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Expansion and orthogonalization of measured modes for structure identification

The purpose was to investigate a new simultaneous expansion/orthogonalization method in comparison with two previously published expansion methods and a widely used orthogonalization technique. Each expansion method uses data from an analytical model of the structure to complete the estimate of the mode shape vectors. Berman and Nagy used Guyan expansion in their work with improving analytical models. In this method, modes are expanded one at a time, producing a set not orthogonal with respect to the mass matrix. Baruch and Bar Itzhack's optimal orthogonalization procedure was used to subsequently adjust the expanded modes. A second expansion technique was presented by O'Callahan, Avitabile, and Reimer and separately by Kammer. Again, modes are expanded individually and orthogonalized after expansion with the same optimal technique as above. Finally, a simultaneous expansion/orthogonalization method was developed from the orthogonal Procrustes problem of computational mathematics. In this method modes are optimally expanded as a set and orthogonal with respect to the mass matrix as a result. Two demonstation problems were selected for the comparison of the methods described. The first problem is an 8 degree of freedom spring-mass problem first presented by Kabe. Several conditions were examined for expansion method including the presence of errors in the measured data and in the analysis models. As a second demonstration problem, data from tests of laboratory scale model truss structures was expanded for system identification. Tests with a complete structure produced a correlated analysis model and the stiffness and mass matrices. Tests of various damaged configurations produced measured data for 6 modes at 14 dof locations.

Smith, Suzanne Weaver

Analysis of the distribution of pitch angles in model galactic disks - Numerical methods and algorithms

An automated mathematical method capable of successfully isolating the many different features in prototype and observed spiral galaxies and of accurately measuring the pitch angles and lengths of these individual features is developed. The method is applied to analyze the evolution of specific features in a prototype galaxy exhibiting flocculent spiral structure. The mathematical-computational method was separated into two components. Initially, the galaxy was partitioned into dense regions constituting features using two different methods. The results obtained using these two partitioning algorithms were very similar, from which it is inferred that no numerical biasing was evident and that capturing of the features was consistent. Standard least-squares methods underestimated the true slope of the cloud distribution and were incapable of approximating an orientation of 45 deg. The problems were overcome by introducing a superior fit least-squares method, developed with the intention of calculating true orientation rather than a regression line.

Russell, William S.

Notes on aerodynamic forces 1 : rectilinear motion

The study of the motion of perfect fluids is of paramount importance for the understanding of the chief phenomena occurring in the air surrounding an aircraft, and for the numerical determination of their effects. The author recently successfully employed some simple methods for the investigation of the flow of a perfect fluid that have never been mentioned in connection with aeronautical problems. These methods appeal particularly to the engineer who is untrained in performing laborious mathematical computations, as they do away with these and allow one to obtain many interesting results by the mere application of some general and well-known principles of mechanics. Discussed here are the kinetic energy of moving fluids, the momentum of a body in a perfect fluid, two dimensional flow, three dimensional flow, and the distribution of the transverse forces of very elongated surfaces of revolution.

Munk, Max M

Motion estimation of objects in KC-135 microgravity

The simulated microgravity environment aboard a KC-135 aircraft flying along a parabolic trajectory was used to study the ability of an autonomous space robot to grasp a freely translating and rotating object. Since the KC-135 cabin environment and the instrumentation for the Extravehicular Activity Helper/Retriever (EVAHR) do not provide a practical intertial reference frame, estimators based on the extended Kalman filter algorithm were used to model the relative translational dynamics of the KC-135 and the EVAHR. The estimator algorithms require intensive mathematical computation and therefore, i860 real-time. Estimator design, implementation concerns, and issues specific to the KC-135 environment are discussed and the architecture of the KC-135 translational state estimator is depicted.

Hewgill, Lisa

Adaptation of a Control Center Development Environment for Industrial Process Control

In the control center, raw telemetry data is received for storage, display, and analysis. This raw data must be combined and manipulated in various ways by mathematical computations to facilitate analysis, provide diversified fault detection mechanisms, and enhance display readability. A development tool called the Graphical Computation Builder (GCB) has been implemented which provides flight controllers with the capability to implement computations for use in the control center. The GCB provides a language that contains both general programming constructs and language elements specifically tailored for the control center environment. The GCB concept allows staff who are not skilled in computer programming to author and maintain computer programs. The GCB user is isolated from the details of external subsystem interfaces and has access to high-level functions such as matrix operators, trigonometric functions, and unit conversion macros. The GCB provides a high level of feedback during computation development that improves upon the often cryptic errors produced by computer language compilers. An equivalent need can be identified in the industrial data acquisition and process control domain: that of an integrated graphical development tool tailored to the application to hide the operating system, computer language, and data acquisition interface details. The GCB features a modular design which makes it suitable for technology transfer without significant rework. Control center-specific language elements can be replaced by elements specific to industrial process control.

Killough, Ronnie L.

