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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. Part 1: The ODE connection and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗
NASA NTRS1990

Differential Sampling For Fast Acquisition Of Frequency

Algorithm rapidly estimates frequency of sinusoidal signal corrupted by zero-mean, additive, white Gaussian noise. Incorporates differential mathematical model of signal, cyclic sampling of signal, and least-squares best-estimate criterion. Adapts to changing signal frequency. Amount of computation required to obtain estimate increases only linearly with number of successive measurements processed.

Kumar, Rajendra↗
NASA NTRS2003

New Total Ozone Algorithm for Application to the Total Ozone Mapping Spectrometer

The Total Ozone Mapping Spectrometer (TOMS) series comprises four instruments providing a total of 25 years of daily global stratospheric ozone data over the sunlit portion of the Earth. A new retrieval algorithm has been developed for TOMS, designated Version 8. The algorithm is based on differential absorption across a pair of wavelength channels chosen close together to minimize the impact of wavelength dependent forward modeling errors. Version 8 enhancements include correction for the presence of tropospheric aerosols and sun glint from water surfaces, a better treatment of variability due to tropospheric ozone and temperature dependence, and an improved forward model, particularly in regions of persistent snow and ice. Among other things, the Version 8 enhancements have reduced latitudinal dependence seen previously in TOMS - Dobson comparisons, predominantly in the Southern Hemisphere's summer, when the tropospheric ozone, temperature, and snow/ice corrections are additive. The basic components of the algorithm and its impact on derived total ozone will be discussed.

Wellemeyer, C.↗
NASA NTRS1974

Arbitrarily Curved and Twisted Space Beams

A derivation of the equations which govern the deformation of an arbitrarily curved and twisted space beam is presented. These equations differ from those of the classical theory in that (1) extensional effects are included; (2) the strain-displacement relations are derived; and (3) the expressions for the stress resultants are developed from the strain displacement relations. It is shown that the torsional stress resultant obtained by the classical approach is basically incorrect except when the cross-section is circular. The governing equations are given in the form of first-order differential equations. A numerical algorithm is given for obtaining the natural vibration characteristics and example problems are presented.

Hunter, W. F.↗
NASA NTRS1982

Comment on 'Time-optimal orbit transfer trajectory for solar sail spacecraft'

An analytic proof is presented to show that the orbital transfer times of an earth-to-Mars solar-sail propelled spacecraft trajectory as calculated by Jayaraman (1980) are incorrect. In particular, different boundary conditions are defined, which indicate that a minimization of the Hamiltonian, which Jayaraman used, can yield the wrong stationary solution. Transfer times are calculated using a neighboring extremal algorithm based on numerical differentiation in conjunction with Krogh's variable order, variable step size integrator, resulting in a transfer time of 322 days at 2 mm/sec-sq, with endpoint restraints satisfied to within 1/1 billion. Finally, it is concluded that minimization of flight time is secondary in importance to maximization of delivered payload and minimization of overall mission cost and risk.

Wood, L. J.↗
NASA NTRS1982

Grid generation by elliptic partial differential equations for a tri-element Augmentor-Wing airfoil

Two efforts to numerically simulate the flow about the Augmentor-Wing airfoil in the cruise configuration using the GRAPE elliptic partial differential equation grid generator algorithm are discussed. The Augmentor-Wing consists of a main airfoil with a slotted trailing edge for blowing and two smaller airfoils shrouding the blowing jet. The airfoil and the algorithm are described, and the application of GRAPE to an unsteady viscous flow simulation and a transonic full-potential approach is considered. The procedure involves dividing a complicated flow region into an arbitrary number of zones and ensuring continuity of grid lines, their slopes, and their point distributions across the zonal boundaries. The method for distributing the body-surface grid points is discussed.

Sorenson, R. L.↗
NASA NTRS1985

Transonic separated solutions for an augmentor-wing

The viscous transonic flow about a multielement airfoil (augmentor-wing) is simulated by coupling full-potential and direct/inverse differential boundary-layer algorithms. Solutions have been obtained for a variety of conditions and are in fair agreement with available experimental data. Typical results from this transonic augmentor-wing code (TAUG-V) require approximately three minutes of CRAY-XMP CPU time. Since this viscous transonic code accounts for most of the important flow physics, yet is still economical, it is a practical tool for the design aerodynamicist.

Flores, J.↗
NASA NTRS1987

A numerical solution of Duffing's equations including the prediction of jump phenomena

Numerical methodology for the solution of Duffing's differential equation is presented. Algorithms for the prediction of multiple equilibrium solutions and jump phenomena are developed. In addition, a filtering algorithm for producing steady state solutions is presented. The problem of a rigidly clamped circular plate subjected to cosinusoidal pressure loading is solved using the developed algorithms (the plate is assumed to be in the geometrically nonlinear range). The results accurately predict regions of solution multiplicity and jump phenomena.

