Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “computational mathematics”

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 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Fitting Nonlinear Curves by use of Optimization Techniques

MULTIVAR is a FORTRAN 77 computer program that fits one of the members of a set of six multivariable mathematical models (five of which are nonlinear) to a multivariable set of data. The inputs to MULTIVAR include the data for the independent and dependent variables plus the user s choice of one of the models, one of the three optimization engines, and convergence criteria. By use of the chosen optimization engine, MULTIVAR finds values for the parameters of the chosen model so as to minimize the sum of squares of the residuals. One of the optimization engines implements a routine, developed in 1982, that utilizes the Broydon-Fletcher-Goldfarb-Shanno (BFGS) variable-metric method for unconstrained minimization in conjunction with a one-dimensional search technique that finds the minimum of an unconstrained function by polynomial interpolation and extrapolation without first finding bounds on the solution. The second optimization engine is a faster and more robust commercially available code, denoted Design Optimization Tool, that also uses the BFGS method. The third optimization engine is a robust and relatively fast routine that implements the Levenberg-Marquardt algorithm.

Hill, Scott A.↗
NASA NTRS2011

Finding Every Root of a Broad Class of Real, Continuous Functions in a Given Interval

One of the most pervasive needs within the Deep Space Network (DSN) Metric Prediction Generator (MPG) view period event generation is that of finding solutions to given occurrence conditions. While the general form of an equation expresses equivalence between its left-hand and right-hand expressions, the traditional treatment of the subject subtracts the two sides, leaving an expression of the form Integral of(x) = 0. Values of the independent variable x satisfying this condition are roots, or solutions. Generally speaking, there may be no solutions, a unique solution, multiple solutions, or a continuum of solutions to a given equation. In particular, all view period events are modeled as zero crossings of various metrics; for example, the time at which the elevation of a spacecraft reaches its maximum value, as viewed from a Deep Space Station (DSS), is found by locating that point at which the derivative of the elevation function becomes zero. Moreover, each event type may have several occurrences within a given time interval of interest. For example, a spacecraft in a low Moon orbit will experience several possible occultations per day, each of which must be located in time. The MPG is charged with finding all specified event occurrences that take place within a given time interval (or pass ), without any special clues from operators as to when they may occur, for the entire spectrum of missions undertaken by the DSN. For each event type, the event metric function is a known form that can be computed for any instant within the interval. A method has been created for a mathematical root finder to be capable of finding all roots of an arbitrary continuous function, within a given interval, to be subject to very lenient, parameterized assumptions. One assumption is that adjacent roots are separated at least by a given amount, xGuard. Any point whose function value is less than ef in magnitude is considered to be a root, and the function values at distances xGuard away from a root are larger than ef, unless there is another root located in this vicinity. A root is considered found if, during iteration, two root candidates differ by less than a pre-specified ex, and the optimum cubic polynomial matching the function at the end and at two interval points (that is within a relative error fraction L at its midpoint) is reliable in indicating whether the function has extrema within the interval. The robustness of this method depends solely on choosing these four parameters that control the search. The roots of discontinuous functions were also found, but at degraded performance.

Tausworthe, Robert C.↗
NASA NTRS2011

Multi-Parameter Aerosol Scattering Sensor

This work relates to the development of sensors that measure specific aerosol properties. These properties are in the form of integrated moment distributions, i.e., total surface area, total mass, etc., or mathematical combinations of these moment distributions. Specifically, the innovation involves two fundamental features: a computational tool to design and optimize such sensors and the embodiment of these sensors in actual practice. The measurement of aerosol properties is a problem of general interest. Applications include, but are not limited to, environmental monitoring, assessment of human respiratory health, fire detection, emission characterization and control, and pollutant monitoring. The objectives for sensor development include increased accuracy and/or dynamic range, the inclusion in a single sensor of the ability to measure multiple aerosol properties, and developing an overall physical package that is rugged, compact, and low in power consumption, so as to enable deployment in harsh or confined field applications, and as distributed sensor networks. Existing instruments for this purpose include scattering photometers, direct-reading mass instruments, Beta absorption devices, differential mobility analyzers, and gravitational samplers. The family of sensors reported here is predicated on the interaction of light and matter; specifically, the scattering of light from distributions of aerosol particles. The particular arrangement of the sensor, e.g. the wavelength(s) of incident radiation, the number and location of optical detectors, etc., can be derived so as to optimize the sensor response to aerosol properties of practical interest. A key feature of the design is the potential embodiment as an extremely compact, integrated microsensor package. This is of fundamental importance, as it enables numerous previously inaccessible applications. The embodiment of these sensors is inherently low maintenance and high reliability by design. The novel and unique features include the underlying computational underpinning that allows the optimization for specific applications, and the physical embodiment that affords the construction of a compact, durable, and reliable integrated package. The advantage appears in the form of increased accuracy relative to existing instruments, and the applications enabled by the physical attributes of the resulting configuration

