Search NASA⌕ Search

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.

At least 289 records · Page 16

Alexandrite laser source for atmospheric lidar measurements

During the past years, there has been a marked increase in interest in the applications of vibronic solid state lasers to meteorology and atmospheric physics. Two airborne lidar programs are now under development in France. The differential absorption lidar (DIAL) method with vibronic solid state lasers is very attractive for water vapor, temperature and pressure measurements. Alexandrite laser and titanium-sapphire are both suitable for these applications. However, only alexandrite rods are commercially available. The requirements on the laser source for airborne dial applications are two fold: (1) a restriction on laser linewidth and a requirement on stability and tunability with a good spectral purity; and (2) a requirement on the time separation between the two pulses. These constraints are summarized.

Pelon, J.↗

ASTEC and MODEL: Controls software development at Goddard Space Flight Center

The ASTEC (Analysis and Simulation Tools for Engineering Controls) software is under development at the Goddard Space Flight Center (GSFC). The design goal is to provide a wide selection of controls analysis tools at the personal computer level, as well as the capability to upload compute-intensive jobs to a mainframe or supercomputer. In the last three years the ASTEC (Analysis and Simulation Tools for Engineering Controls) software has been under development. ASTEC is meant to be an integrated collection of controls analysis tools for use at the desktop level. MODEL (Multi-Optimal Differential Equation Language) is a translator that converts programs written in the MODEL language to FORTRAN. An upgraded version of the MODEL program will be merged into ASTEC. MODEL has not been modified since 1981 and has not kept with changes in computers or user interface techniques. This paper describes the changes made to MODEL in order to make it useful in the 90's and how it relates to ASTEC.

Downing, John P.↗

Calculation of molecular excitation rates

State-to-state collisional excitation rates for interstellar molecules observed by radio astronomers continue to be required to interpret observed line intensities in terms of local temperatures and densities. A problem of particular interest is collisional excitation of water which is important for modeling the observed interstellar masers. In earlier work supported by a different NASA Grant, excitation of water in collisions with He atoms was studied; after many years of successively more refined calculations that problem now seems to be well understood, and discrepancies with earlier experimental data for related (pressure broadening) phenomena are believed to reflect experimental errors. Because of interstellar abundances, excitation by H2, the dominant interstellar species, is much more important than excitation by He, although it has been argued that rates for excitation by these are similar. Under the current grant theoretical study of this problem has begun which is greatly complicated by the additional degrees of freedom which must be included both in determining the interaction potential and also in the molecular scattering calculation. We have now computed the interaction forces for nearly a thousand molecular geometries and are close to having an acceptable global fit to these points which is necessary for the molecular dynamics calculations. Also, extensive modifications have been made to the molecular scattering code, MOLSCAT. These included coding the rotational basis sets and coupling matrix elements required for collisions of an asymmetric top with a linear rotor. A new method for numerical solution of the coupled equations has been incorporated. Because of the long-ranged nature of the water-hydrogen interaction it is necessary to integrate the equations to rather large intermolecular separations, and the integration methods previously available in MOLSCAT are not ideal for such cases. However, the method used by Alexander in his HIBRIDON code is particularly suited for such cases. We have obtained this code and incorporated that part which solves the coupled differential equations as an option in the MOLSCAT program.

