Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Sliding Mode Control of the X-33 with an Engine Failure

Ascent flight control of the X-3 is performed using two XRS-2200 linear aerospike engines. in addition to aerosurfaces. The baseline control algorithms are PID with gain scheduling. Flight control using an innovative method. Sliding Mode Control. is presented for nominal and engine failed modes of flight. An easy to implement, robust controller. requiring no reconfiguration or gain scheduling is demonstrated through high fidelity flight simulations. The proposed sliding mode controller utilizes a two-loop structure and provides robust. de-coupled tracking of both orientation angle command profiles and angular rate command profiles in the presence of engine failure, bounded external disturbances (wind gusts) and uncertain matrix of inertia. Sliding mode control causes the angular rate and orientation angle tracking error dynamics to be constrained to linear, de-coupled, homogeneous, and vector valued differential equations with desired eigenvalues. Conditions that restrict engine failures to robustness domain of the sliding mode controller are derived. Overall stability of a two-loop flight control system is assessed. Simulation results show that the designed controller provides robust, accurate, de-coupled tracking of the orientation angle command profiles in the presence of external disturbances and vehicle inertia uncertainties, as well as the single engine failed case. The designed robust controller will significantly reduce the time and cost associated with flying new trajectory profiles or orbits, with new payloads, and with modified vehicles

Shtessel, Yuri B.↗
NASA NTRS1981

Numerical algorithms for finite element computations on arrays of microprocessors

The development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.

Ortega, J. M.↗
NASA NTRS1990

Digital halftoning methods for selectively partitioning error into achromatic and chromatic channels

A method is described for reducing the visibility of artifacts arising in the display of quantized color images on CRT displays. The method is based on the differential spatial sensitivity of the human visual system to chromatic and achromatic modulations. Because the visual system has the highest spatial and temporal acuity for the luminance component of an image, a technique which will reduce luminance artifacts at the expense of introducing high-frequency chromatic errors is sought. A method based on controlling the correlations between the quantization errors in the individual phosphor images is explored. The luminance component is greatest when the phosphor errors are positively correlated, and is minimized when the phosphor errors are negatively correlated. The greatest effect of the correlation is obtained when the intensity quantization step sizes of the individual phosphors have equal luminances. For the ordered dither algorithm, a version of the method can be implemented by simply inverting the matrix of thresholds for one of the color components.

Mulligan, Jeffrey B.↗
NASA NTRS2003

Efficient Processing of Data for Locating Lightning Strikes

Two algorithms have been devised to increase the efficiency of processing of data in lightning detection and ranging (LDAR) systems so as to enable the accurate location of lightning strikes in real time. In LDAR, the location of a lightning strike is calculated by solving equations for the differences among the times of arrival (DTOAs) of the lightning signals at multiple antennas as functions of the locations of the antennas and the speed of light. The most difficult part of the problem is computing the DTOAs from digitized versions of the signals received by the various antennas. One way (a time-domain approach) to determine the DTOAs is to compute cross-correlations among variously differentially delayed replicas of the digitized signals and to select, as the DTOAs, those differential delays that yield the maximum correlations. Another way (a frequency-domain approach) to determine the DTOAs involves the computation of cross-correlations among Fourier transforms of variously differentially phased replicas of the digitized signals, along with utilization of the relationship among phase difference, time delay, and frequency.

Medelius, Pedro J.↗
NASA NTRS1992

Airborne gravimetry, altimetry, and GPS navigation errors

Proper interpretation of airborne gravimetry and altimetry requires good knowledge of aircraft trajectory. Recent advances in precise navigation with differential GPS have made it possible to measure gravity from the air with accuracies of a few milligals, and to obtain altimeter profiles of terrain or sea surface correct to one decimeter. These developments are opening otherwise inaccessible regions to detailed geophysical mapping. Navigation with GPS presents some problems that grow worse with increasing distance from a fixed receiver: the effect of errors in tropospheric refraction correction, GPS ephemerides, and the coordinates of the fixed receivers. Ionospheric refraction and orbit error complicate ambiguity resolution. Optimal navigation should treat all error sources as unknowns, together with the instantaneous vehicle position. To do so, fast and reliable numerical techniques are needed: efficient and stable Kalman filter-smoother algorithms, together with data compression and, sometimes, the use of simplified dynamics.

