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Results for “Algorithmic differentiation”

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.

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At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Single-shot x-ray phase-contrast and dark-field imaging based on coded binary phase mask

We introduce a coded-mask-based multi-contrast imaging method for high-resolution phase-contrast and dark-field imaging. The method uses a binary phase mask designed to provide an ultra-high-contrast pattern and reference-free single-shot measurement and an algorithm based on maximum-likelihood optimization and automatic differentiation to perform simultaneous reconstruction of absorption, phase, and dark-field object images. Further, we demonstrate that the method has great potential for real-time quantitative phase imaging and wavefront sensing when combined with deep learning.

Qiao, Zhi (ORCID:0000000286285320)↗
DOE OSTI2023

Challenging the Curse of Dimensionality in Multidimensional Numerical Integration by Using a Low-Rank Tensor-Train Format

Numerical integration is a basic step in the implementation of more complex numerical algorithms suitable, for example, to solve ordinary and partial differential equations. The straightforward extension of a one-dimensional integration rule to a multidimensional grid by the tensor product of the spatial directions is deemed to be practically infeasible beyond a relatively small number of dimensions, e.g., three or four. In fact, the computational burden in terms of storage and floating point operations scales exponentially with the number of dimensions. This phenomenon is known as the curse of dimensionality and motivated the development of alternative methods such as the Monte Carlo method. The tensor product approach can be very effective for high-dimensional numerical integration if we can resort to an accurate low-rank tensor-train representation of the integrand function. In this work, we discuss this approach and present numerical evidence showing that it is very competitive with the Monte Carlo method in terms of accuracy and computational costs up to several hundredths of dimensions if the integrand function is regular enough and a sufficiently accurate low-rank approximation is available.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Survey of computational methods for three-dimensional supersonic inviscid flows with shocks

Hyperbolic systems of partial differential equations governing supersonic inviscid flows are discussed and analyzed. Finite-difference analogues for integrating these systems in the interior of fluid domains are described from two points of view: a differential form approach and an integral form approach. The algorithms presented are analyzed for stability and accuracy. The concept of time splitting is discussed and supplied to these methods to achieve increased numerical efficiency. Techniques for treating conditions at the boundaries of the fluid domain and shock-wave discontinuities at surfaces within the domain are described.

Maccormack, R. W.↗
NASA NTRS1976

Computational alternatives to obtain time optimal jet engine control

Two computational methods to determine an open loop time optimal control sequence for a simple single spool turbojet engine are described by a set of nonlinear differential equations. Both methods are modifications of widely accepted algorithms which can solve fixed time unconstrained optimal control problems with a free right end. Constrained problems to be considered have fixed right ends and free time. Dynamic programming is defined on a standard problem and it yields a successive approximation solution to the time optimal problem of interest. A feedback control law is obtained and it is then used to determine the corresponding open loop control sequence. The Fletcher-Reeves conjugate gradient method has been selected for adaptation to solve a nonlinear optimal control problem with state variable and control constraints.

Basso, R. J.↗
NASA NTRS1981

A new solution-adaptive grid generation method for transonic airfoil flow calculations

The clustering algorithm is controlled by a second-order, ordinary differential equation which uses the airfoil surface density gradient as a forcing function. The solution to this differential equation produces a surface grid distribution which is automatically clustered in regions with large gradients. The interior grid points are established from this surface distribution by using an interpolation scheme which is fast and retains the desirable properties of the original grid generated from the standard elliptic equation approach.

Nakamura, S.↗
NASA NTRS1991

Digital CODEC for real-time processing of broadcast quality video signals at 1.8 bits/pixel

Advances in very large scale integration and recent work in the field of bandwidth efficient digital modulation techniques have combined to make digital video processing technically feasible an potentially cost competitive for broadcast quality television transmission. A hardware implementation was developed for DPCM (differential pulse code midulation)-based digital television bandwidth compression algorithm which processes standard NTSC composite color television signals and produces broadcast quality video in real time at an average of 1.8 bits/pixel. The data compression algorithm and the hardware implementation of the codec are described, and performance results are provided.