Flynn, George↗

Spacecraft Station-Keeping Trajectory and Mission Design Tools

Two tools were developed for designing station-keeping trajectories and estimating delta-v requirements for designing missions to a small body such as a comet or asteroid. This innovation uses NPOPT, a non-sparse, general-purpose sequential quadratic programming (SQP) optimizer and the Two-Level Differential Corrector (T-LDC) in LTool (Libration point mission design Tool) to design three kinds of station-keeping scripts: vertical hovering, horizontal hovering, and orbiting. The T-LDC is used to differentially correct several trajectory legs that join hovering points. In a vertical hovering, the maximum and minimum range points must be connected smoothly while maintaining the spacecrafts range from a small body, all within the law of gravity and the solar radiation pressure. The same is true for a horizontal hover. A PatchPoint is an LTool class that denotes a space-time event with some extra information for differential correction, including a set of constraints to be satisfied by T-LDC. Given a set of PatchPoints, each with its own constraint, the T-LDC differentially corrects the entire trajectory by connecting each trajectory leg joined by PatchPoints while satisfying all specified constraints at the same time. Vertical and horizontal hover both are needed to minimize delta-v spent for station keeping. A Python I/F to NPOPT has been written to be used from an LTool script. In vertical hovering, the spacecraft stays along the line joining the Sun and a small body. An instantaneous delta-v toward the anti- Sun direction is applied at the closest approach to the small body for station keeping. For example, the spacecraft hovers between the minimum range (2 km) point and the maximum range (2.5 km) point from the asteroid 1989ML. Horizontal hovering buys more time for a spacecraft to recover if, for any reason, a planned thrust fails, by returning almost to the initial position after some time later via a near elliptical orbit around the small body. The mapping or staging orbit may be similarly generated using T-LDC with a set of constraints. Some delta-v tables are generated for several different asteroid masses.

Chung, Min-Kun J.↗

A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings

The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.

Butler, T. D.↗

A Nonlinear Programming Perspective on Sensitivity Calculations for Systems Governed by State Equations

This paper discusses the calculation of sensitivities. or derivatives, for optimization problems involving systems governed by differential equations and other state relations. The subject is examined from the point of view of nonlinear programming, beginning with the analytical structure of the first and second derivatives associated with such problems and the relation of these derivatives to implicit differentiation and equality constrained optimization. We also outline an error analysis of the analytical formulae and compare the results with similar results for finite-difference estimates of derivatives. We then attend to an investigation of the nature of the adjoint method and the adjoint equations and their relation to directions of steepest descent. We illustrate the points discussed with an optimization problem in which the variables are the coefficients in a differential operator.

Lewis, Robert Michael↗

Residential Demand Flexibility: Modeling Occupant Behavior using Sociodemographic Predictors

Demand flexibility (DF) has the potential to increase the saturation of renewables in the grid and reduce operating costs for both utilities and customers. However, less than 8% of U.S. residential electric customers are enrolled in DF programs. A major research gap on this topic is an uneven understanding of behavioral drivers of electricity use and DF program participation at the household level. In this study, we employ machine learning models to predict residential occupant behavior in activities relevant to DF. We model occupants' extensive decisions (i.e., choice of action) and intensive behaviors (i.e., amount of time spent) during peak and off-peak time periods using the publicly available American Time Use Survey, which includes activities data for approximately 200,000 respondents. In our machine learning models, predictions for both extensive and intensive behavior fell within a +/-20% error margin at the aggregate level. We identify 13 key sociodemographic predictors of DF-related intensive behavior using LASSO inference and beta coefficient ranking. However, these top predictors differ by activity, suggesting potential scope for differential user targeting for DF events and technologies during program design. This work also contributes to understanding when and who might adopt these DF technologies based on their daily routine activities.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

[Elliptic Differential Equations]

Reflection laws of systems of elliptic equations, on-line programming to numerically solve nonlinear integral equations, and reduction of electrostriction problem

ON-LINE PROGRAMMING↗

A computer program to generate equations of motion matrices, L217 (EOM). Volume 1: Engineering and usage

The equations of motion program L217 formulates the matrix coefficients for a set of second order linear differential equations that describe the motion of an airplane relative to its level equilibrium flight condition. Aerodynamic data from FLEXSTAB or Doublet Lattice (L216) programs can be used to derive the equations for quasi-steady or full unsteady aerodynamics. The data manipulation and the matrix coefficient formulation are described.

