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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS2002

Effect of Random Geometric Uncertainty on the Computational Design of a 3-D Flexible Wing

The effect of geometric uncertainty due to statistically independent, random, normally distributed shape parameters is demonstrated in the computational design of a 3-D flexible wing. A first-order second-moment statistical approximation method is used to propagate the assumed input uncertainty through coupled Euler CFD aerodynamic / finite element structural codes for both analysis and sensitivity analysis. First-order sensitivity derivatives obtained by automatic differentiation are used in the input uncertainty propagation. These propagated uncertainties are then used to perform a robust design of a simple 3-D flexible wing at supercritical flow conditions. The effect of the random input uncertainties is shown by comparison with conventional deterministic design results. Sample results are shown for wing planform, airfoil section, and structural sizing variables.

Gumbert, C. R.↗
NASA NTRS2004

Computation of Sensitivity Derivatives of Navier-Stokes Equations using Complex Variables

Accurate computation of sensitivity derivatives is becoming an important item in Computational Fluid Dynamics (CFD) because of recent emphasis on using nonlinear CFD methods in aerodynamic design, optimization, stability and control related problems. Several techniques are available to compute gradients or sensitivity derivatives of desired flow quantities or cost functions with respect to selected independent (design) variables. Perhaps the most common and oldest method is to use straightforward finite-differences for the evaluation of sensitivity derivatives. Although very simple, this method is prone to errors associated with choice of step sizes and can be cumbersome for geometric variables. The cost per design variable for computing sensitivity derivatives with central differencing is at least equal to the cost of three full analyses, but is usually much larger in practice due to difficulty in choosing step sizes. Another approach gaining popularity is the use of Automatic Differentiation software (such as ADIFOR) to process the source code, which in turn can be used to evaluate the sensitivity derivatives of preselected functions with respect to chosen design variables. In principle, this approach is also very straightforward and quite promising. The main drawback is the large memory requirement because memory use increases linearly with the number of design variables. ADIFOR software can also be cumber-some for large CFD codes and has not yet reached a full maturity level for production codes, especially in parallel computing environments.

Vatsa, Veer N.↗
NASA NTRS2015

Introduction to Adjoint Models

In this lecture, some fundamentals of adjoint models will be described. This includes a basic derivation of tangent linear and corresponding adjoint models from a parent nonlinear model, the interpretation of adjoint-derived sensitivity fields, a description of methods of automatic differentiation, and the use of adjoint models to solve various optimization problems, including singular vectors. Concluding remarks will attempt to correct common misconceptions about adjoint models and their utilization.

EnKF↗
NASA NTRS2018

Progress Towards Integrating the Finite-Volume Cubed-Sphere (FV3) Dynamical Core Tangent Linear and Adjoint Models into JEDI

The Joint Effort for Data assimilation Integration (JEDI) -- led by the Joint Center for Satellite Data Assimilation (JCSDA) -- is an inter-organizational endeavor to develop a common framework for performing data assimilation. This extensive framework will ultimately provide solvers, observation operators, interpolation and model interfaces using object oriented modeling. Two partners involved in JEDI use or plan to use the Finite Volume Cubed-Sphere (FV3) dynamical core to produce weather forecasts; these are NASA's Global Modeling and Assimilation Office and NOAA's National Center for Environment Prediction. In this work we present an update on ongoing efforts to integrate the FV3 tangent linear and adjoint models into the prototype JEDI framework. We setup and run a simple cycled data assimilation experiment using 4DVAR on the cubed sphere grid and with the FV3 tangent linear and adjoint models. Development of the observation operators for JEDI is separately underway. Instead of using real observations a simplified set of simulated observations will be used. We discuss the steps required to bring the FV3 linearized model into the object oriented framework and consider what would be the computational requirements of running this configuration for an operational system. FV3 uses a small time-step to ensure that small scales are well resolved, however this presents design challenges when running 4DVAR with the adjoint. An approach to storing the FV3 model trajectory has been developed that maintains the flexibility of using automatic differentiation. We discuss how this approach is incorporated into the framework. Other important uses of adjoint models include computing observation impacts and singular vectors, we consider how these tools can be included in JEDI.

