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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A study on the sensitivity and simultaneous adjustment of a hoop-column antenna surface

The results of a recent surface adjustment of the 15-meter diameter hoop-column antenna are presented. A least-squares differential algorithm is used to adjust the surface shape as close as possible to a perfect parabola. Since the desired perfect parabola is not uniquely known a priori, parameters of the perfect parabola are included in the design vector along with the cable length changes. As an extension to an earlier study, lateral sensitivity is included in the least-squares adjustment procedure. In addition, the effect of cable length uncertainties on the surface RMS error is considered and an error bound is derived. The results in this study indicate an improvement over earlier studies. The sensitivity analysis provided a quantitative measure of the needed accuracy of the cable adjustments in the laboratory. Recommendations are included to further enhance shape adjustment.

Lim, Kyong Been↗
NASA NTRS2018

Solar Sail Transfers from Invariant Objects to L5 Periodic Orbits

The rising interest in a mission to the Sun-Earth L5 point for heliophysics or Trojan asteroid search and the development of solar sails has opened the question of using solar radiation pressure for such a mission. Different solar sail trajectories to the Sun-Earth L5 point are constructed. Different invariant objects in the neighbourhood of Earth are considered for departure: equilibrium points, families of periodic orbits and their associated invariant manifold. Using a multi-objective genetic algorithm, differential correction and the optimal control solver PSOPT the transfers are obtained. The approach followed results in fast solar sail transfers which can be used for the preliminary design of a mission to the Sun-Earth L5 point.

Fernandez, Alvaro↗
NASA NTRSDate not supplied

Toward Adjoint-Based Aeroacoustic Optimization for Propeller and Rotorcraft Applications

The goal of the present project is to build a multidisciplinary, rapid, robust, and accurate computational tool to optimize wing-mounted propeller designs. The full Farassat’s formulation F1Afor aeroacoustic analysis is implemented in the open-source software SU2.This extension enables the prediction of far-field noise generated by moving sources. The formulation is verified, for a stationary and rotating sphere in a wind tunnel and for a tiltrotor in forward flight, by comparing the acoustic predictions ofSU2 with the predictions computed by NASA’s aeroacoustics code ANOPP2. The algorithmic differentiation capability of SU2 provides discretely consistent, adjoint-based sensitivity analysis for this formulation. The adjoint-based sensitivities are verified through comparison with complex-step sensitivities

R Omur Icke↗
NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

An optimization capability is developed for acoustic scattering and shielding of installed propellers and rotors, based on a spacetime Galerkin time domain boundary element method (TDBEM). The time domain approach is particularly suitable for efficient simulation of transient, rotating, and broadband noise sources such as propellers. The use of algorithmic differentiation allows efficient evaluation of design sensitivities required for gradient-based design optimization with a large number of design variables. We present a validation exercise for the coherent broadband scattering capability against an analytical solution, showing excellent agreement. We then demonstrate the optimization tool on a series of inverse design cases with broadband and rotating sources, as well as an optimization problem for a propeller-wing configuration. The results show good performance for optimization problems with the characteristics of realistic installed propeller configurations.

Maks J Groom↗
NASA NTRSDate not supplied

Aeroacoustic Optimization of Installed Propeller Configurations with Scattering and Shielding Effects

An optimization capability is developed for acoustic scattering and shielding of installed propellers and rotors, based on a spacetime Galerkin time domain boundary element method (TDBEM). The time domain approach is particularly suitable for efficient simulation of transient, rotating, and broadband noise sources such as propellers. The use of algorithmic differentiation allows efficient evaluation of design sensitivities required for gradient-based design optimization with a large number of design variables. We present a validation exercise for the coherent broadband scattering capability against an analytical solution, showing excellent agreement. We then demonstrate the optimization tool on a series of inverse design cases with broadband and rotating sources, as well as an optimization problem for a propeller-wing configuration. The results show good performance for optimization problems with the characteristics of realistic installed propeller configurations.