[Activities of ICASE}

This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period October 1, 2000 through March 31, 2001.

Bushnell, Dennis M.

[Activities of ICASE]

This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period April 1, 2001 through September 30, 2001.

Bushnell, Dennis M.

Scientific Visualization & Modeling for Earth Systems Science Education

Providing research experiences for undergraduate students in Earth Systems Science (ESS) poses several challenges at smaller academic institutions that might lack dedicated resources for this area of study. This paper describes the development of an innovative model that involves students with majors in diverse scientific disciplines in authentic ESS research. In studying global climate change, experts typically use scientific visualization techniques applied to remote sensing data collected by satellites. In particular, many problems related to environmental phenomena can be quantitatively addressed by investigations based on datasets related to the scientific endeavours such as the Earth Radiation Budget Experiment (ERBE). Working with data products stored at NASA's Distributed Active Archive Centers, visualization software specifically designed for students and an advanced, immersive Virtual Reality (VR) environment, students engage in guided research projects during a structured 6-week summer program. Over the 5-year span, this program has afforded the opportunity for students majoring in biology, chemistry, mathematics, computer science, physics, engineering and science education to work collaboratively in teams on research projects that emphasize the use of scientific visualization in studying the environment. Recently, a hands-on component has been added through science student partnerships with school-teachers in data collection and reporting for the GLOBE Program (GLobal Observations to Benefit the Environment).

Chaudhury, S. Raj

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.

Telemetry and Science Data Software System

The Telemetry and Science Data Software System (TSDSS) was designed to validate the operational health of a spacecraft, ease test verification, assist in debugging system anomalies, and provide trending data and advanced science analysis. In doing so, the system parses, processes, and organizes raw data from the Aquarius instrument both on the ground and while in space. In addition, it provides a user-friendly telemetry viewer, and an instant pushbutton test report generator. Existing ground data systems can parse and provide simple data processing, but have limitations in advanced science analysis and instant report generation. The TSDSS functions as an offline data analysis system during I&T (integration and test) and mission operations phases. After raw data are downloaded from an instrument, TSDSS ingests the data files, parses, converts telemetry to engineering units, and applies advanced algorithms to produce science level 0, 1, and 2 data products. Meanwhile, it automatically schedules upload of the raw data to a remote server and archives all intermediate and final values in a MySQL database in time order. All data saved in the system can be straightforwardly retrieved, exported, and migrated. Using TSDSS s interactive data visualization tool, a user can conveniently choose any combination and mathematical computation of interesting telemetry points from a large range of time periods (life cycle of mission ground data and mission operations testing), and display a graphical and statistical view of the data. With this graphical user interface (GUI), the data queried graphs can be exported and saved in multiple formats. This GUI is especially useful in trending data analysis, debugging anomalies, and advanced data analysis. At the request of the user, mission-specific instrument performance assessment reports can be generated with a simple click of a button on the GUI. From instrument level to observatory level, the TSDSS has been operating supporting functional and performance tests and refining system calibration algorithms and coefficients, in sync with the Aquarius/SAC-D spacecraft. At the time of this reporting, it was prepared and set up to perform anomaly investigation for mission operations preceding the Aquarius/SAC-D spacecraft launch on June 10, 2011.

Bates, Lakesha

A Framework for Robust Multivariable Optimization of Integrated Circuits in Space Applications

Application Specific Integrated Circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way which facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as framework of software modules, templates and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation. Templates provide a starting point for both while toolbox functions minimize the code required. Once a test bench has been coded to optimize a particular circuit, it is also used to verify the final design. The combination of test bench and cost function can then serve as a template for similar circuits or be re-used to migrate the design to different processes by re-running it with the new process specific device models. The system has been used in the design of time to digital converters for laser ranging and time-of-flight mass spectrometry to optimize analog, mixed signal and digital circuits such as charge sensitive amplifiers, comparators, delay elements, radiation tolerant dual interlocked (DICE) flip-flops and two of three voter gates.

DuMonthier, Jeffrey

Robust Multivariable Optimization and Performance Simulation for ASIC Design

Application-specific-integrated-circuit (ASIC) design for space applications involves multiple challenges of maximizing performance, minimizing power, and ensuring reliable operation in extreme environments. This is a complex multidimensional optimization problem, which must be solved early in the development cycle of a system due to the time required for testing and qualification severely limiting opportunities to modify and iterate. Manual design techniques, which generally involve simulation at one or a small number of corners with a very limited set of simultaneously variable parameters in order to make the problem tractable, are inefficient and not guaranteed to achieve the best possible results within the performance envelope defined by the process and environmental requirements. What is required is a means to automate design parameter variation, allow the designer to specify operational constraints and performance goals, and to analyze the results in a way that facilitates identifying the tradeoffs defining the performance envelope over the full set of process and environmental corner cases. The system developed by the Mixed Signal ASIC Group (MSAG) at the Goddard Space Flight Center is implemented as a framework of software modules, templates, and function libraries. It integrates CAD tools and a mathematical computing environment, and can be customized for new circuit designs with only a modest amount of effort as most common tasks are already encapsulated. Customization is required for simulation test benches to determine performance metrics and for cost function computation.