Greenberg, Paul S.↗
NASA NTRS2014

Training Knowledge Bots for Physics-Based Simulations Using Artificial Neural Networks

Millions of complex physics-based simulations are required for design of an aerospace vehicle. These simulations are usually performed by highly trained and skilled analysts, who execute, monitor, and steer each simulation. Analysts rely heavily on their broad experience that may have taken 20-30 years to accumulate. In addition, the simulation software is complex in nature, requiring significant computational resources. Simulations of system of systems become even more complex and are beyond human capacity to effectively learn their behavior. IBM has developed machines that can learn and compete successfully with a chess grandmaster and most successful jeopardy contestants. These machines are capable of learning some complex problems much faster than humans can learn. In this paper, we propose using artificial neural network to train knowledge bots to identify the idiosyncrasies of simulation software and recognize patterns that can lead to successful simulations. We examine the use of knowledge bots for applications of computational fluid dynamics (CFD), trajectory analysis, commercial finite-element analysis software, and slosh propellant dynamics. We will show that machine learning algorithms can be used to learn the idiosyncrasies of computational simulations and identify regions of instability without including any additional information about their mathematical form or applied discretization approaches.

Samareh, Jamshid A.↗
NASA NTRS1982

Sensitivity analysis of helicopter IMC decelerating steep approach and landing performance to navigation system parameters

Results of a study to investigate, by means of a computer simulation, the performance sensitivity of helicopter IMC DSAL operations as a function of navigation system parameters are presented. A mathematical model representing generically a navigation system is formulated. The scenario simulated consists of a straight in helicopter approach to landing along a 6 deg glideslope. The deceleration magnitude chosen is 03g. The navigation model parameters are varied and the statistics of the total system errors (TSE) computed. These statistics are used to determine the critical navigation system parameters that affect the performance of the closed-loop navigation, guidance and control system of a UH-1H helicopter.

Karmali, M. S.↗
NASA NTRS1989

Computer algebra and operators

The symbolic computation of operator expansions is discussed. Some of the capabilities that prove useful when performing computer algebra computations involving operators are considered. These capabilities may be broadly divided into three areas: the algebraic manipulation of expressions from the algebra generated by operators; the algebraic manipulation of the actions of the operators upon other mathematical objects; and the development of appropriate normal forms and simplification algorithms for operators and their actions. Brief descriptions are given of the computer algebra computations that arise when working with various operators and their actions.

Fateman, Richard↗
NASA NTRS2006

Using Satellite Data in Weather Forecasting: I

The GOES Product Generation System (GPGS) is a set of computer codes and scripts that enable the assimilation of real-time Geostationary Operational Environmental Satellite (GOES) data into regional-weather-forecasting mathematical models. The GPGS can be used to derive such geophysical parameters as land surface temperature, the amount of precipitable water, the degree of cloud cover, the surface albedo, and the amount of insolation from satellite measurements of radiant energy emitted by the Earth and its atmosphere. GPGS incorporates a priori information (initial guesses of thermodynamic parameters of the atmosphere) and radiometric measurements from the geostationary operational environmental satellites along with mathematical models of physical principles that govern the transfer of energy in the atmosphere. GPGS solves the radiative-transfer equation and provides the resulting data products in formats suitable for use by weather-forecasting computer programs. The data-assimilation capability afforded by GPGS offers the potential to improve local weather forecasts ranging from 3 hours to 2 days - especially with respect to temperature, humidity, cloud cover, and the probability of precipitation. The improvements afforded by GPGS could be of interest to news media, utility companies, and other organizations that utilize regional weather forecasts.

