Random differential equations in control theory
Control processes and optimization problems solutions by stochastic differential equations, discussing dynamic models and programming, linear filtering and optimal feedback
Wonham, W. M.↗
SEARCH · Search NASA
Results for “Differentiable programming”
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.
Study of non-linear optimization techniques
Nonlinear optimization techniques in dynamic programming and solution of ordinary nonlinear differential equations by Runge-Kutta method
Shanks, E. B.↗
Experimental physics characteristics of a heavy-metal-reflected fast-spectrum critical assembly
A zero-power critical assembly was designed, constructed, and operated for the purpose of conducting a series of benchmark experiments dealing with the physics characteristics of a UN-fueled, Li-7 cooled, Mo-reflected, drum-controlled compact fast reactor for use with a space-power electric conversion system. The experimental program consisted basically of measuring the differential neutron spectra and the changes in critical mass that accompanied the stepwise addition of (Li-7)3N, Hf, Ta, and W to a basic core fueled with U metal in a pin-type Ta honeycomb structure. In addition, experimental results were obtained on power distributions, control characteristics, neutron lifetime, and reactivity worths of numerous absorber, structural, and scattering materials.
Heneveld, W. H.↗
The specification of distributed boundary conditions in numerical simulation of the ionosphere
The approach described makes it possible to use boundary conditions which do not have to be associated with any particular point of the solution interval. The approach was applied in a program which solves simultaneously the coupled differential equations describing the concentrations of the O(+) ions, their temperature, the electron temperature and the concentrations of O2(+), NO(+) and N2(+) ions. Several versions of the proposed scheme are described for various kinds of boundary conditions. Attention is given to a given columnar ionic content, a given incoming or outgoing flux, or a given height of the peak concentration.
Waldman, H.↗
In situ correlative measurements for the ultraviolet differential absorption lidar and the high spectral resolution lidar air quality remote sensors: 1980 PEPE/NEROS program
In situ correlative measurements were obtained with a NASA aircraft in support of two NASA airborne remote sensors participating in the Environmental Protection Agency's 1980persistent elevated pollution episode (PEPE) and Northeast regional oxidant study (NEROS) field program in order to provide data for evaluating the capability of two remote sensors for measuring mixing layer height, and ozone and aerosol concentrations in the troposphere during the 1980 PEPE/NEROS program. The in situ aircraft was instrumented to measure temperature, dewpoint temperature, ozone concentrations, and light scattering coefficient. In situ measurements for ten correlative missions are given and discussed. Each data set is presented in graphical and tabular format aircraft flight plans are included.
Gregory, G. L.↗
Plasma and magnetospheric research
Methods employed in the analysis of plasmas and the magnetosphere are examined. Computer programs which generate distribution functions are used in the analysis of charging phenomena and non maxwell plasmas in terms of density and average energy. An analytical model for spin curve analysis is presented. A program for the analysis of the differential ion flux probe on the space shuttle mission is complete. Satellite data analysis for ion heating, plasma flows in the polar cap, polar wind flow, and density and temperature profiles for several plasmasphere transits are included.
Comfort, R. H.↗
PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 1: Theory document (version 1.1)
Panel aerodynamics (PAN AIR) is a system of computer programs designed to analyze subsonic and supersonic inviscid flows about arbitrary configurations. A panel method is a program which solves a linear partial differential equation by approximating the configuration surface by a set of panels. An overview of the theory of potential flow in general and PAN AIR in particular is given along with detailed mathematical formulations. Fluid dynamics, the Navier-Stokes equation, and the theory of panel methods were also discussed.
Magnus, A. E.↗
Ground resonance analysis using a substructure modeling approach
A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented.
Chen, S. Y.↗
Ground resonance analysis using a substructure modeling approach
A convenient and versatile procedure for modeling and analyzing ground resonance phenomena is described and illustrated. A computer program is used which dynamically couples differential equations with nonlinear and time dependent coefficients. Each set of differential equations may represent a component such as a rotor, fuselage, landing gear, or a failed damper. Arbitrary combinations of such components may be formulated into a model of a system. When the coupled equations are formed, a procedure is executed which uses a Floquet analysis to determine the stability of the system. Illustrations of the use of the procedures along with the numerical examples are presented.