Maks J Groom↗
NASA NTRS1994

A real-time algorithm for integrating differential satellite and inertial navigation information during helicopter approach

A real-time, high-rate precision navigation Kalman filter algorithm is developed and analyzed. This Navigation algorithm blends various navigation data collected during terminal area approach of an instrumented helicopter. Navigation data collected include helicopter position and velocity from a global position system in differential mode (DGPS) as well as helicopter velocity and attitude from an inertial navigation system (INS). The goal of the Navigation algorithm is to increase the DGPS accuracy while producing navigational data at the 64 Hertz INS update rate. It is important to note that while the data was post flight processed, the Navigation algorithm was designed for real-time analysis. The design of the Navigation algorithm resulted in a nine-state Kalman filter. The Kalman filter's state matrix contains position, velocity, and velocity bias components. The filter updates positional readings with DGPS position, INS velocity, and velocity bias information. In addition, the filter incorporates a sporadic data rejection scheme. This relatively simple model met and exceeded the ten meter absolute positional requirement. The Navigation algorithm results were compared with truth data derived from a laser tracker. The helicopter flight profile included terminal glideslope angles of 3, 6, and 9 degrees. Two flight segments extracted during each terminal approach were used to evaluate the Navigation algorithm. The first segment recorded small dynamic maneuver in the lateral plane while motion in the vertical plane was recorded by the second segment. The longitudinal, lateral, and vertical averaged positional accuracies for all three glideslope approaches are as follows (mean plus or minus two standard deviations in meters): longitudinal (-0.03 plus or minus 1.41), lateral (-1.29 plus or minus 2.36), and vertical (-0.76 plus or minus 2.05).

Hoang, TY↗
NASA NTRS1994

A Real-Time Algorithm for Integrating Differential Satellite and Inertial Navigation Information During Helicopter Approach

A real-time, high-rate precision navigation Kalman filter algorithm is developed and analyzed. This navigation algorithm blends various navigation data collected during terminal area approach of an instrumented helicopter. Navigation data collected include helicopter position and velocity from a global position system in differential mode (DGPS) as well as helicopter velocity and attitude from an inertial navigation system (INS). The goal of the navigation algorithm is to increase the DGPS accuracy while producing navigational data at the 64 Hertz INS update rate. It is important to note that while the data was post flight processed, the navigation algorithm was designed for real-time analysis. The design of the navigation algorithm resulted in a nine-state Kalman filter. The Kalman filter's state matrix contains position, velocity, and velocity bias components. The filter updates positional readings with DGPS position, INS velocity, and velocity bias information. In addition, the filter incorporates a sporadic data rejection scheme. This relatively simple model met and exceeded the ten meter absolute positional requirement. The navigation algorithm results were compared with truth data derived from a laser tracker. The helicopter flight profile included terminal glideslope angles of 3, 6, and 9 degrees. Two flight segments extracted during each terminal approach were used to evaluate the navigation algorithm. The first segment recorded small dynamic maneuver in the lateral plane while motion in file vertical plane was recorded by the second segment. The longitudinal, lateral, and vertical averaged positional accuracies for all three glideslope approaches are as follows (mean +/- two standard deviations in meters): longitudinal (-0.03 +/- 1.41), lateral (-1.29 +/- 2.36), and vertical (-0.76 +/- 2.05).

