Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - CALCUS, OPERATIONAL”

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 577 records · Page 32

Analysis of the anisotropic viscoplastic-damage response of composite laminates - Continuum basis and computational algorithms

The mathematical structure underlying the rate equations of a recently-developed constitutive model for the coupled viscoplastic-damage response of anisotropic composites is critically examined. In this regard, a number of tensor projection operators have been identified, and their properties were exploited to enable the development of a general computational framework for their numerical implementation using the Euler fully-implicit integration method. In particular, this facilitated (i) the derivation of explicit expressions of the (consistent) material tangent stiffnesses that are valid for both three-dimensional as well as subspace (e.g. plane stress) formulations, (ii) the implications of the symmetry or unsymmetry properties of these tangent operators from a thermodynamic standpoint, and (iii) the development of an effective time-step control strategy to ensure accuracy and convergence of the solution. In addition, the special limiting case of inviscid elastoplasticity is treated. The results of several numerical simulations are given to demonstrate the effectiveness of the schemes developed.

Saleeb, A. F.↗

A Formally Verified Floating-Point Implementation of the Compact Position Reporting Algorithm

The Automatic Dependent Surveillance-Broadcast (ADS-B) system allows aircraft to communicate their current state, including position and velocity information, to other aircraft in their vicinity and to ground stations. The Compact Position Reporting (CPR) algorithm is the ADS-B module responsible for the encoding and decoding of aircraft positions. CPR is highly sensitive to computer arithmetic since it heavily relies on functions that are intrinsically unstable such as floor and modulo. In this paper, a formally-verified double-precision floating-point implementation of the CPR algorithm is presented. The verification proceeds in three steps. First, an alternative version of CPR, which reduces the floating-point rounding error is proposed. Then, the Prototype Verification System (PVS) is used to formally prove that the ideal real-number counterpart of the improved algorithm is mathematically equivalent to the standard CPR definition. Finally, the static analyzer Frama-C is used to verify that the double-precision implementation of the improved algorithm is correct with respect to its operational requirement. The alternative algorithm is currently being considered for inclusion in the revised version of the ADS-B standards document as the reference implementation of the CPR algorithm.

Laura Titolo↗

The human operator in manual preview tracking /an experiment and its modeling via optimal control/

A manual preview tracking experiment and its results are presented. The preview drastically improves the tracking performance compared to zero-preview tracking. Optimal discrete finite preview control is applied to determine the structure of a mathematical model of the manual preview tracking experiment. Variable parameters in the model are adjusted to values which are consistent to the published data in manual control. The model with the adjusted parameters is found to be well correlated to the experimental results.

Tomizuka, M.↗

A Temperature Sensor using a Silicon-on-Insulator (SOI) Timer for Very Wide Temperature Measurement

A temperature sensor based on a commercial-off-the-shelf (COTS) Silicon-on-Insulator (SOI) Timer was designed for extreme temperature applications. The sensor can operate under a wide temperature range from hot jet engine compartments to cryogenic space exploration missions. For example, in Jet Engine Distributed Control Architecture, the sensor must be able to operate at temperatures exceeding 150 C. For space missions, extremely low cryogenic temperatures need to be measured. The output of the sensor, which consisted of a stream of digitized pulses whose period was proportional to the sensed temperature, can be interfaced with a controller or a computer. The data acquisition system would then give a direct readout of the temperature through the use of a look-up table, a built-in algorithm, or a mathematical model. Because of the wide range of temperature measurement and because the sensor is made of carefully selected COTS parts, this work is directly applicable to the NASA Fundamental Aeronautics/Subsonic Fixed Wing Program--Jet Engine Distributed Engine Control Task and to the NASA Electronic Parts and Packaging (NEPP) Program. In the past, a temperature sensor was designed and built using an SOI operational amplifier, and a report was issued. This work used an SOI 555 timer as its core and is completely new work.

Patterson, Richard L.↗

S-193 scatterometer transfer function analysis for data processing

A mathematical model for converting raw data measurements of the S-193 scatterometer into processed values of radar scattering coefficient is presented. The argument is based on an approximation derived from the Radar Equation and actual operating principles of the S-193 Scatterometer hardware. Possible error sources are inaccuracies in transmitted wavelength, range, antenna illumination integrals, and the instrument itself. The dominant source of error in the calculation of scattering coefficent is accuracy of the range. All other ractors with the possible exception of illumination integral are not considered to cause significant error in the calculation of scattering coefficient.

Johnson, L.↗

Mathematical synthesization of complex structures

A mathematical synthesization approach for rapidly modeling and analyzing complex structures comprised of hundreds or thousands of repeating individual structural members, interconnecting hardware, and other components was described. The techniques are applicable to any structure with repeating structural members. The capabilities are embodied within the Interactive Design and Evaluation of Advanced Spacecraft (IDEAS) computer-aided design system. IDEAS has a full range of integrated spacecraft modeling, design, analysis, performance, and cost estimating capabilities which include about 40 technical program and executive, data base, and file management systems. With IDEAS, a single user at an interactive terminal can create, design, analyze, and conduct parametric studies of Earth orbiting spacecraft in a timely, cost-efficient manner. The system is particularly useful in the conceptual design phases of advanced space missions when a multiplicity of concepts must be evaluated. The IDEAS interactive finite-element modeling capabilities are discussed. The mathematical synthesization programs were structured not only to provide a detailed finite-element model of the structure but also to automatically perform the many auxiliary computations needed to analyze the spacecraft in its orbital operational environment.