Shalkhauser, Mary JO↗
NASA NTRS1996

MGLab: An Interactive Multigrid Environment

MGLab is a set of Matlab functions that defines an interactive environment for experimenting with multigrid algorithms. The package solves two-dimensional elliptic partial differential equations discretized using either finite differences or finite volumes, depending on the problem. Built-in problems include the Poisson equation, the Helmholtz equation, a convection-diffusion problem, and a discontinuous coefficient problem. A number of parameters controlling the multigrid V-cycle can be set using a point-and-click mechanism. The menu-based user interface also allows a choice of several Krylov subspace methods, including CG, GMRES(k), and Bi-CGSTAB, which can be used either as stand-alone solvers or as multigrid acceleration schemes. The package exploits Matlab's visualization and sparse matrix features and has been structured to be easily extensible.

Bordner, James↗
NASA NTRS2003

Efficient Development of High Fidelity Structured Volume Grids for Hypersonic Flow Simulations

A new technique for the control of grid line spacing and intersection angles of a structured volume grid, using elliptic partial differential equations (PDEs) is presented. Existing structured grid generation algorithms make use of source term hybridization to provide control of grid lines, imposing orthogonality implicitly at the boundary and explicitly on the interior of the domain. A bridging function between the two types of grid line control is typically used to blend the different orthogonality formulations. It is shown that utilizing such a bridging function with source term hybridization can result in the excessive use of computational resources and diminishes robustness. A new approach, Anisotropic Lagrange Based Trans-Finite Interpolation (ALBTFI), is offered as a replacement to source term hybridization. The ALBTFI technique captures the essence of the desired grid controls while improving the convergence rate of the elliptic PDEs when compared with source term hybridization. Grid generation on a blunt cone and a Shuttle Orbiter is used to demonstrate and assess the ALBTFI technique, which is shown to be as much as 50% faster, more robust, and produces higher quality grids than source term hybridization.

Alter, Stephen J.↗
NASA NTRS2008

Numerical Determination of Critical Conditions for Thermal Ignition

The determination of ignition or thermal explosion in an oxidizing porous body of material, as described by a dimensionless reaction-diffusion equation of the form .tu = .2u + .e-1/u over the bounded region O, is critically reexamined from a modern perspective using numerical methodologies. First, the classic stationary model is revisited to establish the proper reference frame for the steady-state solution space, and it is demonstrated how the resulting nonlinear two-point boundary value problem can be reexpressed as an initial value problem for a system of first-order differential equations, which may be readily solved using standard algorithms. Then, the numerical procedure is implemented and thoroughly validated against previous computational results based on sophisticated path-following techniques. Next, the transient nonstationary model is attacked, and the full nonlinear form of the reaction-diffusion equation, including a generalized convective boundary condition, is discretized and expressed as a system of linear algebraic equations. The numerical methodology is implemented as a computer algorithm, and validation computations are carried out as a prelude to a broad-ranging evaluation of the assembly problem and identification of the watershed critical initial temperature conditions for thermal ignition. This numerical methodology is then used as the basis for studying the relationship between the shape of the critical initial temperature distribution and the corresponding spatial moments of its energy content integral and an attempt to forge a fundamental conjecture governing this relation. Finally, the effects of dynamic boundary conditions on the classic storage problem are investigated and the groundwork is laid for the development of an approximate solution methodology based on adaptation of the standard stationary model.

Luo, W.↗
DOE OSTI2020

Fault Current Control and Protection in a Standalone DC Microgrid Using Adaptive Droop and Current Derivative

This report presents a novel fault detection, characterization, and fault current control algorithm for a standalone solar-photovoltaic (PV) based dc microgrids. The protection scheme is based on the current derivative algorithm. The overcurrent and current directional/differential comparison based protection schemes are incorporated for the dc microgrid fault characterization. For a low impedance fault, the fault current is controlled based on the current/voltage thresholds and current direction. Generally, the droop method is used to control the power-sharing between the converters by controlling the reference voltage. In this article, an adaptive droop scheme is also proposed to control the fault current by calculating a virtual resistance R droop , and to control the converter output reference voltage. For a high impedance fault, differential comparison method is used to characterize the fault. These algorithms effectively control the converter pulsewidth and reduce the flow of source current from a particular converter, which helps to increase the fault clearing time. Additionally, a trip signal is sent to the corresponding dc circuit breaker (DCCB), to isolate the faulted converter, feeder or a dc bus. The dc microgrid protection design procedure is detailed, and the performance of the proposed method is verified by simulation analysis.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRSDate not supplied