Colombo, Oscar L.↗
NASA NTRS1982

Geometrically derived difference formulae for the numerical integration of trajectory problems

An initial value problem for the autonomous system of ordinary differential equations dy/dt = f(y), where y is a vector, is considered. In a number of practical applications the interest lies in obtaining the curve traced by the solution y. These applications include the computation of trajectories in mechanical problems. The term 'trajectory problem' is employed to refer to these cases. Lambert and McLeod (1979) have introduced a method involving local rotation of the axes in the y-plane for the two-dimensional case. The present investigation continues the study of difference schemes specifically derived for trajectory problems. A simple geometrical way of constructing such methods is presented, and the local accuracy of the schemes is investigated. A circularly exact, fixed-step predictor-corrector algorithm is defined, and a variable-step version of a circularly exact algorithm is presented.

Mcleod, R. J. Y.↗
NASA NTRSDate not supplied

A Generalized, Compactly-Supported Correlation Function for Data Assimilation Applications

Correlation functions play an essential role in modern data assimilation, where they are used to model covariances given a set of tunable parameters or applied as tapering functions to localize covariances in ensemble-based schemes. One of the most widely-used correlation functions in data assimilation is the Gaspari and Cohn (1999) piecewise-rational, compactly-supported parametric correlation function (hereafter referred to as GC99). The GC99 correlation function is useful due to its tunable cut-off parameter c and Gaussian-like shape achieved when the parameter a is set to one-half. These properties are attractive for tapering functions in data assimilation applications. However, the GC99 correlation function is homogeneous over Euclidean 3-space and isotropic when restricted to the sphere, properties that may be less than ideal for some geophysical applications. GC99 is also compactly-supported on a sphere of fixed radius, which requires tuning of the cut-off parameter c that can depend on the specific application. This work presents a generalization of the GC99 correlation function that allows the cut-off parameter c and shape parameter a to vary over space to gain more flexibility in shape while maintaining its compact support property. The function, which we call the Generalized Gaspari Cohn (GenGC) correlation function, introduces inhomogeneity in Euclidean 3-space and anisotropy when restricted to the sphere by allowing both parameters c and a to vary, as functions, over the spatial domain. The GC99 correlation function is a special case of GenGC where the functions c and a are held constant, as fixed parameters rather than functions. The GenGC correlation function also generalizes the follow-on to the work of Gaspari and Cohn (1999) presented in Gaspari et al. (2006), which allowed a to vary while keeping c fixed. We illustrate through simple one- and two-dimensional examples the variety of inhomogeneous and anisotropic correlation functions GenGC can produce by varying c and a over space, and suggest applications where they may be useful in data assimilation, such as covariance modeling or localization. In particular, we describe how the GenGC correlation function can be used to construct covariances using correlation length and variance fields derived from dynamics. For example, the correlation length field for advective dynamics is governed by a partial differential equation (PDE) in N spatial dimensions, where N is the number of space dimensions of the state. Correlation length fields can be determined from this PDE and used with GenGC to construct the corresponding correlations. We can then approximate the full covariance by rescaling by the variance, which also satisfies a PDE in N spatial dimensions for advective dynamics. Thus we can approximate the full covariance without solving the covariance PDE, which is in 2N spatial dimensions, by solving just two PDEs each in only N spatial dimensions. This approach to evolving the correlation length and variance fields, then reconstructing the correlations using GenGC, is suggested as an alternative to current methods of covariance modeling in data assimilation algorithms.