Garrett, L. B.↗

Computer-aided design and distributed system technology development for large space structures

Proposed large space structures have many characteristics that make them difficult to analyze and control. They are highly flexible, with components mathematically modeled by partial differential equations or very large systems of ordinary differential equations. They have many resonant frequencies, typically low and closely spaced. Natural damping may be low and/or improperly modeled. Coupled with stringent operational requirements of orientation, shape control, and vibration suppression, and the inability to perform adequate ground testing, these characteristics present an unconventional identification and control design problem to the systems theorist. Some of the research underway within Langley's Spacecraft Control Branch, Guidance and Control Division aimed at developing theory and algorithms to treat large space structures systems identification and control problems is described. The research areas to be considered are computer-aided design algorithms, and systems identification and control of distributed systems.

Armstrong, Ernest S.↗

Fully automatic guidance and control for rotorcraft nap-of-the-Earth flight following planned profiles. Volume 1: Real-time piloted simulation

Developing a single-pilot, all-weather nap-of-the-earth (NOE) capability requires fully automatic NOE (ANOE) navigation and flight control. Innovative guidance and control concepts are investigated in a four-fold research effort that: (1) organizes the on-board computer-based storage and real-time updating of NOE terrain profiles and obstacles in course-oriented coordinates indexed to the mission flight plan; (2) defines a class of automatic anticipative pursuit guidance algorithms and necessary data preview requirements to follow the vertical, lateral, and longitudinal guidance commands dictated by the updated flight profiles; (3) automates a decision-making process for unexpected obstacle avoidance; and (4) provides several rapid response maneuvers. Acquired knowledge from the sensed environment is correlated with the forehand knowledge of the recorded environment (terrain, cultural features, threats, and targets), which is then used to determine an appropriate evasive maneuver if a nonconformity of the sensed and recorded environments is observed. This four-fold research effort was evaluated in both fixed-based and moving-based real-time piloted simulations, thereby, providing a practical demonstration for evaluating pilot acceptance of the automated concepts, supervisory override, manual operation, and re-engagement of the automatic system. Volume one describes the major components of the guidance and control laws as well as the results of the piloted simulations. Volume two describes the complete mathematical model of the fully automatic guidance system for rotorcraft NOE flight following planned flight profiles.

Clement, Warren F.↗

Experimental validation of clock synchronization algorithms

The objective of this work is to validate mathematically derived clock synchronization theories and their associated algorithms through experiment. Two theories are considered, the Interactive Convergence Clock Synchronization Algorithm and the Midpoint Algorithm. Special clock circuitry was designed and built so that several operating conditions and failure modes (including malicious failures) could be tested. Both theories are shown to predict conservative upper bounds (i.e., measured values of clock skew were always less than the theory prediction). Insight gained during experimentation led to alternative derivations of the theories. These new theories accurately predict the behavior of the clock system. It is found that a 100 percent penalty is paid to tolerate worst-case failures. It is also shown that under optimal conditions (with minimum error and no failures) the clock skew can be as much as three clock ticks. Clock skew grows to six clock ticks when failures are present. Finally, it is concluded that one cannot rely solely on test procedures or theoretical analysis to predict worst-case conditions.

Palumbo, Daniel L.↗

Transfer of contrast sensitivity in linear visual networks

Contrast sensitivity is a useful measure of the ability of an observer to distinguish contrast signals from noise. Although usually applied to human observers, contrast sensitivity can also be defined operationally for individual visual neurons. In a model linear neuron consisting of a filter and noise source, this operational measure is a function of filter gain, noise power spectrum, signal duration, and a performance criterion. This definition allows one to relate the sensitivities of linear neurons at different levels in the visual pathway. Mathematical formulas describing these relationships are derived, and the general model is applied to the specific problem of relating the sensitivities of parvocellular LGN neurons and cortical simple cells in the primate.

Watson, Andrew B.↗

PSC algorithm description

An overview of the performance seeking control (PSC) algorithm and details of the important components of the algorithm are given. The onboard propulsion system models, the linear programming optimization, and engine control interface are described. The PSC algorithm receives input from various computers on the aircraft including the digital flight computer, digital engine control, and electronic inlet control. The PSC algorithm contains compact models of the propulsion system including the inlet, engine, and nozzle. The models compute propulsion system parameters, such as inlet drag and fan stall margin, which are not directly measurable in flight. The compact models also compute sensitivities of the propulsion system parameters to change in control variables. The engine model consists of a linear steady state variable model (SSVM) and a nonlinear model. The SSVM is updated with efficiency factors calculated in the engine model update logic, or Kalman filter. The efficiency factors are used to adjust the SSVM to match the actual engine. The propulsion system models are mathematically integrated to form an overall propulsion system model. The propulsion system model is then optimized using a linear programming optimization scheme. The goal of the optimization is determined from the selected PSC mode of operation. The resulting trims are used to compute a new operating point about which the optimization process is repeated. This process is continued until an overall (global) optimum is reached before applying the trims to the controllers.

