic (FL) technique that is similar to the way humans think and make decisions. FL controllers are used in multiple industries; examples include control engineering, computer vision, pattern recognition, statistics, and data analysis. Presented is a study on the development of a PD motor controller written in very high speed hardware description language (VHDL), and implemented in FL. Four distinct abstractions compose the FL controller, they are the fuzzifier, the rule-base, the fuzzy inference system (FIS), and the defuzzifier. FL is similar to, but different from, Boolean logic; where the output value may be equal to 0 or 1, but it could also be equal to any decimal value between them. This controller is unique because of its VHDL implementation, which uses integer mathematics. To compensate for VHDL's inability to synthesis floating point numbers, a scale factor equal to 10(sup (N/4) is utilized; where N is equal to data word size. The scaling factor shifts the decimal digits to the left of the decimal point for increased precision. PD controllers are ideal for use with servo motors, where position control is effective. This paper discusses control methods for motion-base platforms where a constant velocity equivalent to a spectral resolution of 0.25 cm(exp -1) is required; however, the control capability of this controller extends to various other platforms.

Monroe, Author Gene S., Jr.↗
NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗
NASA NTRS2007

On Flow Stagnation in a Tube Radiator

An analysis of the physical process for occurrence of flow stagnation in a space tube-radiator is performed and the mechanism and mathematic description for the flow stagnation are presented. Two causes for pressure drop unbalance between tubes of the radiator are identified: non-uniform cooling environment and different local flow resistances between the tubes. This analysis provides a theoretical basis for experimental simulations of the flow stagnation in a ground-based lab as well as two suggested methods to experimentally simulate flow stagnation. Criteria for the flow stagnation, depending on the viscosity data regressive polynomial, are derived from the extreme condition of the pressure drop in colder tubes. A preliminary numerical calculation is conducted for a space tube-radiator model which confirms the physical and mathematical analyses. The prediction by the criteria for flow stagnation in the tube-radiator model coincides with the numerical calculation result.

Motil, Brian↗
NASA NTRS2008

Method and apparatus to assess compartment syndrome

A method and apparatus for measuring pressure buildup in a body compartment that encases muscular tissue. The method includes assessing the body compartment configuration and identifying the effect of pulsatile components on at least one compartment dimension. This process is used in preventing tissue necrosis, and in decisions of whether to perform surgery on the body compartment for prevention of Compartment Syndrome. An apparatus is used for measuring excess pressure in the body compartment having components for imparting ultrasonic waves such as a transducer, placing the transducer to impart the ultrasonic waves, capturing the reflected imparted ultrasonic waves, and converting them to electrical signals, a pulsed phase-locked loop device for assessing a body compartment configuration and producing an output signal, and means for mathematically manipulating the output signal to thereby categorize pressure build-up in the body compartment from the mathematical manipulations.

Ueno, Toshiaki↗
NASA NTRS2008

Expressions Module for the Satellite Orbit Analysis Program

The Expressions Module is a software module that has been incorporated into the Satellite Orbit Analysis Program (SOAP). The module includes an expressions- parser submodule built on top of an analytical system, enabling the user to define logical and numerical variables and constants. The variables can capture output from SOAP orbital-prediction and geometric-engine computations. The module can combine variables and constants with built-in logical operators (such as Boolean AND, OR, and NOT), relational operators (such as >, <, or =), and mathematical operators (such as addition, subtraction, multiplication, division, modulus, exponentiation, differentiation, and integration). Parentheses can be used to specify precedence of operations. The module contains a library of mathematical functions and operations, including logarithms, trigonometric functions, Bessel functions, minimum/ maximum operations, and floating- point-to-integer conversions. The module supports combinations of time, distance, and angular units and has a dimensional- analysis component that checks for correct usage of units. A parser based on the Flex language and the Bison program looks for and indicates errors in syntax. SOAP expressions can be built using other expressions as arguments, thus enabling the user to build analytical trees. A graphical user interface facilitates use.

Edmonds, Karina↗