Kroll, R. I.↗

A Two Micron Coherent Differential Absorption Lidar Development

A pulsed, 2-micron coherent Differential Absorption Lidar (DIAL)/Integrated Path Differential Absorption (IPDA) transceiver, developed under the Laser Risk Reduction Program (LRRP) at NASA, is integrated into a fully functional lidar instrument. This instrument measures atmospheric CO2 profiles (by DIAL) from a ground platform. It allows the investigators to pursue subsequent in science-driven deployments, and provides a unique tool for Active Sensing of CO2 Emissions over Night, Days, and Seasons (ASCENDS) validation that was strongly advocated in the recent ASCENDS Workshop. Keywords: Differential Absorption Lidar, Near Infrared Laser,

Yu, Jirong↗

A New Approach to Mission Classification and Risk Management for NASA Space Flight Missions

The NASA risk classification system is meant to uide space mission development from formulation through completion of implementation. It is also meant to be the basis on which program and project managers develop and implement appropriate mission assurance and risk management strategies for the mission. In order to be useful, the risk classification system needs to provide consistent and reproducible classification results so that missions may be designed with the appropriate components, subsystems, and testing philosophy, all of which impacts mission schedule and cost. In a cost-constrained environment, a clear, robust, and reproducible approach to mission implementation becomes more critical than ever before. Once a project's risk classification level is established, the managers can define the appropriate management controls, systems engineering processes, mission assurance requirements, safety, and testing for that mission. The current NASA mission classification system will be reviewed before a new system is proposed.NASA manages space flight missions according to a four-tiered classification which assumes increasing levels of risk. We argue that risk does not change between classes. What changes are the means available to reduce risk. In performance-driven missions, the project will spend money in order to maintain performance without reducing margins. In cost-constrained missions, performance will be reduced in order to stay within budget or to maintain schedule: measurement requirements may be traded, design life may be reduced, or both. We then propose a new approach to the classification of NASA space flight missions, based on an assessment of how flexible the requirements, how exquisite the measurements, how long the lifetime, and how rigid the budget.Our proposed approach makes possible a clearer differentiation between classification levels and more effective guidance to program and project managers.

Bordi, Francesco↗

Control of Fractional Diffusion Problems via Dynamic Programming Equations

In this study, we explore the approximation of feedback control of integro-differential equations containing a fractional Laplacian term. To obtain feedback control for the state variable of this nonlocal equation, we use the Hamilton–Jacobi–Bellman equation. It is well known that this approach suffers from the curse of dimensionality, and to mitigate this problem we couple semi-Lagrangian schemes for the discretization of the dynamic programming principle with the use of Shepard approximation. This coupling enables approximation of high-dimensional problems. Numerical convergence toward the solution of the continuous problem is provided together with linear and nonlinear examples. The robustness of the method with respect to disturbances of the system is illustrated by comparisons with an open-loop control approach.

97 MATHEMATICS AND COMPUTING↗

Dynamic characteristics of a variable-mass flexible missile

The general motion of a variable mass flexible missile with internal flow and aerodynamic forces is considered. The resulting formulation comprises six ordinary differential equations for rigid body motion and three partial differential equations for elastic motion. The simultaneous differential equations are nonlinear and possess time-dependent coefficients. The differential equations are solved by a semi-analytical method leading to a set of purely ordinary differential equations which are then solved numerically. A computer program was developed for the numerical solution and results are presented for a given set of initial conditions.

Meirovitch, L.↗

Unsteady turbulent boundary layer analysis

The governing equations for an unsteady turbulent boundary layer on a swept infinite cylinder, composed of a continuity equation, a pair of momentum equations and a pair of turbulent energy equations which include upstream history efforts, are solved numerically. An explicit finite difference analog to the partial differential equations is formulated and developed into a computer program. Calculations were made for a variety of unsteady flows in both two and three dimensions but primarily for two dimensional flow fields in order to first understand some of the fundamental physical aspects of unsteady turbulent boundary layers. Oscillating free stream flows without pressure gradient, oscillating retarded free stream flows and monotonically time-varying flows have all been studied for a wide frequency range. It was found that to the lowest frequency considered, the lower frequency bound being determined by economic considerations (machine time), there were significant unsteady effects on the turbulent boundary layer.

