Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “coordinate transformation”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Nonlinear feedback control of multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms: (1) as closed kinematic chains, and (2) as a force constrained mechanical system working on the same object simultaneously. In both formulations a new dynamic control method is discussed. It is based on a feedback linearization and simultaneous output decoupling technique. Applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, by choosing a general output equation, researchers can superimpose the position and velocity error feedback with the force-torque error feedback in the task space simultaneously.

Tarn, T. J.↗
NASA NTRS1988

New nonlinear control algorithms for multiple robot arms

Multiple coordinated robot arms are modeled by considering the arms as closed kinematic chains and as a force-constrained mechanical system working on the same object simultaneously. In both formulations, a novel dynamic control method is discussed. It is based on feedback linearization and simultaneous output decoupling technique. By applying a nonlinear feedback and a nonlinear coordinate transformation, the complicated model of the multiple robot arms in either formulation is converted into a linear and output decoupled system. The linear system control theory and optimal control theory are used to design robust controllers in the task space. The first formulation has the advantage of automatically handling the coordination and load distribution among the robot arms. In the second formulation, it was found that by choosing a general output equation it became possible simultaneously to superimpose the position and velocity error feedback with the force-torque error feedback in the task space.

Tarn, T. J.↗
NASA NTRS1985

Application of singular value decomposition to structural dynamics systems with constraints

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

Juang, J.-N.↗
NASA NTRS1992

Registering and resampling images in STSDAS

Registering different images can be difficult, especially if the images to be registered are images at different wavelengths, where features in one image may look entirely different or be absent from the second image. Using two new packages soon to be added to the STSDAS package, REGISTER and RESAMPLE, this job is done automatically. The REGISTER package allows the user to determine the amount of translation, rotation, and/or magnification needed to make two images, spectra, or time series congruent. The methods implemented to compute the registration parameters use: a set of the pixel coordinates of the same features identified in two files, or the FITS coordinate transformation parameters in the headers of two data files, or a single feature identified as the peak of a cross-correlation between two vectors. The coefficients describing the registration are defined by the equations (for a two-dimensional image): x = a + bx + cy, y = d + ex + fy, where (X,Y) are the pixel coordinates of a feature in the reference image, (x,y) are the pixel coordinates of a feature in the secondary image, and the computed coefficients are a, b, c, d, e, and f. Results may be produced by linking the output of REGISTER to RESAMPLE in a command language procedure. The output from REGISTER and the input to RESAMPLE consists of a matrix of coefficients (a through f above) fully specifying the registration. The RESAMPLE package resamples simple vector or image data for a given amount of translation, rotation (images only), and magnification, or reflection of the science data. Specific options included are: image rotation about the FITS reference pixel; scale changes, i.e. magnification or demagnification (for images, independently on both axes); simple translation; reflection (for images, about one or both axes); and resampling and registration to a reference data set. Output from the RESAMPLE task is the resampled image which may then be displayed and compared with the reference image.

Williamson, R. L., II↗
NASA NTRS1979

Numerical solution of the Navier-Stokes equations for laminar, transonic flows

An implicit finite difference solution of the Navier-Stokes equations yielded time histories of the transonic laminar flow development about a circular cylinder and NACA-0018 airfoil. Reynolds numbers ranged from those corresponding to purely laminar flow to those corresponding to significant turbulence in the boundary layer. Body thermal conditions of an adiabatic wall and a specified body temperature were considered. Versatility in treating arbitrary bodies was incorporated by using numerically generated, body-fitted coordinate transformations. Solution of the simultaneous difference equations for the dependent variables was obtained using an accelerated Gauss-Seidel iterative scheme. Computational results are presented in the form of velocity vector fields, Mach number contours, aerodynamic coefficients, heat transfer rates at the body surface, and body temperature distributions. Truncation analyses of first and second derivative difference approximations resulted in general criteria for numerically generated coordinates so that flow near a body is more accurately represented.

Turner, L., III↗
NASA NTRS1980

Implicit Finite-Difference Simulations of Three-Dimensional Compressible Flow

An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a "thin-layer" approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid or viscous solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

Pulliam, Thomas H.↗
NASA NTRS1978

On implicit finite-difference simulations of three-dimensional flow

An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a 'thin layer' approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid and laminar-turbulent solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.