GC99↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
NASA NTRS1983

Measurement of ultrasonic fields in transparent media using a scanning differential interferometer

An experimental system for the detection of three dimensional acoustic fields in optically transparent media using a dual beam differential interferometer is described. In this system, two coherent, parallel, focused laser beams are passed through the specimen and the interference fringe pattern which results when these beams are combined shifts linearly by an amount which is related to the optical pathlength difference between the two beams. It is shown that for small signals, the detector output is directly proportional to the amplitude of the acoustic field integrated along the optical beam path through the specimen. A water tank and motorized optical platform were constructed to allow these dual beams to be scanned through an ultrasonic field generated by a piezoelectric transducer at various distances from the transducer. Scan data for the near, Fresnel, and far zones of a uniform, circular transducer are presented and an algorithm for constructing the radial field profile from this integrated optical data, assuming cylindrical symmetry, is described.

Dockery, G. D.↗
NASA NTRS1988

A feedback linearization approach to spacecraft control using momentum exchange devices

Recent developments in the area of nonlinear control theory have shown how coordiante changes in the state and input spaces can be used with nonlinear feedback to transform certain nonlinear ordinary differential equations into equivalent linear equations. These feedback linearization techniques are applied to resolve two problems arising in the control of spacecraft equipped with control moment gyroscopes (CMGs). The first application involves the computation of rate commands for the gimbals that rotate the individual gyroscopes to produce commanded torques on the spacecraft. The second application is to the long-term management of stored momentum in the system of control moment gyroscopes using environmental torques acting on the vehicle. An approach to distributing control effort among a group of redundant actuators is described that uses feedback linearization techniques to parameterize sets of controls which influence a specified subsystem in a desired way. The approach is adapted for use in spacecraft control with double-gimballed gyroscopes to produce an algorithm that avoids problematic gimbal configurations by approximating sets of gimbal rates that drive CMG rotors into desirable configurations. The momentum management problem is stated as a trajectory optimization problem with a nonlinear dynamical constraint. Feedback linearization and collocation are used to transform this problem into an unconstrainted nonlinear program. The approach to trajectory optimization is fast and robust. A number of examples are presented showing applications to the proposed NASA space station.

Dzielski, John Edward↗
NASA NTRS1988

Adaptive independent joint control of manipulators - Theory and experiment

The author presents a simple decentralized adaptive control scheme for multijoint robot manipulators based on the independent joint control concept. The proposed control scheme for each joint consists of a PID (proportional integral and differential) feedback controller and a position-velocity-acceleration feedforward controller, both with adjustable gains. The static and dynamic couplings that exist between the joint motions are compensated by the adaptive independent joint controllers while ensuring trajectory tracking. The proposed scheme is implemented on a MicroVAX II computer for motion control of the first three joints of a PUMA 560 arm. Experimental results are presented to demonstrate that trajectory tracking is achieved despite strongly coupled, highly nonlinear joint dynamics. The results confirm that the proposed decentralized adaptive control of manipulators is feasible, in spite of strong interactions between joint motions. The control scheme presented is computationally very fast and is amenable to parallel processing implementation within a distributed computing architecture, where each joint is controlled independently by a simple algorithm on a dedicated microprocessor.

Seraji, H.↗
NASA NTRS1991

Data analysis using scale-space filtering and Bayesian probabilistic reasoning

This paper describes a program for analysis of output curves from Differential Thermal Analyzer (DTA). The program first extracts probabilistic qualitative features from a DTA curve of a soil sample, and then uses Bayesian probabilistic reasoning to infer the mineral in the soil. The qualifier module employs a simple and efficient extension of scale-space filtering suitable for handling DTA data. We have observed that points can vanish from contours in the scale-space image when filtering operations are not highly accurate. To handle the problem of vanishing points, perceptual organizations heuristics are used to group the points into lines. Next, these lines are grouped into contours by using additional heuristics. Probabilities are associated with these contours using domain-specific correlations. A Bayes tree classifier processes probabilistic features to infer the presence of different minerals in the soil. Experiments show that the algorithm that uses domain-specific correlation to infer qualitative features outperforms a domain-independent algorithm that does not.