Chen, S.-Y.↗
Automated Surface Profilometer
Computer-controlled system saves time and labor. Electromechanical scanning system automatically measures deviation of sheets and plates from flatness. Quickly measures surface profile and detects bumps, bulges, and indentations as small as 0.001 in. in height or depth. X-y table moves specimen to programmed locations under digital linear variable differential transformer (LVDT) while computer records surface-height readings of LVDT. Resulting graphical display shows surface contour.
Chern, E. James↗
Prediction of pressure fluctuation in sounding rockets and manifolded recovery systems
The determination of altitude by means of barometric sensors in sounding rocket applications is discussed. A method for predicting the performance of such sensing systems is needed. A method is developed for predicting the pressure-time response of a volume subjected to subsonic air flow through from one to four passages. The pressure calculation is based on one-dimensional gas flow with friction. A computed program has been developed which solves the differential equations using a self-starting predictor-corrector integration technique. The input data required are the pressure sensing system dimensions, pressure forcing function(s) at the inlet port(s), and a trajectory over the time of analysis (altitude-velocity-time), if the forcing function is trajectory dependent. The program then computes the pressure-temperature history of the gas in the manifold over the time interval specified.
Laudadio, J. F.↗
The 2nd phase of the LEANDRE program: Water-vapor DIAL measurement
As a follow-on of the backscattered lidar, a differential absorption lidar (LEANDRE 2) is now being developed as part of the LEANDRE program for airborne meteorological studies. The primary measurement objective of LEANDRE 2 is water vapor. Pressure and temperature measurements are aimed at a second stage. The goals are to obtain a horizontal resolution of a few hundred meters for a vertical resolution of less than a hundred meters, with an absolute accuracy of 10 percent for humidity measurement. As compatibility is an important feature between the 2 first phases of LEANDRE, most of the LEANDRE 1 sub-system will be used and adapted for LEANDRE 2. For example, detection electronics, central computer, detectors and telescope will be the same. However, important modifications have to be done on the laser source, and spectral control has to be added. Most of the work is thus devoted to those developments, and the status is presented here.
Quaglia, P.↗
Root locus diagrams by digital computer
Adaptation of root locus method to programming on IBM 7074 digital computer
DIFFERENTIAL EQUATION↗
Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage
A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.
Miller, R. D.↗
Application of Aerosol Hygroscopicity Measured at the Atmospheric Radiation Measurement Program's Southern Great Plains Site to Examine Composition and Evolution
A Differential Mobility Analyzer/Tandem Differential Mobility Analyzer (DMA/TDMA) was used to measure submicron aerosol size distributions, hygroscopicity, and occasionally volatility during the May 2003 Aerosol Intensive Operational Period (IOP) at the Central Facility of the Atmospheric Radiation Measurement Program's Southern Great Plains (ARM SGP) site. Hygroscopic growth factor distributions for particles at eight dry diameters ranging from 0.012 micrometers to 0.600 micrometers were measured throughout the study. For a subset of particle sizes, more detailed measurements were occasionally made in which the relative humidity or temperature to which the aerosol was exposed was varied over a wide range. These measurements, in conjunction with backtrajectory clustering, were used to infer aerosol composition and to gain insight into the processes responsible for evolution. The hygroscopic growth of both the smallest and largest particles analyzed was typically less than that of particles with dry diameters of about 0.100 micrometers. It is speculated that condensation of secondary organic aerosol on nucleation mode particles is largely responsible for the minimal hygroscopic growth observed at the smallest sizes considered. Growth factor distributions of the largest particles characterized typically contained a nonhygroscopic mode believed to be composed primarily of dust. A model was developed to characterize the hygroscopic properties of particles within a size distribution mode through analysis of the fixed size hygroscopic growth measurements. The performance of this model was quantified through comparison of the measured fixed size hygroscopic growth factor distributions with those simulated through convolution of the size-resolved concentration contributed by each of the size modes and the mode-resolved hygroscopicity. This transformation from sizeresolved hygroscopicity to mode-resolved hygroscopicity facilitated examination of changes in the hygroscopic properties of particles within a size distribution mode that accompanied changes in the sizes of those particles. This model was used to examine three specific cases in which the sampled aerosol evolved slowly over a period of hours or days.
