Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical optimization”

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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
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 NTRS1967

CINDA - Chrysler Improved Numerical Differencing Analyzer computer program

Dimensionless multioption systems compiler computer program constructs and analyzes a mathematical model of any arbitrary one, two, or three dimensional lumped parameter representation of a physical system. It automatically optimizes the utilization of computer core space and is more general and versatile than BETA.

Gaski, J. D.↗
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 NTRS2020

Designing Shading Schemes for Microphone Phased Arrays

A technique is proposed for designing sensor weightings, or array shading functions, for microphone phased arrays. The presented method attempts to maintain mathematical simplicity while maximizing array gain for a desired mainlobe beamwidth. It does so using the two-parameter optimization of a family of functions. The shading design process is described and applied to an array used recently in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel. Several variants of the method are compared to an existing shading scheme for the array, along with a more general optimization formulation. Results are presented for both an idealized point source and experimental data from the wind tunnel test. The shading schemes are shown to improve the behavior of array operations, but have a stronger impact on visual interpretation of maps than on source level calculations. The study results show that the two-parameter optimization scheme provides favorable characteristics while maintaining implementation simplicity.

Christopher J Bahr↗
NASA NTRS1992

Domain decomposition: A bridge between nature and parallel computers

Domain decomposition is an intuitive organizing principle for a partial differential equation (PDE) computation, both physically and architecturally. However, its significance extends beyond the readily apparent issues of geometry and discretization, on one hand, and of modular software and distributed hardware, on the other. Engineering and computer science aspects are bridged by an old but recently enriched mathematical theory that offers the subject not only unity, but also tools for analysis and generalization. Domain decomposition induces function-space and operator decompositions with valuable properties. Function-space bases and operator splittings that are not derived from domain decompositions generally lack one or more of these properties. The evolution of domain decomposition methods for elliptically dominated problems has linked two major algorithmic developments of the last 15 years: multilevel and Krylov methods. Domain decomposition methods may be considered descendants of both classes with an inheritance from each: they are nearly optimal and at the same time efficiently parallelizable. Many computationally driven application areas are ripe for these developments. A progression is made from a mathematically informal motivation for domain decomposition methods to a specific focus on fluid dynamics applications. To be introductory rather than comprehensive, simple examples are provided while convergence proofs and algorithmic details are left to the original references; however, an attempt is made to convey their most salient features, especially where this leads to algorithmic insight.

Keyes, David E.↗
NASA NTRS2015

Extension of an Object-Oriented Optimization Tool: User's Reference Manual

The National Aeronautics and Space Administration Armstrong Flight Research Center has developed a cost-effective and flexible object-oriented optimization (O (sup 3)) tool that leverages existing tools and practices and allows easy integration and adoption of new state-of-the-art software. This object-oriented framework can integrate the analysis codes for multiple disciplines, as opposed to relying on one code to perform analysis for all disciplines. Optimization can thus take place within each discipline module, or in a loop between the O (sup 3) tool and the discipline modules, or both. Six different sample mathematical problems are presented to demonstrate the performance of the O (sup 3) tool. Instructions for preparing input data for the O (sup 3) tool are detailed in this user's manual.

Multidisciplinary design optimization↗
NASA NTRS1973

Shuttle cryogenic supply system. Optimization study. Volume 5 B-1: Programmers manual for math models

A computer program for rapid parametric evaluation of various types of cryogenics spacecraft systems is presented. The mathematical techniques of the program provide the capability for in-depth analysis combined with rapid problem solution for the production of a large quantity of soundly based trade-study data. The program requires a large data bank capable of providing characteristics performance data for a wide variety of component assemblies used in cryogenic systems. The program data requirements are divided into: (1) the semipermanent data tables and source data for performance characteristics and (2) the variable input data which contains input parameters which may be perturbated for parametric system studies.