Holdaway, Daniel↗
NASA NTRS2022

Effective Uncertainty Quantification for Multi-Angle Polarimetric Aerosol Remote Sensing Over Ocean

Multi-angle polarimetric (MAP) measurements can enable detailed characterization of aerosol microphysical and optical properties and improve atmospheric correction in ocean color remote sensing. Advanced retrieval algorithms have been developed to obtain multiple geophysical parameters in the atmosphere–ocean system. Theoretical pixel-wise retrieval uncertainties based on error propagation have been used to quantify retrieval performance and determine the quality of data products. However, standard error propagation techniques in high-dimensional retrievals may not always represent true retrieval errors well due to issues such as local minima and the nonlinear dependence of the forward model on the retrieved parameters near the solution. In this work, we analyze these theoretical uncertainty estimates and validate them using a flexible Monte Carlo approach. The Fast Multi-Angular Polarimetric Ocean coLor (FastMAPOL) retrieval algorithm, based on efficient neural network forward models, is used to conduct the retrievals and uncertainty quantification on both synthetic HARP2 (Hyper-Angular Rainbow Polarimeter 2) and AirHARP (airborne version of HARP2) datasets. In addition, for practical application of the uncertainty evaluation technique in operational data processing, we use the automatic differentiation method to calculate derivatives analytically based on the neural network models. Both the speed and accuracy associated with uncertainty quantification for MAP retrievals are addressed in this study. Pixel-wise retrieval uncertainties are further evaluated for the real AirHARP field campaign data. The uncertainty quantification methods and results can be used to evaluate the quality of data products, as well as guide MAP algorithm development for current and future satellite systems such as NASA’s Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission.

PACE↗
NASA NTRSDate not supplied

Blade and Takeoff Trajectory Optimization of a Propeller-Driven Electric Aircraft with Acoustic Constraints

In this work, a multi-disciplinary toolchain is described and used to optimize the takeoff trajectory of a electrified general aviation aircraft, subjected to acoustic constraints. The Dymos multi-disciplinary optimal control library is used to optimize the trajectory, with propeller aerodynamic and acoustic models provided by blade element momentum theory (CCBlade.jl) and acoustic analogy (AcousticAnalogies.jl) codes, respectively. Each model is implemented in the OpenMDAO framework, with all derivatives calculated either analytically or via automatic differentiation tools. The toolchain is applied to a hypothetical electrified form of the Cirrus SR20 and compared to the conventional piston-driven form.

Aerodynamics↗
NASA NTRSDate not supplied

Blade and Takeoff Trajectory Optimization of a Propeller-Driven Electric Aircraft with Acoustic Constraints

In this work, a multi-disciplinary toolchain is described and used to optimize the takeoff trajectory of a electrified general aviation aircraft, subjected to acoustic constraints. The Dymos multi-disciplinary optimal control library is used to optimize the trajectory, with propeller aerodynamic and acoustic models provided by blade element momentum theory (CCBlade.jl) and acoustic analogy (AcousticAnalogies.jl) codes, respectively. Each model is implemented in the OpenMDAO framework, with all derivatives calculated either analytically or via automatic differentiation tools. The toolchain is applied to a hypothetical electrified form of the Cirrus SR20 and compared to the conventional piston-driven form.

gradient-based optimization↗
NASA NTRS1995

Flight test evaluation of the Stanford University/United Airlines differential GPS Category 3 automatic landing system

Test flights were conducted to evaluate the capability of Differential Global Positioning System (DGPS) to provide the accuracy and integrity required for International Civil Aviation Organization (ICAO) Category (CAT) 3 precision approach and landings. These test flights were part of a Federal Aviation Administration (FAA) program to evaluate the technical feasibility of using DGPS based technology for CAT 3 precision approach and landing applications. A United Airlines Boeing 737-300 (N304UA) was equipped with DGPS receiving equipment and additional computing capability provided by Stanford University. The test flights were conducted at NASA Ames Research Center's Crows Landing Flight Facility, Crows Landing, California. The flight test evaluation was based on completing 100 approaches and autolandings; 90 touch and go, and 10 terminating with a full stop. Two types of accuracy requirements were evaluated: 1) Total system error, based on the Required Navigation Performance (RNP), and 2) Navigation sensor error, based on ICAO requirements for the Microwave Landing System (MLS). All of the approaches and autolandings were evaluated against ground truth reference data provided by a laser tracker. Analysis of these approaches and autolandings shows that the Stanford University/United Airlines system met the requirements for a successful approach and autolanding 98 out of 100 approaches and autolandings, based on the total system error requirements as specified in the FAA CAT 3 Level 2 Flight Test Plan.