Nobbs, Steven G.↗

Results of NASA's First Autonomous Formation Flying Experiment: Earth Observing-1 (EO-1)

NASA's first autonomous formation flying mission completed its primary goal of demonstrating an advanced technology called enhanced formation flying. To enable this technology, the Flight Dynamics Analysis Branch at the Goddard Space Flight Center implemented a universal 3-axis formation flying algorithm in an autonomous executive flight code onboard the New Millennium Program's (NMP) Earth Observing-1 (EO-1) spacecraft. This paper describes the mathematical background of the autonomous formation flying algorithm, the onboard flight design and the validation results of this unique system. Results from fully autonomous maneuver control are presented as comparisons between the onboard EO-1 operational autonomous control system called AutoCon, its ground-based predecessor used in operations, and the original standalone algorithm. Maneuvers discussed encompass reactionary, routine formation maintenance, and inclination control. Orbital data is also examined to verify that all formation flying requirements were met.

Folta, David↗

Results Of NASA's First Autonomous Formation Flying Experiment: Earth Observing-1 (EO-1)

NASA's first autonomous formation flying mission completed its primary goal of demonstrating an advanced technology called Enhanced Formation Flying. To enable this technology, a team at the Goddard Space Flight Center implemented a universal 3-axis formation flying algorithm in an autonomous executive flight code onboard the New Millennium Program's (NMP) Earth Observing-1 (EO-1) spacecraft. This paper describes the mathematical background of the autonomous formation flying algorithm, the onboard flight design and the validation results of this unique system. Results from fully autonomous maneuver control are presented as comparisons between the onboard EO-1 operational autonomous control system called AutoCon(trademark), its ground-based predecessor used in operations, and the original standalone algorithm. Maneuvers discussed encompass reactionary, routine formation maintenance, and inclination control. Orbital data is also examined to verify that all formation flying requirements were met.

Folta, David↗

The Beginner's Guide to Wind Tunnels with TunnelSim and TunnelSys

The Beginner's Guide to Wind Tunnels is a Web-based, on-line textbook that explains and demonstrates the history, physics, and mathematics involved with wind tunnels and wind tunnel testing. The Web site contains several interactive computer programs to demonstrate scientific principles. TunnelSim is an interactive, educational computer program that demonstrates basic wind tunnel design and operation. TunnelSim is a Java (Sun Microsystems Inc.) applet that solves the continuity and Bernoulli equations to determine the velocity and pressure throughout a tunnel design. TunnelSys is a group of Java applications that mimic wind tunnel testing techniques. Using TunnelSys, a team of students designs, tests, and post-processes the data for a virtual, low speed, and aircraft wing.

Benson, Thomas J.↗

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

Carpenter, Mark H.↗

Category B Plastic Pane Testing for JSC 66320 Rev A Requirements Verifiable Through Acceptance Testing

JSC 66320, Revision A, Optical Property Requirements for Glasses, Ceramics, and Plastics in Spacecraft Window Systems, lists several quantitative requirements that spacecraft windowpanes must meet. Recently, we were asked to establish a capability at the Kennedy Space Center to perform these measurements on category B plastic panes, i.e., plastic panes that could be used on a spacecraft for long-focal-length photography and piloting. Two of the criteria, normal wavefront and 30-degree wavefront attributes, can be measured with existing equipment and processes (see NASA TM NESC-RP-14-00951, April 2016) and are not discussed in this document. However, the other six criteria-haze, wedge angle, birefringence, reflectance, transmittance, and color balance-required substantial development and are the subject of this document. In this document, we do not discuss the rationale behind the requirements, but we did engage in discussions with the authors of JSC 66320 in order to better understand the requirements and the verifications being imposed on windows and their testing. Accordingly, this document presents our best understanding of the requested requirements and verifications. We also present our methodology for performing each of the six measurements, along with applicable mathematics and a description, with photos, of the hardware used. In addition, we supply the results of a test on a low-quality in-house plastic window as an example of the system operation. Only requirements that can be met by acceptance test and analysis, as opposed to optical inspection, are considered in this document.

spaceflight windows↗

Calculation of two-dimensional inlet flow fields in a supersonic free stream by an implicit marching code with nonorthogonal mesh generation: User's manual

An implicit, shock-capturing finite-difference code which is used to calculate two-dimensional inlet flow fields in a supersonic free stream is explained. The Euler equations are subjected to general nonorthogonal transformation and a body-fitted coordinate system is employed. The mathematical formulation of the problem is given along with the numerical algorithm. Initial and boundary conditions, numerical stability, program limitations, and accuracy is discussed. An overall program logic as well as instructions for program use and operation are also furnished.

Biringen, S. H.↗