Gasparini, Roberto↗
Inelastic, nonlinear analysis of stiffened shells of revolution by numerical integration
This paper describes the latest addition to the STARS system of computer programs, STARS-2P, for the plastic, large deflection analysis of axisymmetrically loaded shells of revolution. The STARS system uses a numerical integration scheme to solve the governing differential equations. Several unique features for shell of revolution programs that are included in the STARS-2P program are described. These include orthotropic nonlinear kinematic hardening theory, a variety of shell wall cross sections and discrete ring stiffeners, cyclic and nonproportional mechanical and thermal loading capability, the coupled axisymmetric large deflection elasto-plastic torsion problem, an extensive restart option, arbitrary branching capability, and the provision for the inelastic treatment of smeared stiffeners, isogrid, and waffle wall constructions. To affirm the validity of the results, comparisons with available theoretical and experimental data are presented.
Levine, H. S.↗
Field-Programmable Gate Array Computer in Structural Analysis: An Initial Exploration
This paper reports on an initial assessment of using a Field-Programmable Gate Array (FPGA) computational device as a new tool for solving structural mechanics problems. A FPGA is an assemblage of binary gates arranged in logical blocks that are interconnected via software in a manner dependent on the algorithm being implemented and can be reprogrammed thousands of times per second. In effect, this creates a computer specialized for the problem that automatically exploits all the potential for parallel computing intrinsic in an algorithm. This inherent parallelism is the most important feature of the FPGA computational environment. It is therefore important that if a problem offers a choice of different solution algorithms, an algorithm of a higher degree of inherent parallelism should be selected. It is found that in structural analysis, an 'analog computer' style of programming, which solves problems by direct simulation of the terms in the governing differential equations, yields a more favorable solution algorithm than current solution methods. This style of programming is facilitated by a 'drag-and-drop' graphic programming language that is supplied with the particular type of FPGA computer reported in this paper. Simple examples in structural dynamics and statics illustrate the solution approach used. The FPGA system also allows linear scalability in computing capability. As the problem grows, the number of FPGA chips can be increased with no loss of computing efficiency due to data flow or algorithmic latency that occurs when a single problem is distributed among many conventional processors that operate in parallel. This initial assessment finds the FPGA hardware and software to be in their infancy in regard to the user conveniences; however, they have enormous potential for shrinking the elapsed time of structural analysis solutions if programmed with algorithms that exhibit inherent parallelism and linear scalability. This potential warrants further development of FPGA-tailored algorithms for structural analysis.
Singleterry, Robert C., Jr.↗
Magnetic Field Solver
The Magnetic Field Solver computer program calculates the magnetic field generated by a group of collinear, cylindrical axisymmetric electromagnet coils. Given the current flowing in, and the number of turns, axial position, and axial and radial dimensions of each coil, the program calculates matrix coefficients for a finite-difference system of equations that approximates a two-dimensional partial differential equation for the magnetic potential contributed by the coil. The program iteratively solves these finite-difference equations by use of the modified incomplete Cholesky preconditioned-conjugate-gradient method. The total magnetic potential as a function of axial (z) and radial (r) position is then calculated as a sum of the magnetic potentials of the individual coils, using a high-accuracy interpolation scheme. Then the r and z components of the magnetic field as functions of r and z are calculated from the total magnetic potential by use of a high-accuracy finite-difference scheme. Notably, for the finite-difference calculations, the program generates nonuniform two-dimensional computational meshes from nonuniform one-dimensional meshes. Each mesh is generated in such a way as to minimize the numerical error for a benchmark one-dimensional magnetostatic problem.
Ilin, Andrew V.↗