Kaufmann, David N.↗
NASA NTRS1995

Flight test evaluation of the E-systems Differential GPS category 3 automatic landing system

Test flights were conducted to evaluate the capability of Differential Global Positioning System (DGPS) to provide the accuracy and integrity required for International Civil Aviation Organization (ICAO) Category (CAT) III precision approach and landings. These test flights were part of a Federal Aviation Administration (FAA) program to evaluate the technical feasibility of using DGPS based technology for CAT III precision approach and landing applications. An IAI Westwind 1124 aircraft (N24RH) was equipped with DGPS receiving equipment and additional computing capability provided by E-Systems. The test flights were conducted at NASA Ames Research Center's Crows Landing Flight Facility, Crows Landing, California. The flight test evaluation was based on completing 100 approaches and landings. The navigation sensor error accuracy requirements were based on ICAO requirements for the Microwave Landing System (MLS). All of the approaches and landings were evaluated against ground truth reference data provided by a laser tracker. Analysis of these approaches and landings shows that the E-Systems DGPS system met the navigation sensor error requirements for a successful approach and landing 98 out of 100 approaches and landings, based on the requirements specified in the FAA CAT III Level 2 Flight Test Plan. In addition, the E-Systems DGPS system met the integrity requirements for a successful approach and landing or stationary trial for all 100 approaches and landings and all ten stationary trials, based on the requirements specified in the FAA CAT III Level 2 Flight Test Plan.

Kaufmann, David N.↗
NASA NTRS1982

The use of differential pressure feedback in an automatic flight control system

A feasibility study has been performed to evaluate the performance of a system whereby a control surface is positioned with differential pressure as the feedback variable. Analogous to a position command system, the control surface is commanded to move until a certain differential pressure is achieved at a given point on the surface. Frequency response tests and theoretical considerations indicate that the pressure feedback transfer function is first order, with a break frequency up to 50 rad/sec. There exist applications to the outer loops of flight control systems as well. Stability augmentation, gust alleviation, and stall prevention appear to be possible by feeding back differential pressure across lifting and control surfaces.

Levy, D. W.↗
NASA NTRS1999

Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization

Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.

Green, Lawrence↗
NASA NTRS1992

Differential GPS/inertial navigation approach/landing flight test results

In November of 1990 a joint Honeywell/NASA-Langley differential GPS/inertial flight test was conducted at Wallops Island, Virginia. The test objective was to acquire a system performance database and demonstrate automatic landing using an integrated differential GPS/INS (Global Positioning System/inertial navigation system) with barometric and radar altimeters. The flight test effort exceeded program objectives with over 120 landings, 36 of which were fully automatic differential GPS/inertial landings. Flight test results obtained from post-flight data analysis are discussed. These results include characteristics of differential GPS/inertial error, using the Wallops Island Laser Tracker as a reference. Data on the magnitude of the differential corrections and vertical channel performance with and without radar altimeter augmentation are provided.

Snyder, Scott↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Calculation of machine precision second order derivatives using dual-complex numbers

It is well known that both complex and dual numbers can be employed to obtain machine precision first-order derivatives; however, neither, on their own, can compute machine precision 2nd order derivatives. To address this limitation, it is demonstrated in this paper that combined dual-complex numbers can be used to compute machine precision 1st and 2nd order derivatives. The dual-complex approach is simpler than utilizing multicomplex or hyper-dual numbers as existing dual libraries can be used as is or easily augmented to accept complex numbers, and the complexity of developing, integrating, and deploying multicomplex or hyper-dual libraries is avoided. The efficacy of this approach is demonstrated for both univariate and multivariate functions. Finally, source code examples using the Python, Julia, and Mathematica languages are provided as supplemental material.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Unveiling nano-scale crystal deformation using coherent X-ray dynamical diffraction

Visualization of internal deformation fields in crystalline materials helps bridge the gap between theoretical models and practical applications. Applying Bragg coherent diffraction imaging under X-ray dynamical diffraction conditions provides a promising approach to the longstanding challenge of investigating the deformation fields in micron-sized crystals. Here, we present an automatic differentiation-based reconstruction method that integrates dynamical scattering theory to accurately reconstruct deformation fields in large crystals. Using this forward model, our simulated and experimental results demonstrate that three-dimensional local strain information inside a large crystal can be accurately reconstructed under coherent X-ray dynamical diffraction conditions with Bragg coherent X-ray diffraction imaging. These findings open an avenue for extending the investigation of local deformation fields to microscale crystals while maintaining nanoscale resolution, leveraging the enhanced coherence and brightness of advanced X-ray sources.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Jacobian sparsity detection using Bloom filters

Determining Jacobian sparsity structure is an important step in the efficient computation of sparse Jacobians. We introduce a new method for determining Jacobian sparsity patterns by combining bit vector probing with Bloom filters. In conclusion, we further refine Bloom filter probing by combining it with hierarchical probing to yield a highly effective strategy for Jacobian sparsity pattern determination.

Bloom filter↗