Source record↗
NASA NTRSDate not supplied

Comparison and Application of Battery Modeling Methods for Conceptual Electric Aircraft

Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.

power↗
NASA NTRS1976

First order impulsive solutions

A mathematically rigorous derivation is given of first order corrections to multi-impulse approximations to the solutions to space flight optimization problems with bang-bang control. The rocket was subjected to an inverse square gravitational force and to a thrust force with constant magnitude. The mass decreased linearly with time. An optimal impulsive solution was obtained for a problem with given initial and final conditions. The method was then used to obtain first-order corrections to the initial values of the costate variables. Indications are given on how the theory may be extended to higher order corrections. The theory was applied to intercept and rendezvous problems.

Andrus, J. F.↗
NASA NTRS1987

Dynamic sensing of 6-axis external force and moment applied to a robot end

A dynamic force sensing method is proposed for a robot manipulator. A 6-axis wrist force sensor which is commonly used for robot force sensing does not take the direct measurement of the force and moment applied to an end effector externally from the environment of the manipulator, but takes the resultant of the gravity, the inertial force and moment on the end effector, and the external force and moment. The separation of gravitational and inertial force and moment from the measurement of the force sensor is crucial to achieving dynamically accurate force sensing and fast manipulator motion under force feedback control. A mathematical model is derived for the force sensing process and the separation of the force and moment as a nonlinear optimal state estimation problem formulated. Then an approximate solution is given using extended Kalman filtering techniques.

Yokota, Masaru Uchiyama↗
NASA NTRS1991

Planning and executing motions for multibody systems in free-fall

The purpose of this research is to develop an end-to-end system that can be applied to a multibody system in free-fall to analyze its possible motions, save those motions in a database, and design a controller that can execute those motions. A goal is for the process to be highly automated and involve little human intervention. Ideally, the output of the system would be data and algorithms that could be put in ROM to control the multibody system in free-fall. The research applies to more than just robots in space. It applies to any multibody system in free-fall. Mathematical techniques from nonlinear control theory were used to study the nature of the system dynamics and its possible motions. Optimization techniques were applied to plan motions. Image compression techniques were proposed to compress the precomputed motion data for storage. A linearized controller was derived to control the system while it executes preplanned trajectories.

Cameron, Jonathan M.↗
NASA NTRS1995

Apparent Thermal Conductivity Of Multilayer Insulation

Mathematical model of apparent or effective thermal conductivity between two successive layers of multilayer thermal insulation (MLI) offers potential for optimizing performance of insulation. One gains understanding of how each physical mechanism contributes to overall flow of heat through MLI blanket. Model helps analyze engineering tradeoffs among such parameters as number of layers, thicknesses of gaps between layers, types of spacers placed in gaps, weight, overall thickness, and effects of foregoing on apparent thermal conductivity through blanket.

Mcintosh, Glen E.↗
NASA NTRS2000

Design and Analysis of Precise Pointing Systems

The mathematical models of Glovebox Integrated Microgravity Isolation Technology (g- LIMIT) dynamics/control system, which include six degrees of freedom (DOF) equations of motion, mathematical models of position sensors, accelerometers and actuators, and acceleration and position controller, were developed using MATLAB and TREETOPS simulations. Optimal control parameters of G-LIMIT control system were determined through sensitivity studies and its performance were evaluated with the TREETOPS model of G-LIMIT dynamics and control system. The functional operation and performance of the Tektronix DTM920 digital thermometer were studied and the inputs to the crew procedures and training of the DTM920 were documented.