Combined Bernstein Polynomial, Optimal Reciprocal Collision Avoidance, Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of Differential Dynamic Programming (DDP) with the Optimal Reciprocal Collision Avoidance (ORCA) algorithm as the basis for a new algorithm, titled Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance DDP (COBRA-DDP), for trajectory replanning and collision avoidance for Urban Air Mobility (UAM) vehicles. State-constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm start the state constrained DDP algorithms to decrease computation time. Its benefits and effectiveness of the algorithm are demonstrated on a UAM Vertical Takeoff and Landing (VTOL) vehicle simulation with highly nonlinear dynamics.

Optimal Reciprocal Collision Avoidance↗
NASA NTRS1980

Research on the application of a decoupling algorithm for structure analysis

The mathematical theory for decoupling mth-order matrix differential equations is presented. It is shown that the decoupling precedure can be developed from the algebraic theory of matrix polynomials. The role of eigenprojectors and latent projectors in the decoupling process is discussed and the mathematical relationships between eigenvalues, eigenvectors, latent roots, and latent vectors are developed. It is shown that the eigenvectors of the companion form of a matrix contains the latent vectors as a subset. The spectral decomposition of a matrix and the application to differential equations is given.

Denman, E. D.↗
NASA NTRS2011

Exploring the Use of Radar for a Physically Based Lightning Cessation Nowcasting Tool

NASA s Marshall Space Flight Center (MSFC) and the University of Alabama in Huntsville (UAHuntsville) are collaborating with the 45th Weather Squadron (45WS) at Cape Canaveral Air Force Station (CCAFS) to enable improved nowcasting of lightning cessation. This project centers on use of dual-polarimetric radar capabilities, and in particular, the new C-band dual-polarimetric weather radar acquired by the 45WS. Special emphasis is placed on the development of a physically based operational algorithm to predict lightning cessation. While previous studies have developed statistically based lightning cessation algorithms, we believe that dual-polarimetric radar variables offer the possibility to improve existing algorithms through the inclusion of physically meaningful trends reflecting interactions between in-cloud electric fields and hydrometeors. Specifically, decades of polarimetric radar research using propagation differential phase has demonstrated the presence of distinct phase and ice crystal alignment signatures in the presence of strong electric fields associated with lightning. One question yet to be addressed is: To what extent can these ice-crystal alignment signatures be used to nowcast the cessation of lightning activity in a given storm? Accordingly, data from the UAHuntsville Advanced Radar for Meteorological and Operational Research (ARMOR) along with the NASA-MSFC North Alabama Lightning Mapping Array are used in this study to investigate the radar signatures present before and after lightning cessation. Thus far, our case study results suggest that the negative differential phase shift signature weakens and disappears after the analyzed storms ceased lightning production (i.e., after the last lightning flash occurred). This is a key observation because it suggests that while strong electric fields may still have been present, the lightning cessation signature encompassed the period of the polarimetric negative phase shift signature. To the extent this behavior is repeatable in other cases, even if only in a substantial fraction of those cases, the case analyses suggests that differential propagation phase may prove to be a useful parameter for future lightning cessation algorithms. Indeed, analysis of 15+ cases has shown additional indications of the weakening and disappearance of this ice alignment signature with lightning cessation. A summary of results will be presented.

Schultz, Elise V.↗
NASA NTRS1989

Numerical optimization in Hilbert space using inexact function and gradient evaluations

Trust region algorithms provide a robust iterative technique for solving non-convex unstrained optimization problems, but in many instances it is prohibitively expensive to compute high accuracy function and gradient values for the method. Of particular interest are inverse and parameter estimation problems, since function and gradient evaluations involve numerically solving large systems of differential equations. A global convergence theory is presented for trust region algorithms in which neither function nor gradient values are known exactly. The theory is formulated in a Hilbert space setting so that it can be applied to variational problems as well as the finite dimensional problems normally seen in trust region literature. The conditions concerning allowable error are remarkably relaxed: relative errors in the gradient error condition is automatically satisfied if the error is orthogonal to the gradient approximation. A technique for estimating gradient error and improving the approximation is also presented.