Hoang, Ty↗
DOE OSTI2025

Energy-momentum-conserving stochastic differential equations and algorithms for the nonlinear Landau-Fokker-Planck equation

Coulomb collision is a fundamental diffusion process in plasmas that can be described by the Landau-Fokker-Planck (LFP) equation or the stochastic differential equation (SDE). While energy and momentum are conserved exactly in the LFP equation, they are conserved only on average by the conventional corresponding SDEs, suggesting that the underlying stochastic process may not be well defined by such SDEs. Here, in this study, we derive new SDEs with exact energy-momentum conservation for the Coulomb collision by factorizing the collective effect of field particles into individual particles and enforcing Newton's third law. These SDEs, when interpreted in the Stratonovich sense, have a particularly simple form that represents pure diffusion between particles without drag. To demonstrate that the new SDEs correspond to the LFP equation, we develop numerical algorithms that converge to the SDEs and preserve discrete conservation laws. Simulation results are presented in a benchmark of various relaxation processes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Spectrally accurate, reverse-mode differentiable bounce-averaging algorithm and its applications

We present a fast, spectrally (exponentially) accurate, automatically differentiable bounce-averaging algorithm that is used to simplify kinetic models. Using this algorithm, implemented in the DESC stellarator optimisation suite, we can perform efficient optimisation of many objectives to improve stellarator performance, such as the effective ripple 𝜖 eff metric for the neoclassical transport coefficient in the low collisionality regime and proxies for energetic particle confinement. For the first time, we optimise a finite-beta stellarator to directly reduce neoclassical ripple transport using reverse-mode differentiation. This ensures the computational cost of differentiation is independent of the number of controllable parameters.

fusion plasma↗
NASA NTRS1972

DDA realizations of attitude algorithms.

Digital differential analyzer (DDA) realization of the direction cosine, Euler angle, and quaternion algorithms. It is shown that, for any one of the three attitude algorithms, 27 DDAs are needed. This number is considerably smaller than those obtained by others for the cases of Euler angle and quaternion algorithms.

Yeh, Y.↗
NASA NTRS1985

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, J. H.↗
NASA NTRS1988

Towards developing robust algorithms for solving partial differential equations on MIMD machines

Methods for efficient computation of numerical algorithms on a wide variety of MIMD machines are proposed. These techniques reorganize the data dependency patterns to improve the processor utilization. The model problem finds the time-accurate solution to a parabolic partial differential equation discretized in space and implicitly marched forward in time. The algorithms are extensions of Jacobi and SOR. The extensions consist of iterating over a window of several timesteps, allowing efficient overlap of computation with communication. The methods increase the degree to which work can be performed while data are communicated between processors. The effect of the window size and of domain partitioning on the system performance is examined both by implementing the algorithm on a simulated multiprocessor system.

Saltz, Joel H.↗
DOE OSTI2024

Parallel Variable Population Multi-Objective Optimizer (pvpmoo) v1.0

This is a parallel variable population multi-objective optimizer with an adaptive unified differential evolution algorithm or a genetic algorithm. It can also be used for single objective optimization. Some features of this code include: 1) The population size varies from generation to generation to save the total # of objective function evaluations. 2) The population is uniformly distributed to a number of parallel processors for simultaneous objective function evaluation. 3) The objective function evaluation can be attained from an external simulation program with control variables in its input file and objectives calculated from its output files. 4) The optimizer includes an adaptive unified differential evolution algorithm and a real value genetic algorithm. The parameters in the unified differential evolution algorithm can be chosen to attain any mutation schemes in the published literature.

Qiang, Ji↗
NASA NTRS1975

A least mean squares CUBIC algorithm for on-line differential of sampled analog signals

A digital computer algorithm is developed for on-line time differentiation of sampled analog voltage signals. The derivative is obtained by employing a least mean squares technique. The recursive algorithm results in a considerable reduction in computer time compared to a complete new solution of the normal equations each time a new data point is accepted. Implementation of the algorithm on a digital computer is discussed. Examples are simulated on a DEC PDP-8 computer.

Allum, J. H. J.↗
NASA NTRS1981

Symbolic Solution of Linear Differential Equations

An algorithm for solving linear constant-coefficient ordinary differential equations is presented. The computational complexity of the algorithm is discussed and its implementation in the FORMAC system is described. A comparison is made between the algorithm and some classical algorithms for solving differential equations.

Feinberg, R. B.↗