Moyer, E. T., Jr.↗
NASA NTRS1990

Multistage estimation of received carrier signal parameters under very high dynamic conditions of the receiver

A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.

Kumar, Rajendra↗
NASA NTRS1994

A mathematical model for simulating noise suppression of lined ejectors

A mathematical model containing the essential features embodied in the noise suppression of lined ejectors is presented. Although some simplification of the physics is necessary to render the model mathematically tractable, the current model is the most versatile and technologically advanced at the current time. A system of linearized equations and the boundary conditions governing the sound field are derived starting from the equations of fluid dynamics. A nonreflecting boundary condition is developed. In view of the complex nature of the equations, a parametric study requires the use of numerical techniques and modern computers. A finite element algorithm that solves the differential equations coupled with the boundary condition is then introduced. The numerical method results in a matrix equation with several hundred thousand degrees of freedom that is solved efficiently on a supercomputer. The model is validated by comparing results either with exact solutions or with approximate solutions from other works. In each case, excellent correlations are obtained. The usefulness of the model as an optimization tool and the importance of variable impedance liners as a mechanism for achieving broadband suppression within a lined ejector are demonstrated.

Watson, Willie R.↗
NASA NTRS1991

Multistage estimation of received carrier signal parameters under very high dynamic conditions of the receiver

A multistage estimator is provided for the parameters of a received carrier signal possibly phase-modulated by unknown data and experiencing very high Doppler, Doppler rate, etc., as may arise, for example, in the case of Global Positioning Systems (GPS) where the signal parameters are directly related to the position, velocity and jerk of the GPS ground-based receiver. In a two-stage embodiment of the more general multistage scheme, the first stage, selected to be a modified least squares algorithm referred to as differential least squares (DLS), operates as a coarse estimator resulting in higher rms estimation errors but with a relatively small probability of the frequency estimation error exceeding one-half of the sampling frequency, provides relatively coarse estimates of the frequency and its derivatives. The second stage of the estimator, an extended Kalman filter (EKF), operates on the error signal available from the first stage refining the overall estimates of the phase along with a more refined estimate of frequency as well and in the process also reduces the number of cycle slips.

Kumar, Rajendra↗
NASA NTRS2020

Design of Autonomous Medical Response Agent (AMRA) Aggregate Information Dashboard (AID)

Future astronauts in deep space missions will rely on tools and technologies empowering them to self-diagnose and self-treat medical conditions. Given communications delays and limited bandwidth in future long-duration exploration missions (LDEMs), medical decision support technologies must empower the crew to manage routine medical activities, acute medical incidents, as well as emergency medical scenarios independently from ground support.The Autonomous Medical Response Agent (AMRA) is envisioned as a digital tool enabling crew to issue medical complaints and interact with a medical decision support algorithm which develops a differential diagnosis and recommends a treatment protocol for the condition. AMRA will draw from individual crew medical history in addition to crew symptoms to more efficiently identify high-risk medical conditions. A new symptom could be indicative of a chronic condition or a normal adaptation to long-duration spaceflight, but could just as easily be indicative of an adverse vehicle condition affecting the entire crew.While real-time communication with a flight surgeon may not possible, the crew will nonetheless require a means to communicate and document both routine and emergency medical incidents to ground support. Conversely, flight surgeons and medical specialists on the ground will need to understand information such as crew vitals or responses to medical check-ups and examinations within the larger context of crew schedule, mission activities, and vehicle performance. A user interface which establishes communication protocols between an individual crew member and AMRA, as well as ground support to the crew is a significant area of research demanding input and consideration.The design of AMRA AID is intended to: a) represent routine medical activities as well as new (unplanned) medical incidents within the larger context of crew schedule and mission activities, and b) increase confidence between ground support and crew members over the course of LDEMs. Maintaining situation awareness of unplanned medical incidents between ground and crew will be a critical element within LDEMs. Two medical incidents headache and difficulty breathing are being explored within a user interface prototype which captures communications protocols between crew members and mission control, human health monitoring, vehicle or environmental monitoring, as well as crew schedule and mission activities holistically.