Kim, Young K.↗
NASA NTRS1999

Data Structure and Parallel Decomposition Considerations on a Fibonacci Grid

The Fibonacci grid, proposed by Swinbank and Purser (see companion abstract), provides attractive properties for global numerical atmospheric prediction by offering an optimally homogeneous, geometrically regular, and approximately isotropic discretization, with only the polar regions requiring special numerical treatment. It is a mathematical idealization, applied to the sphere, of the multi-spiral patterns often found in botanical structures, such as in pine cones and sunflower heads. Computationally, it is natural to organize the domain, into zones, in each of which the same pair, or triple, of "Fibonacci spirals" dominate. But the further subdivision of such zones into "tiles" of a shape and size suitable for distribution to the processors of a massively parallel computer requires very careful consideration if the subsequent spatial computations along the respective spirals, especially those computations (such as compact differencing schemes) that involve recursion, can be implemented in an efficient "load-balanced "manner without requiring excessive amounts of inter-processor communications. In this paper we show how certain "number theoretic" properties of the Fibonacci sequence (whose numbers prescribe the multiplicity of successive spirals) may be exploited in the decomposition of grid zones into tidy arrangements of triangular grid tiles, each tile possessing one side approximately parallel to the constant-latitude zone boundary. We also describe how the spatially recursive processes may be decomposed across such a tiling, and the directionality of the recursions reversed on alternate grid lines, to ensure a very high degree of load balancing throughout the execution of the computations required for one time step of a global model.

Michalakes, John↗
NASA NTRS2000

Optimization of Microelectronic Devices for Sensor Applications

The NASA/JPL goal to reduce payload in future space missions while increasing mission capability demands miniaturization of active and passive sensors, analytical instruments and communication systems among others. Currently, typical system requirements include the detection of particular spectral lines, associated data processing, and communication of the acquired data to other systems. Advances in lithography and deposition methods result in more advanced devices for space application, while the sub-micron resolution currently available opens a vast design space. Though an experimental exploration of this widening design space-searching for optimized performance by repeated fabrication efforts-is unfeasible, it does motivate the development of reliable software design tools. These tools necessitate models based on fundamental physics and mathematics of the device to accurately model effects such as diffraction and scattering in opto-electronic devices, or bandstructure and scattering in heterostructure devices. The software tools must have convenient turn-around times and interfaces that allow effective usage. The first issue is addressed by the application of high-performance computers and the second by the development of graphical user interfaces driven by properly developed data structures. These tools can then be integrated into an optimization environment, and with the available memory capacity and computational speed of high performance parallel platforms, simulation of optimized components can proceed. In this paper, specific applications of the electromagnetic modeling of infrared filtering, as well as heterostructure device design will be presented using genetic algorithm global optimization methods.

Cwik, Tom↗
NASA NTRS2014

Supersonic Wing Optimization Using SpaRibs

This research investigates the advantages of using curvilinear spars and ribs, termed SpaRibs, to design a supersonic aircraft wing-box in comparison to the use of classic design concepts that employ straight spars and ribs. The objective is to achieve a more efficient load-bearing mechanism and to passively control the deformation of the structure under the flight loads. Moreover, the use of SpaRibs broadens the design space and allows for natural frequencies and natural mode shape tailoring. The SpaRibs concept is implemented in a new optimization MATLAB-based framework referred to as EBF3SSWingOpt. This optimization scheme performs both the sizing and the shaping of the internal structural elements, connecting the optimizer with the analysis software. The shape of the SpaRibs is parametrically defined using the so called Linked Shape method. Each set of SpaRibs is placed in a one by one square domain of the natural space. The set of curves is subsequently transformed in the physical space for creating the wing structure geometry layout. The shape of each curve of each set is unique; however, mathematical relations link the curvature in an effort to reduce the number of design variables. The internal structure of a High Speed Commercial Transport aircraft concept developed by Boeing is optimized subjected to stress, subsonic flutter and supersonic flutter constraints. The results show that the use of the SpaRibs allows for the reduction of the aircraft's primary structure weight without violating the constraints. A weight reduction of about 15 percent is observed.

Locatelli, David↗
NASA NTRS1975

The human controller in car following

The man machine interface between the human driver and his automobile during car following tasks was examined. A direct connection between models of the human operator and the theory of optimal control was established for car following situations involving both linear and nonlinear car dynamics. Results obtained from several types of mathematical models are discussed. Conventional parameter identification techniques were used to obtain the parameters of these models by comparing their performance to data obtained by aerial photogrammetry. The results indicate that there are two general classes of model structures: models assumed to have preview information and models without preview.

Burnham, G. O.↗