Jedlovec, Gary J.↗
NASA NTRS2010

Simulation of Propellant Loading System Senior Design Implement in Computer Algorithm

Propellant loading from the Storage Tank to the External Tank is one of the very important and time consuming pre-launch ground operations for the launch vehicle. The propellant loading system is a complex integrated system involving many physical components such as the storage tank filled with cryogenic fluid at a very low temperature, the long pipe line connecting the storage tank with the external tank, the external tank along with the flare stack, and vent systems for releasing the excess fuel. Some of the very important parameters useful for design purpose are the prediction of pre-chill time, loading time, amount of fuel lost, the maximum pressure rise etc. The physics involved for mathematical modeling is quite complex due to the fact the process is unsteady, there is phase change as some of the fuel changes from liquid to gas state, then conjugate heat transfer in the pipe walls as well as between solid-to-fluid region. The simulation is very tedious and time consuming too. So overall, this is a complex system and the objective of the work is student's involvement and work in the parametric study and optimization of numerical modeling towards the design of such system. The students have to first become familiar and understand the physical process, the related mathematics and the numerical algorithm. The work involves exploring (i) improved algorithm to make the transient simulation computationally effective (reduced CPU time) and (ii) Parametric study to evaluate design parameters by changing the operational conditions

Bandyopadhyay, Alak↗
NASA NTRS1987

Turbomachinery

The discipline research in turbomachinery, which is directed toward building the tools needed to understand such a complex flow phenomenon, is based on the fact that flow in turbomachinery is fundamentally unsteady or time dependent. Success in building a reliable inventory of analytic and experimental tools will depend on how the time and time-averages are treated, as well as on who the space and space-averages are treated. The raw tools at disposal (both experimentally and computational) are truly powerful and their numbers are growing at a staggering pace. As a result of this power, a case can be made that a situation exists where information is outstripping understanding. The challenge is to develop a set of computational and experimental tools which genuinely increase understanding of the fluid flow and heat transfer in a turbomachine. Viewgraphs outline a philosophy based on working on a stairstep hierarchy of mathematical and experimental complexity to build a system of tools, which enable one to aggressively design the turbomachinery of the next century. Examples of the types of computational and experimental tools under current development at Lewis, with progress to date, are examined. The examples include work in both the time-resolved and time-averaged domains. Finally, an attempt is made to identify the proper place for Lewis in this continuum of research.

Simoneau, Robert J.↗
NASA NTRS2010

Computer-Controlled Cylindrical Polishing Process for Large X-Ray Mirror Mandrels

We are developing high-energy grazing incidence shell optics for hard-x-ray telescopes. The resolution of a mirror shells depends on the quality of cylindrical mandrel from which they are being replicated. Mid-spatial-frequency axial figure error is a dominant contributor in the error budget of the mandrel. This paper presents our efforts to develop a deterministic cylindrical polishing process in order to keep the mid-spatial-frequency axial figure errors to a minimum. Simulation software is developed to model the residual surface figure errors of a mandrel due to the polishing process parameters and the tools used, as well as to compute the optical performance of the optics. The study carried out using the developed software was focused on establishing a relationship between the polishing process parameters and the mid-spatial-frequency error generation. The process parameters modeled are the speeds of the lap and the mandrel, the tool s influence function, the contour path (dwell) of the tools, their shape and the distribution of the tools on the polishing lap. Using the inputs from the mathematical model, a mandrel having conical approximated Wolter-1 geometry, has been polished on a newly developed computer-controlled cylindrical polishing machine. The preliminary results of a series of polishing experiments demonstrate a qualitative agreement with the developed model. We report our first experimental results and discuss plans for further improvements in the polishing process. The ability to simulate the polishing process is critical to optimize the polishing process, improve the mandrel quality and significantly reduce the cost of mandrel production

Khan, Gufran S.↗
NASA NTRS1985

On the numerical computation of nonlinear force-free magnetic fields

An algorithm has been developed to extrapolate nonlinear force-free magnetic fields from a source surface, given the proper boundary conditions. The results of this work; describing the mathematical formalism that was developed, the numerical techniques employed, and the stability criteria developed for these numerical schemes are presented. An analytical solution is used for a test case; the results show that the computational accuracy for the case of a nonlinear force-free magnetic field was on the order of a few percent ( 5%).

Wu, S. T.↗
NASA NTRSDate not supplied

Computationally Guided Development of Components for High Energy Density Solid-State Lithium-Sulfur Batteries