Kulkarni, Deepak↗
NASA NTRS2008

Development of Position-sensitive Transition-edge Sensor X-ray Detectors

We report on the development of position-sensitive transition-edge sensors (PoST's) for future x-ray astronomy missions such as the International X-ray Observatory (IXO), currently under study by NASA and ESA. PoST's consist of multiple absorbers each with a different thermal coupling to one or more transition-edge sensor (TES). This differential thermal coupling between absorbers and TES's results in different characteristic pulse shapes and allows position discrimination between the different pixels. The development of PoST's is motivated by a desire to achieve maximum focal-plane area with the least number of readout channels and as such. PoST's are ideally suited to provide a focal-plane extension to the Constellation-X microcalorimeter array. We report the first experimental results of our latest one and two channel PoST's, which utilize fast thermalizing electroplated Au/Bi absorbers coupled to low noise Mo/Au TES's - a technology already successfully implemented in our arrays of single pixel TES's. We demonstrate 6 eV energy resolution coupled with spatial sensitivity in the keV energy range. We also report on the development of signal processing algorithms to optimize energy and position sensitivity of our detectors.

Smith, S. J.↗
NASA NTRS2019

Use of Polarimetric Radar Measurements to Constrain Simulated Convective Cell Evolution: A Pilot Study with Lagrangian Tracking

To probe the potential value of a radar-driven field campaign to constrain simulation of isolated convection subject to a strong aerosol perturbation, convective cells observed by the operational KHGX weather radar in the vicinity of Houston, Texas, are examined individually and statistically. Cells observed in a single case study of onshore flow conditions during July 2013 are first examined and compared with cells in a regional model simulation. Observed and simulated cells are objectively identified and tracked from observed or calculated positive specific differential phase (K(sub DP)) above the melting level, which is related to the presence of supercooled liquid water. Several observed and simulated cells are subjectively selected for further examination. Below the melting level, we compare sequential cross sections of retrieved and simulated raindrop size distribution parameters. Above the melting level, we examine time series of KDP and radar differential reflectivity (Z(sub DR)) statistics from observations and calculated from simulated supercooled rain properties, alongside simulated vertical wind and supercooled rain mixing ratio statistics. Results indicate that the operational weather radar measurements offer multiple constraints on the properties of simulated convective cells, with substantial value added from derived K(sub DP) and retrieved rain properties. The value of collocated three-dimensional lightning mapping array measurements, which are relatively rare in the continental US, supports the choice of Houston as a suitable location for future field studies to improve the simulation and understanding of convective updraft physics. However, rapid evolution of cells between routine volume scans motivates consideration of adaptive scan strategies or radar imaging technologies to amend operational weather radar capabilities. A 3-year climatology of isolated cell tracks, prepared using a more efficient algorithm, yields additional relevant information. Isolated cells are found within the KHGX domain on roughly 40 % of days year-round, with greatest concentration in the northwest quadrant, but roughly 5-fold more cells occur during June through September. During this enhanced occurrence period, the cells initiate following a strong diurnal cycle that peaks in the early afternoon, typically follow a south-to-north flow, and dissipate within 1 h, consistent with the case study examples. Statistics indicate that ∼ 150 isolated cells initiate and dissipate within 70 km of the KHGX radar during the enhanced occurrence period annually, and roughly 10 times as many within 200 km, suitable for multi-instrument Lagrangian observation strategies. In addition to ancillary meteorological and aerosol measurements, robust vertical wind speed retrievals would add substantial value to a radar-driven field campaign.

Fridlind, Ann M.↗
NASA NTRS2022

Differential Ranging Experiments with NASA’s High-Gain Deep Space Network Antennas

Radar experiments are currently under way at the Goldstone Deep Space Communications Complex (GDSCC) to determine the range of cis-lunar objects using a single high-gain 34m antenna transmitting 20 kW at X-band wavelengths, and two 34m receivers located at the GDSCC. The 34m antennas of the Deep Space Network (DSN) have effective fields-of-view of approximately 1 milli-radians, hence predetermined pointing predicts with accuracies on the order of 1 milli-degree are required. The extremely accurate 1 nano-second timing distribution of the DSN network enables sub-meter level ranging in the radial direction, by measuring delays in phase-modulated pseudonoise (PN) echoes reflected from the target. In this paper we demonstrate experimental verification of the proposed techniques by post-processing radar reflections obtained from a decommissioned geo-synchronous satellite. The characteristics of correlation-based delay measurements obtained simultaneously with two different receiving antennas are described. These are the fundamental quantities used to form the “time difference of arrival” (TDOA) observables commonly used in GPS positioning algorithms, and the results interpreted in the context of hyperbolic position location that could be used in the future to monitor spacecraft in cis-lunar space.