DuMonthier, Jeffrey

A Systems Analysis Approach to Understanding the Physiological Adaptation to Spaceflight

This book is a summary of interdisciplinary research (physiology, space medicine, engineering, computer science, mathematics) that spans two decades (1972-1992). The research was an attempt to use systems analysis, mathematical modeling, computer simulations, and database systems to integrate the biomedical spaceflight data that was being collected during this period. The goal of the effort was to achieve a better understanding of the human physiological response to short-term and long-term space travel. The activity was primarily devoted to analyzing the biomedical results of Skylab (1973-74), a series of three space missions which is still ranked as the most comprehensive of all long-term biomedical space studies to date. This work was begun as a coordinated effort between the National Aeronautics and Space Administration (Johnson Space Center) and the General Electric Company’s Space Division (Houston, TX). It was the intent that this multidisciplined, integrative approach could reveal aspects of the then-new science of microgravity adaptation that were not obvious by adhering to the traditional methodology of examining each organ system in isolation. Some joint work with the Russians, including the Apollo-Soyez test project and a joint bedrest study was also supported during this period. In the 1980’s the systems analysis group’s effort was redirected to support the science management of human and animal experiments on the Space Shuttle. A few examples from this era are also included in the book. Parts of this work have been published elsewhere, presented at technical meetings, and documented in reports with limited distribution. These publications will be referenced throughout the text and the interested reader is advised to use these as resource material where additional details are desired. The intent of this book is not to reproduce these documents but rather to present a coherent view of the integrative analysis under one cover. This volume contains the first detailed publication (other than in internal reports) of an extensive metabolic balance analysis of Skylab data, the development and validation of the “Whole-Body Algorithm,” and simulation studies of diverse hypogravic environments. An analysis of cardiovascular deconditioning and a description of the calcium regulatory model are also new. A long period has passed between the completion of the main body of work represented in this book and its publication in this form. It was inevitable that new research efforts would lead to developments related to the spaceflight problems addressed and thereby make some of our biomedical conclusions obsolete. Although in some cases reference to more recent work have been included, for the most part this book should be considered an historical summary demonstrating the approach and utility of systems analysis and computer modeling in the NASA Life Sciences program at the time the studies were conducted.

Leonard, Joel I.

Mathematical modeling and computer simulation of isoelectric focusing with electrochemically defined ampholytes

A mathematical model of isoelectric focusing at the steady state has been developed for an M-component system of electrochemically defined ampholytes. The model is formulated from fundamental principles describing the components' chemical equilibria, mass transfer resulting from diffusion and electromigration, and electroneutrality. The model consists of ordinary differential equations coupled with a system of algebraic equations. The model is implemented on a digital computer using FORTRAN-based simulation software. Computer simulation data are presented for several two-component systems showing the effects of varying the isoelectric points and dissociation constants of the constituents.

Palusinski, O. A.

Proceedings, Conference on the Computing Environment for Mathematical Software

Recent advances in software and hardware technology which make it economical to create computing environments appropriate for specialized applications are addressed. Topics included software tools, FORTRAN standards activity, and features of languages, operating systems, and hardware that are important for the development, testing, and maintenance of mathematical software.

Source record

Computer simulation of the mathematical modeling involved in constitutive equation development: Via symbolic computations

Development of new material models for describing the high temperature constitutive behavior of real materials represents an important area of research in engineering disciplines. Derivation of mathematical expressions (constitutive equations) which describe this high temperature material behavior can be quite time consuming, involved and error prone; thus intelligent application of symbolic systems to facilitate this tedious process can be of significant benefit. A computerized procedure (SDICE) capable of efficiently deriving potential based constitutive models, in analytical form is presented. This package, running under MACSYMA, has the following features: partial differentiation, tensor computations, automatic grouping and labeling of common factors, expression substitution and simplification, back substitution of invariant and tensorial relations and a relational data base. Also limited aspects of invariant theory were incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). Finally not only calculation of flow and/or evolutionary laws were accomplished but also the determination of history independent nonphysical coefficients in terms of physically measurable parameters, e.g., Young's modulus, was achieved. The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet predefined order and simplify expressions so as to limit expression growth. Results are displayed when applicable utilizing index notation.

Arnold, S. M.

Application of technology developed for flight simulation at NASA. Langley Research Center

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations including mathematical model computation and data input/output to the simulators must be deterministic and be completed in as short a time as possible. Personnel at NASA's Langley Research Center are currently developing the use of supercomputers for simulation mathematical model computation for real-time simulation. This, coupled with the use of an open systems software architecture, will advance the state-of-the-art in real-time flight simulation.

Cleveland, Jeff I., II