All electric vertical take-off and landing vehicles (eVTOL) for urban air mobility (UAM) concepts face numerous challenging technical barriers before their introduction into the consumer marketplace. The most challenging of these technical barriers to overcome is developing an energy storage system capable of meeting the rigorous aerospace safety and performance criteria1. The performance metrics for eVTOL craft, such as specific energy, specific power, and safety, exceed those of electric automobiles by a factor of two to four. Current state-of-the-art (SOA) lithium-ion batteries are incapable of meeting the key performance criteria of energy and safety for eVTOL. Therefore, next generation advanced chemistries and designs must be developed to meet required performance metrics for electric aviation2. Beyond lithium-ion chemistries, such as lithium-sulfur, show promise in their high energy, while limitations exist in their power and cyclability due to low electrical conductivity and high intermediate solubility in organic liquid electrolytes. Several strategies to overcome the low electrical conductivity involve the use of selenium as a dopant in the active sulfur material, along with the incorporation of 2-dimensional electron-conducting holey-graphene to improve the composite cathodes electronic conductivity. Furthermore, combining this chemistry with a solid-electrolyte avoids the components’ dissolution issues3. However, the development of composite solid-state cathodes is non-trivial as several components must be intimately mixed so that the active component has sufficient access to both electrons and lithium ions to undergo full electrochemical conversion. Mathematical modeling of battery components can assist experimental design through a robust and rigorous combination of computational modeling techniques covering multiple length scales. The objective is to leverage modern computational materials methods combined with battery multiphysics tools to develop radically advanced compatible cathode and electrolyte materials, build and test solid state lithium-sulfur cells and packs. A NASA-based cross-organizational team of high-powered experts combined integrated computational predictive modeling, fundamental chemistry analysis, advanced material science, and battery cell development to tackle this very challenging, multidisciplinary problem. This presentation will show a multiscale computational modeling approach that has produced a novel particle dynamics method called Solid Electrolyte Sphere Approximation Model (SESAM). SESAM modeling targets the 1-10 µm scale structures and provides electromechanical and grain interactions for predictive design guidelines for the manufacturing of solid-state components. Parameters such as particle size and volume fraction of the constituent materials were modeled and experimentally fabricated to optimize electrochemical performance through improved microstructure design. Experimental feedback was provided through ionic and electronic conductivity assessment and structural analysis of developed materials and cell components.

battery↗
NASA NTRS1972

Numerical method and FORTRAN program for the solution of an axisymmetric electrostatic collector design problem

The numerical calculation is described of the steady-state flow of electrons in an axisymmetric, spherical, electrostatic collector for a range of boundary conditions. The trajectory equations of motion are solved alternately with Poisson's equation for the potential field until convergence is achieved. A direct (noniterative) numerical technique is used to obtain the solution to Poisson's equation. Space charge effects are included for initial current densities as large as 100 A/sq cm. Ways of dealing successfully with the difficulties associated with these high densities are discussed. A description of the mathematical model, a discussion of numerical techniques, results from two typical runs, and the FORTRAN computer program are included.

Reese, O. W.↗
NASA NTRS1973

Electrochemical carbon dioxide concentrator: Math model

A steady state computer simulation model of an Electrochemical Depolarized Carbon Dioxide Concentrator (EDC) has been developed. The mathematical model combines EDC heat and mass balance equations with empirical correlations derived from experimental data to describe EDC performance as a function of the operating parameters involved. The model is capable of accurately predicting performance over EDC operating ranges. Model simulation results agree with the experimental data obtained over the prediction range.

Marshall, R. D.↗
NASA NTRS1974

Houston Operations Predictor/Estimator (HOPE) programming manual, volume 1

The programming techniques used to implement the equations and mathematical techniques of the Houston Operations Predictor/Estimator (HOPE) orbit determination program on the UNIVAC 1108 computer are described. Detailed descriptions are given of the program structure, the internal program structure, the internal program tables and program COMMON, modification and maintainence techniques, and individual subroutine documentation.

Daly, J. K.↗
NASA NTRS1976

An engineering treatise on the CARE II dual mode and coverage models

A mathematical model used to calculate the reliability of any dual-mode, spare-switching computer system was described, and some illustrative examples were presented. The possibility of extending the resultant computer program further was also examined, enabling it, in particular, to accommodate computer configurations involving more than two modes of operation.

Source record↗
NASA NTRS1975

Cardiovascular imaging and image processing: Theory and practice - 1975; Proceedings of the Conference, Stanford University, Stanford, Calif., July 10-12, 1975

The present collection of papers outlines advances in ultrasonography, scintigraphy, and commercialization of medical technology as applied to cardiovascular diagnosis in research and clinical practice. Particular attention is given to instrumentation, image processing and display. As necessary concomitants to mathematical analysis, recently improved magnetic recording methods using tape or disks and high-speed computers of large capacity are coming into use. Major topics include Doppler ultrasonic techniques, high-speed cineradiography, three-dimensional imaging of the myocardium with isotopes, sector-scanning echocardiography, and commercialization of the echocardioscope. Individual items are announced in this issue.

Harrison, D. C.↗