Cheung, Kar-Ming↗
NASA NTRS2004

Toward a Global Map of Raindrop Size Distributions: Rain-Type Classification and Its Implications for Validating Global Rainfall Products - Part 1

Variability in the global distribution of precipitation is recognized as a key element in assessing the impact of climate change for life on earth. The response of precipitation to climate forcings is, however, poorly understood because of discrepancies in the magnitude and sign of climatic trends in satellite-based rainfall estimates. Quantifying and ultimately removing these biases is critical for studying the response of the hydrologic cycle to climate change. In addition, estimates of random errors owing to variability in algorithm assumptions on local spatial and temporal scales are critical for establishing how strongly their products should be weighted in data assimilation or model validation applications and for assigning a level of confidence to climate trends diagnosed from the data. This paper explores the potential for refining assumed drop size distributions (DSDs) in global radar rainfall algorithms by establishing a link between satellite observables and information gleaned from regional validation experiments where polarimetric radar, Doppler radar, and disdrometer measurements can be used to infer raindrop size distributions. By virtue of the limited information available in the satellite retrieval framework, the current method deviates from approaches adopted in the ground-based radar community that attempt to relate microphysical processes and resultant DSDs to local meteorological conditions. Instead, the technique exploits the fact that different microphysical pathways for rainfall production are likely to lead to differences in both the DSD of the resulting raindrops and the three-dimensional structure of associated radar reflectivity profiles. Objective rain-type classification based on the complete three-dimensional structure of observed reflectivity profiles is found to partially mitigate random and systematic errors in DSDs implied by differential reflectivity measurements. In particular, it is shown that vertical and horizontal reflectivity structure obtained from spaceborne radar can be used to reproduce significant differences in Z(sub dr) between the easterly and westerly climate regimes observed in the Tropical Rainfall Measuring Mission Large-scale Biosphere-Atmosphere (TRMM-LBA) field experiment as well as the even larger differences between Amazonian rainfall and that observed in eastern Colorado. As such, the technique offers a potential methodology for placing locally observed DSD information into a global framework.

L'Ecuyer, Tristan S.↗
NASA NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗
NASA NTRS2003

Global and Local Helioseismic Studies of Solar Convection Zone Dynamics Using SOI-MDI on SOHO

Our joint collaborative analyses of global mode data to characterize the solar differential rotation (e.g. Thompson et al. 1996, Schou et al. 1998), and most recently to detect and analyze temporal variations in angular velocity Omega profiles both within the convection zone and in the deeper radiative interior (e.g. Howe et al 2000a,b; Toomre et al. 2000), have led to a series of fascinating discoveries. These should be pursued further as the solar cycle continues. The physical deductions being made from these studies have been greatly strengthened by utilizing both SOI-MDI and GONG data in order to have two independent observational realizations of Doppler images spanning a five-year interval, using two separate procedures to determine global mode splittings, and then analyzing those splitting data sets using both RLS and SOLA inversion procedures. There are considerable subtleties in the effects of instrumental response functions and calibrations, sensitivity of peak finding algorithms and their mode leakage estimates, and stochastic variations in mode amplitudes that can all contribute to apparent changes in the Omega profiles being inferred from sequences of helioseismic data. We have come to understand the implications of many of these calibration and analysis steps, greatly aided by frequent multi-week collaborative working sessions in our Helioseismic Analysis Facility (HAF) at JILA involving many members of the SO1 dynamics and inversion team, including most of our Co-Is during the summer months when we hold intensive working sessions. Considerable further focused attention is required in a collaborative setting on such global mode issues as we continue studying the changing sun.

Toomre, Juri↗