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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Development of an Automatic Differentiation Version of the FPX Rotor Code

The ADIFOR2.0 automatic differentiator is applied to the FPX rotor code along with the grid generator GRGN3. The FPX is an eXtended Full-Potential CFD code for rotor calculations. The automatic differentiation version of the code is obtained, which provides both non-geometry and geometry sensitivity derivatives. The sensitivity derivatives via automatic differentiation are presented and compared with divided difference generated derivatives. The study shows that automatic differentiation method gives accurate derivative values in an efficient manner.

Hu, Hong↗
NASA NTRS1994

Parallel Calculation of Sensitivity Derivatives for Aircraft Design using Automatic Differentiation

Sensitivity derivative (SD) calculation via automatic differentiation (AD) typical of that required for the aerodynamic design of a transport-type aircraft is considered. Two ways of computing SD via code generated by the ADIFOR automatic differentiation tool are compared for efficiency and applicability to problems involving large numbers of design variables. A vector implementation on a Cray Y-MP computer is compared with a coarse-grained parallel implementation on an IBM SP1 computer, employing a Fortran M wrapper. The SD are computed for a swept transport wing in turbulent, transonic flow; the number of geometric design variables varies from 1 to 60 with coupling between a wing grid generation program and a state-of-the-art, 3-D computational fluid dynamics program, both augmented for derivative computation via AD. For a small number of design variables, the Cray Y-MP implementation is much faster. As the number of design variables grows, however, the IBM SP1 becomes an attractive alternative in terms of compute speed, job turnaround time, and total memory available for solutions with large numbers of design variables. The coarse-grained parallel implementation also can be moved easily to a network of workstations.

Bischof, c. H.↗
NASA NTRS1993

Sensitivity derivatives for advanced CFD algorithm and viscous modelling parameters via automatic differentiation

The computational technique of automatic differentiation (AD) is applied to a three-dimensional thin-layer Navier-Stokes multigrid flow solver to assess the feasibility and computational impact of obtaining exact sensitivity derivatives typical of those needed for sensitivity analyses. Calculations are performed for an ONERA M6 wing in transonic flow with both the Baldwin-Lomax and Johnson-King turbulence models. The wing lift, drag, and pitching moment coefficients are differentiated with respect to two different groups of input parameters. The first group consists of the second- and fourth-order damping coefficients of the computational algorithm, whereas the second group consists of two parameters in the viscous turbulent flow physics modelling. Results obtained via AD are compared, for both accuracy and computational efficiency with the results obtained with divided differences (DD). The AD results are accurate, extremely simple to obtain, and show significant computational advantage over those obtained by DD for some cases.

Green, Lawrence L.↗
NASA NTRS1994

Applications of automatic differentiation in computational fluid dynamics

Automatic differentiation (AD) is a powerful computational method that provides for computing exact sensitivity derivatives (SD) from existing computer programs for multidisciplinary design optimization (MDO) or in sensitivity analysis. A pre-compiler AD tool for FORTRAN programs called ADIFOR has been developed. The ADIFOR tool has been easily and quickly applied by NASA Langley researchers to assess the feasibility and computational impact of AD in MDO with several different FORTRAN programs. These include a state-of-the-art three dimensional multigrid Navier-Stokes flow solver for wings or aircraft configurations in transonic turbulent flow. With ADIFOR the user specifies sets of independent and dependent variables with an existing computer code. ADIFOR then traces the dependency path throughout the code, applies the chain rule to formulate derivative expressions, and generates new code to compute the required SD matrix. The resulting codes have been verified to compute exact non-geometric and geometric SD for a variety of cases. in less time than is required to compute the SD matrix using centered divided differences.

Green, Lawrence L.↗
NASA NTRS1992

Automatic differentiation as a tool in engineering design

Automatic Differentiation (AD) is a tool that systematically implements the chain rule of differentiation to obtain the derivatives of functions calculated by computer programs. AD is assessed as a tool for engineering design. The forward and reverse modes of AD, their computing requirements, as well as approaches to implementing AD are discussed. The application of two different tools to two medium-size structural analysis problems to generate sensitivity information typically necessary in an optimization or design situation is also discussed. The observation is made that AD is to be preferred to finite differencing in most cases, as long as sufficient computer storage is available; in some instances, AD may be the alternative to consider in lieu of analytical sensitivity analysis.

Barthelemy, Jean-Francois↗
NASA NTRS1992

Automatic Differentiation as a tool in engineering design

Automatic Differentiation (AD) is a tool that systematically implements the chain rule of differentiation to obtain the derivatives of functions calculated by computer programs. In this paper, it is assessed as a tool for engineering design. The paper discusses the forward and reverse modes of AD, their computing requirements, and approaches to implementing AD. It continues with application to two different tools to two medium-size structural analysis problems to generate sensitivity information typically necessary in an optimization or design situation. The paper concludes with the observation that AD is to be preferred to finite differencing in most cases, as long as sufficient computer storage is available.