Yashar, M.↗
NASA NTRS2020

Application of Sparse Identification of Nonlinear Dynamics for Physics-Informed Learning

Advances in machine learning and deep neural networks has enabled complex engineering tasks like image recognition, anomaly detection, regression, and multi-objective optimization, to name but a few. The complexity of the algorithm architecture, e.g., the number of hidden layers in a deep neural network, typically grows with the complexity of the problems they are required to solve, leaving little room for interpreting (or explaining) the path that results in a specific solution. This drawback is particularly relevant for autonomous aerospace and aviation systems, where certifications require a complete understanding of the algorithm behavior in all possible scenarios. Including physics knowledge in such data-driven tools may improve the interpretability of the algorithms, thus enhancing model validation against events with low probability but relevant for system certification. Such events include, for example, spacecraft or aircraft sub-system failures, for which data may not be available in the training phase. This paper investigates a recent physics-informed learning algorithm for identification of system dynamics, and shows how the governing equations of a system can be extracted from data using sparse regression. The learned relationships can be utilized as a surrogate model which, unlike typical data-driven surrogate models, relies on the learned underlying dynamics of the system rather than large number of fitting parameters. The work shows that the algorithm can reconstruct the differential equations underlying the observed dynamics using a single trajectory when no uncertainty is involved. However, the training set size must increase when dealing with stochastic systems, e.g., nonlinear dynamics with random initial conditions.

Corbetta, Matteo↗
NASA NTRS1995

Spectral identification of minerals using imaging spectrometry data: Evaluating the effects of signal to noise and spectral resolution using the tricorder algorithm

The rapid development of sophisticated imaging spectrometers and resulting flood of imaging spectrometry data has prompted a rapid parallel development of spectral-information extraction technology. Even though these extraction techniques have evolved along different lines (band-shape fitting, endmember unmixing, near-infrared analysis, neural-network fitting, and expert systems to name a few), all are limited by the spectrometer's signal to noise (S/N) and spectral resolution in producing useful information. This study grew from a need to quantitatively determine what effects these parameters have on our ability to differentiate between mineral absorption features using a band-shape fitting algorithm. We chose to evaluate the AVIRIS, HYDICE, MIVIS, GERIS, VIMS, NIMS, and ASTER instruments because they collect data over wide S/N and spectral-resolution ranges. The study evaluates the performance of the Tricorder algorithm, in differentiating between mineral spectra in the 0.4-2.5 micrometer spectral region. The strength of the Tricorder algorithm is in its ability to produce an easily understood comparison of band shape that can concentrate on small relevant portions of the spectra, giving it an advantage over most unmixing schemes, and in that it need not spend large amounts of time reoptimizing each time a new mineral component is added to its reference library, as is the case with neural-network schemes. We believe the flexibility of the Tricorder algorithm is unparalleled among spectral-extraction techniques and that the results from this study, although dealing with minerals, will have direct applications to spectral identification in other disciplines.

Swayze, Gregg A.↗
NASA NTRS1991

Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I - The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics

Spurious stable as well as unstable steady state numerical solutions, spurious asymptotic numerical solutions of higher period, and even stable chaotic behavior can occur when finite difference methods are used to solve nonlinear differential equations (DE) numerically. The occurrence of spurious asymptotes is independent of whether the DE possesses a unique steady state or has additional periodic solutions and/or exhibits chaotic phenomena. The form of the nonlinear DEs and the type of numerical schemes are the determining factor. In addition, the occurrence of spurious steady states is not restricted to the time steps that are beyond the linearized stability limit of the scheme. In many instances, it can occur below the linearized stability limit. Therefore, it is essential for practitioners in computational sciences to be knowledgeable about the dynamical behavior of finite difference methods for nonlinear scalar DEs before the actual application of these methods to practical computations. It is also important to change the traditional way of thinking and practices when dealing with genuinely nonlinear problems. In the past, spurious asymptotes were observed in numerical computations but tended to be ignored because they all were assumed to lie beyond the linearized stability limits of the time step parameter delta t. As can be seen from the study, bifurcations to and from spurious asymptotic solutions and transitions to computational instability not only are highly scheme dependent and problem dependent, but also initial data and boundary condition dependent, and not limited to time steps that are beyond the linearized stability limit.

Yee, H. C.↗
NASA NTRS1979

Numerical methods of solving a system of multi-dimensional nonlinear equations of the diffusion type

The principles of conservation and stability of difference schemes achieved using the iteration control method were examined. For the schemes obtained of the predictor-corrector type, the conversion was proved for the control sequences of approximate solutions to the precise solutions in the Sobolev metrics. Algorithms were developed for reducing the differential problem to integral relationships, whose solution methods are known, were designed. The algorithms for the problem solution are classified depending on the non-linearity of the diffusion coefficients, and practical recommendations for their effective use are given.

Agapov, A. V.↗