Singleton, R. E.↗

Modeling the internal combustion engine

A flexible and computationally economical model of the internal combustion engine was developed for use on large digital computer systems. It is based on a system of ordinary differential equations for cylinder-averaged properties. The computer program is capable of multicycle calculations, with some parameters varying from cycle to cycle, and has restart capabilities. It can accommodate a broad spectrum of reactants, permits changes in physical properties, and offers a wide selection of alternative modeling functions without any reprogramming. It readily adapts to the amount of information available in a particular case because the model is in fact a hierarchy of five models. The models range from a simple model requiring only thermodynamic properties to a complex model demanding full combustion kinetics, transport properties, and poppet valve flow characteristics. Among its many features the model includes heat transfer, valve timing, supercharging, motoring, finite burning rates, cycle-to-cycle variations in air-fuel ratio, humid air, residual and recirculated exhaust gas, and full combustion kinetics.

Zeleznik, F. J.↗

Modeling the growth dynamics of four candidate crops for Controlled Ecological Life Support Systems (CELSS)

The production of food for human life support for advanced space missions will require the management of many different crops. The research to design these food production capabilities along with the waste management to recycle human metabolic wastes and inedible plant components are parts of Controlled Ecological Life Support Systems (CELSS). Since complete operating CELSS were not yet built, a useful adjunct to the research developing the various pieces of a CELSS are system simulation models that can examine what is currently known about the possible assembly of subsystems into a full CELSS. The growth dynamics of four crops (wheat, soybeans, potatoes, and lettuce) are examined for their general similarities and differences within the context of their important effects upon the dynamics of the gases, liquids, and solids in the CELSS. Data for the four crops currently under active research in the CELSS program using high-production hydroponics are presented. Two differential equations are developed and applied to the general characteristics of each crop growth pattern. Model parameters are determined by closely approximating each crop's data.

Volk, Tyler↗

The Design of a Remote Sensing Data Acquisition Campaign for Precision Agriculture and Some Early Results

In the 1970s NASA and the Department of Agriculture attempted to use the new Landsat MSS system for agricultural purposes. The program had relatively little success. With the advent of differential GPS, yield monitors on harvest equipment and higher spatial resolution remote sensing systems it seemed likely the situation should be reexamined. Therefore, a campaign of data acquisition involving remote sensing and other modalities with dependent research was assembled and funded by the Space Grant Consortia in Alabama and Georgia. The design of the remote sensing data acquisition was driven by the biology and physics of the crop system and limited by the available sensor platforms. Major parameters included crop stage, spatial resolution, seasonal and daily weather conditions, and which portion of the EM spectrum would actually capture the most discriminating information. Joint visible and Near IR with Thermal IR would permit use of existing indices, such as greenness, as well as phenomena driven by the plant' s evapotranspiration. Spatial resolution in the 2-5 meter range was chosen, avoiding many complexities caused by aliasing crop row spacing at, higher resolutions yet finer than the harvester's tightest recording rate. This dictates use of an airborne system. Use of an airborne system also makes scheduling around weather much simpler than use of satellite data. Active video calibration was recognized as essential if quantitative measures were ever to be obtained or reproduced. The system would also have to have onboard geoOF1 Based on these elements 3 data acquisitions have been flown. Seven flight lines were flown twice in 1998 and 16 lines flown in 1999. Total raw data is several GBytes. All of the data has now been geometrically corrected and some preliminary analysis accomplished. The thermal bands have an extremely high correlation with yield. For one@test case with corn, correlation in excess of 0.86 was obtained from a data acquisition two months prior to harvest! Soil images show significant within field variation in clay, soil brightness and emissivity. Light wind has been found to effect the reflectance and temperature of broad leaf crops, including soybeans, cotton and peanuts. Clearly, this work has already demonstrated some very important results. With continued development of the remote sensing technology there is good reason to believe this research will soon be able to help the individual farmer.

Rickmanl, D.↗