Carter, Richard G.↗
NASA NTRS1986

Performance analysis of image processing algorithms for classification of natural vegetation in the mountains of southern California

The earth's forests fix carbon from the atmosphere during photosynthesis. Scientists are concerned that massive forest removals may promote an increase in atmospheric carbon dioxide, with possible global warming and related environmental effects. Space-based remote sensing may enable the production of accurate world forest maps needed to examine this concern objectively. To test the limits of remote sensing for large-area forest mapping, we use Landsat data acquired over a site in the forested mountains of southern California to examine the relative capacities of a variety of popular image processing algorithms to discriminate different forest types. Results indicate that certain algorithms are best suited to forest classification. Differences in performance between the algorithms tested appear related to variations in their sensitivities to spectral variations caused by background reflectance, differential illumination, and spatial pattern by species. Results emphasize the complexity between the land-cover regime, remotely sensed data and the algorithms used to process these data.

Yool, S. R.↗
NASA NTRS2011

Exploring the Use of Radar for Physically-Based Nowcasting of Lightning Cessation

NASA's Marshall Space Flight Center and the University of Alabama in Huntsville (UAHuntsville) are collaborating with the 45th Weather Squadron (45WS) at Cape Canaveral Air Force Station (CCAFS) to enable improved nowcasting of lightning cessation. This project centers on use of dual-polarimetric radar capabilities, and in particular, the new C-band dual polarimetric weather radar acquired by the 45WS. Special emphasis is placed on the development of a physically-based operational algorithm to predict lightning cessation. While previous studies have developed statistically based lightning cessation algorithms driven primarily by trending in the actual total lightning flash rate, we believe that dual polarimetric radar variables offer the possibility to improve existing algorithms through the inclusion of physically meaningful trends reflecting interactions between in-cloud electric fields and ice-microphysics. Specifically, decades of polarimetric radar research using propagation differential phase has demonstrated the presence of distinct phase and ice crystal alignment signatures in the presence of strong electric fields associated with lightning. One question yet to be addressed is: To what extent can propagation phase-based ice-crystal alignment signatures be used to nowcast the cessation of lightning activity in a given storm? Accordingly, data from the UAHuntsville Advanced Radar for Meteorological and Operational Research (ARMOR) along with the NASA-MSFC North Alabama Lightning Mapping Array are used in this study to investigate the radar signatures present before and after lightning cessation. Thus far our case study results suggest that the negative differential phase shift signature weakens and disappears after the analyzed storms ceased lightning production (i.e., after the last lightning flash occurred). This is a key observation because it suggests that while strong electric fields may still have been present, the lightning cessation signature was encompassed in the period of the polarimetric negative phase shift signature. To the extent this behavior is repeatable in other cases, even if only in a substantial fraction of those cases, the analysis suggests that differential propagation phase may prove to be a useful parameter for future lightning cessation algorithms. Indeed, a preliminary analysis of 15+ cases has shown additional indications of the weakening and disappearance of this ice alignment signature with lightning cessation. A summary of these case-study results is presented.

Schultz, Elise V.↗
NASA NTRS1981

Scaled Runge-Kutta algorithms for handling dense output

Low order Runge-Kutta algorithms are developed which determine the solution of a system of ordinary differential equations at any point within a given integration step, as well as at the end of each step. The scaled Runge-Kutta methods are designed to be used with existing Runge-Kutta formulas, using the derivative evaluations of these defining algorithms as the core of the system. For a slight increase in computing time, the solution may be generated within the integration step, improving the efficiency of the Runge-Kutta algorithms, since the step length need no longer be severely reduced to coincide with the desired output point. Scaled Runge-Kutta algorithms are presented for orders 3 through 5, along with accuracy comparisons between the defining algorithms and their scaled versions for a test problem.

Horn, M. K.↗
NASA NTRS1982

Iterative algorithms for large sparse linear systems on parallel computers

Algorithms for assembling in parallel the sparse system of linear equations that result from finite difference or finite element discretizations of elliptic partial differential equations, such as those that arise in structural engineering are developed. Parallel linear stationary iterative algorithms and parallel preconditioned conjugate gradient algorithms are developed for solving these systems. In addition, a model for comparing parallel algorithms on array architectures is developed and results of this model for the algorithms are given.

Adams, L. M.↗