Barthelemy, Jean-Francois M.↗
NASA NTRS1998

First- and Second-Order Sensitivity Analysis of a P-Version Finite Element Equation Via Automatic Differentiation

Sensitivity analysis is a technique for determining derivatives of system responses with respect to design parameters. Among many methods available for sensitivity analysis, automatic differentiation has been proven through many applications in fluid dynamics and structural mechanics to be an accurate and easy method for obtaining derivatives. Nevertheless, the method can be computational expensive and can require a high memory space. This project will apply an automatic differentiation tool, ADIFOR, to a p-version finite element code to obtain first- and second- order then-nal derivatives, respectively. The focus of the study is on the implementation process and the performance of the ADIFOR-enhanced codes for sensitivity analysis in terms of memory requirement, computational efficiency, and accuracy.

Hou, Gene↗
NASA NTRSDate not supplied

Q-Law for Rapid Assessment of Low Thrust Cislunar Trajectories Via Automatic Differentiation

Q-Law is a Lyapunov-based control law used to determine optimal controls for a low thrust trajectory. One major issue with its use is the difficult derivatives re-quired for calculating optimal controls at a given time. In this paper, an implementation of Q-Law with automatic differentiation via a Python package called JAX is applied. With automatic differentiation, the difficult derivatives for Q-Law’s optimal controls are calculated with ease, and derivatives of final states with respect to Q-Law’s weights are found enabling gradient-based optimization of Q-Law for the first time. Different search and optimization methods for finding optimal weights are then compared using the LEO to GEO problem, and it was found that gradient-free methods like design of experiments and genetic algorithm produced the best results, but they took the longest time to get a solution, while the gradient-based method found a locally optimal result in a much faster time. Overall, the run time for a single propagation is manageable and well-suited for a mission designer to use as an initial guess generator for trajectory optimization, or for simple orbit transfer analysis.

Nathan Steffen↗
NASA NTRS1996

Optimum Shape Design Using Automatic Differentiation in Reverse Mode

This paper shows how to use automatic differentiation in reverse mode as a powerful tool in optimization procedures. It is also shown that for aerodynamic applications the gradients have to be as accurate as possible. In particular, the effect of having the exact gradient of he first or second order spatial discretization schemes is presented. We show that the loss of precision in the gradient affects not only the convergence, but also the final shape. Both two and three dimensional configurations of transonic and supersonic flows have been investigated. These cases involve up to several thousand control parameters.

Hafez, M.↗
NASA NTRS1992

Automatic differentiation of advanced CFD codes for multidisciplinary design

Automated multidisciplinary design of aircraft and other flight vehicles requires the optimization of complex performance objectives with respect to a number of design parameters and constraints. The effect of these independent design variables on the system performance criteria can be quantified in terms of sensitivity derivatives which must be calculated and propagated by the individual discipline simulation codes. Typical advanced CFD analysis codes do not provide such derivatives as part of a flow solution; these derivatives are very expensive to obtain by divided (finite) differences from perturbed solutions. It is shown that sensitivity derivatives can be obtained accurately and efficiently using the ADIFOR source translator for automatic differentiation. In particular, it is demonstrated that the 3-D, thin-layer Navier-Stokes, multigrid flow solver called TLNS3D is amenable to automatic differentiation in the forward mode even with its implicit iterative solution algorithm and complex turbulence modeling. It is significant that by using computational differentiation, consistent discrete nongeometric sensitivity derivatives have been obtained from an aerodynamic 3-D CFD code in a relatively short time, e.g., O(man-week) not O(man-year).

Bischof, C.↗
NASA NTRS1994

Automatic differentiation for design sensitivity analysis of structural systems using multiple processors

An automatic differentiation tool (ADIFOR) is incorporated into a finite element based structural analysis program for shape and non-shape design sensitivity analysis of structural systems. The entire analysis and sensitivity procedures are parallelized and vectorized for high performance computation. Small scale examples to verify the accuracy of the proposed program and a medium scale example to demonstrate the parallel vector performance on multiple CRAY C90 processors are included.

Nguyen, Duc T.↗
NASA NTRS1995

Automatic differentiation evaluated as a tool for rotorcraft design and optimization

This paper investigates the use of automatic differentiation (AD) as a means for generating sensitivity analyses in rotorcraft design and optimization. This technique transforms an existing computer program into a new program that performs sensitivity analysis in addition to the original analysis. The original FORTRAN program calculates a set of dependent (output) variables from a set of independent (input) variables, the new FORTRAN program calculates the partial derivatives of the dependent variables with respect to the independent variables. The AD technique is a systematic implementation of the chain rule of differentiation, this method produces derivatives to machine accuracy at a cost that is comparable with that of finite-differencing methods. For this study, an analysis code that consists of the Langley-developed hover analysis HOVT, the comprehensive rotor analysis CAMRAD/JA, and associated preprocessors is processed through the AD preprocessor ADIFOR 2.0. The resulting derivatives are compared with derivatives obtained from finite-differencing techniques. The derivatives obtained with ADIFOR 2.0 are exact within machine accuracy and do not depend on the selection of step-size, as are the derivatives obtained with finite-differencing techniques.

Walsh, Joanne L.↗
NASA NTRS1999

Determination of Stability and Control Derivatives using Computational Fluid Dynamics and Automatic Differentiation

With the recent interest in novel control effectors there is a need to determine the stability and control derivatives of new aircraft configurations early in the design process. These derivatives are central to most control law design methods and would allow the determination of closed-loop control performance of the vehicle. Early determination of the static and dynamic behavior of an aircraft may permit significant improvement in configuration weight, cost, stealth, and performance through multidisciplinary design. The classical method of determining static stability and control derivatives - constructing and testing wind tunnel models - is expensive and requires a long lead time for the resultant data. Wind tunnel tests are also limited to the preselected control effectors of the model. To overcome these shortcomings, computational fluid dynamics (CFD) solvers are augmented via automatic differentiation, to directly calculate the stability and control derivatives. The CFD forces and moments are differentiated with respect to angle of attack, angle of sideslip, and aircraft shape parameters to form these derivatives. A subset of static stability and control derivatives of a tailless aircraft concept have been computed by two differentiated inviscid CFD codes and verified for accuracy with central finite-difference approximations and favorable comparisons to a simulation database.

Park, Michael A.↗
NASA NTRS1991

Precise automatic differential stellar photometry

The factors limiting the precision of differential stellar photometry are reviewed. Errors due to variable atmospheric extinction can be reduced to below 0.001 mag at good sites by utilizing the speed of robotic telescopes. Existing photometric systems produce aliasing errors, which are several millimagnitudes in general but may be reduced to about a millimagnitude in special circumstances. Conventional differential photometry neglects several other important effects, which are discussed in detail. If all of these are properly handled, it appears possible to do differential photometry of variable stars with an overall precision of 0.001 mag with ground based robotic telescopes.

Young, Andrew T.↗
NASA NTRS2021

Adaptive Data Screening for Multi-Angle Polarimetric Aerosol and Ocean Color Remote Sensing Accelerated by Automatic Differentiation

Remote sensing measurements from multi-angle polarimeters (MAPs) contain rich aerosol microphysical property information, and these sensors have been used to perform retrievals in optically complex atmosphere and ocean systems. Previous studies have concluded that, generally, five moderately separated viewing angles in each spectral band provide sufficient accuracy for aerosol property retrievals, with performance gradually saturating as angles are added above that threshold. The Hyper-Angular Rainbow Polarimeter (HARP) instruments provide high angular sampling with a total of 90-120 unique angles across four bands, a capability developed mainly for liquid cloud retrievals. In practice, not all view angles are optimal for aerosol retrievals due to impacts of clouds, sun glint, and other impediments. The many viewing angles of HARP can provide resilience to these effects, if the impacted views are screened from the dataset, as the remaining views may be sufficient for successful analysis. In this study, we discuss how the number of available viewing angles impacts aerosol and ocean color retrieval uncertainties, as applied to two versions of the HARP instrument. AirHARP is an airborne prototype that was deployed in the ACEPOL field campaign, while HARP2 is an instrument in development for the upcoming NASA Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission. Based on synthetic data, we find that a total of 20-30 angles across all bands (i.e. five to eight viewing angles per band) are sufficient to achieve good retrieval performance. Following from this result, we develop an adaptive multi-angle polarimetric data screening (MAPDS) approach to evaluate data quality by comparing measurements with their best-fitted forward model. The FastMAPOL retrieval algorithm is used to retrieve scene geophysical values, by matching an efficient, deep learning-based, radiative transfer emulator to observations. The data screening method effectively identifies and removes viewing angles affected by thin cirrus clouds and other anomalies, improving retrieval performance. This was tested with AirHARP data, and we found agreement with the High Spectral Resolution Lidar-2 (HSRL-2) aerosol data. The data screening approach can be applied to modern satellite remote sensing missions, such as PACE, where a large amount of multi-angle, hyperspectral, polarimetric measurements will be collected.

multi-angle polarimeter↗
NASA NTRS1998

Optimization Issues with Complex Rotorcraft Comprehensive Analysis

This paper investigates the use of the general purpose automatic differentiation (AD) tool called Automatic Differentiation of FORTRAN (ADIFOR) as a means of generating sensitivity derivatives for use in Boeing Helicopter's proprietary comprehensive rotor analysis code (VII). ADIFOR transforms an existing computer program into a new program that performs a sensitivity analysis in addition to the original analysis. In this study both the pros (exact derivatives, no step-size problems) and cons (more CPU, more memory) of ADIFOR are discussed. The size (based on the number of lines) of the VII code after ADIFOR processing increased by 70 percent and resulted in substantial computer memory requirements at execution. The ADIFOR derivatives took about 75 percent longer to compute than the finite-difference derivatives. However, the ADIFOR derivatives are exact and are not functions of step-size. The VII sensitivity derivatives generated by ADIFOR are compared with finite-difference derivatives. The ADIFOR and finite-difference derivatives are used in three optimization schemes to solve a low vibration rotor design problem.

Walsh, Joanne L.↗