Pulliam, T. H.↗
DOE OSTI2020

Lift & Learn: Physics-informed machine learning for large-scale nonlinear dynamical systems

In this work, we present Lift & Learn, a physics-informed method for learning low-dimensional models for large-scale dynamical systems. The method exploits knowledge of a system’s governing equations to identify a coordinate transformation in which the system dynamics have quadratic structure. This transformation is called a lifting map because it often adds auxiliary variables to the system state. The lifting map is applied to data obtained by evaluating a model for the original nonlinear system. This lifted data is projected onto its leading principal components, and low-dimensional linear and quadratic matrix operators are fit to the lifted reduced data using a least-squares operator inference procedure. Analysis of our method shows that the Lift & Learn models are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches. This preservation of system physics makes the Lift & Learn models robust to changes in inputs. Numerical experiments on the FitzHugh–Nagumo neuron activation model and the compressible Euler equations demonstrate the generalizability of our model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

On the Error Covariance Correction Step of an ESKF Attitude Update

The attitude states of an error-state Kalman filter (ESKF) behave differently than most other states in the system due to their multiplicative (rather than additive) nature. One way in which they differ is an error covariance correction step after an ESKF error reset, which is not required for, for example, position and velocity states. This covariance correction step is not intuitive, and it has only been recently derived for coordinate transform matrices. The author of this memo, however, found the provided derivation in [1] confusing due to a lack of clarity surrounding the invoked reference frames, and clarity is required as there are at least 4 different ways to parameterize small-angle attitude errors in an ESKF. Furthermore, while reproducing the work, the author of this memo found a more straightforward derivation that provides additional insight into the correction step. This memo offers a derivation of the attitude error covariance correction step of an ESKF, which pays specific attention to the coordinate reference frames.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

Use of Collocated KWAJEX Satellite, Aircraft, and Ground Measurements for Understanding Ambiguities in TRMM Radiometer Rain Profile Algorithm

Coordinated ground, aircraft, and satellite observations are analyzed from the 1999 TRMM Kwajalein Atoll field experiment (KWAJEX) to better understand the relationships between cloud microphysical processes and microwave radiation intensities in the context of physical evaluation of the Level 2 TRMM radiometer rain profile algorithm and uncertainties with its assumed microphysics-radiation relationships. This talk focuses on the results of a multi-dataset analysis based on measurements from KWAJEX surface, air, and satellite platforms to test the hypothesis that uncertainties in the passive microwave radiometer algorithm (TMI 2a12 in the nomenclature of TRMM) are systematically coupled and correlated with the magnitudes of deviation of the assumed 3-dimensional microphysical properties from observed microphysical properties. Re-stated, this study focuses on identifying the weaknesses in the operational TRMM 2a12 radiometer algorithm based on observed microphysics and radiation data in terms of over-simplifications used in its theoretical microphysical underpinnings. The analysis makes use of a common transform coordinate system derived from the measuring capabilities of the aircraft radiometer used to survey the experimental study area, i.e., the 4-channel AMPR radiometer flown on the NASA DC-8 aircraft. Normalized emission and scattering indices derived from radiometer brightness temperatures at the four measuring frequencies enable a 2-dimensional coordinate system that facilities compositing of Kwajalein S-band ground radar reflectivities, ARMAR Ku-band aircraft radar reflectivities, TMI spacecraft radiometer brightness temperatures, PR Ku-band spacecraft radar reflectivities, bulk microphysical parameters derived from the aircraft-mounted cloud microphysics laser probes (including liquid/ice water contents, effective liquid/ice hydrometeor radii, and effective liquid/ice hydrometeor variances), and rainrates derived from any of the individual ground, aircraft, or satellite algorithms applied to the radar or radiometer measurements, or their combination. The results support the study's underlying hypothesis, particularly in context of ice phase processes, in that the cloud regions where the 2a12 algorithm's microphysical database most misrepresents the microphysical conditions as determined by the laser probes, are where retrieved surface rainrates are most erroneous relative to other reference rainrates as determined by ground and aircraft radar. In reaching these conclusions, TMI and PR brightness temperatures and reflectivities have been synthesized from the aircraft AMPR and ARMAR measurements with the analysis conducted in a composite framework to eliminate measurement noise associated with the case study approach and single element volumes obfuscated by heterogeneous beam filling effects. In diagnosing the performance of the 2a12 algorithm, weaknesses have been found in the cloud-radiation database used to provide microphysical guidance to the algorithm for upper cloud ice microphysics. It is also necessary to adjust a fractional convective rainfall factor within the algorithm somewhat arbitrarily to achieve satisfactory algorithm accuracy.

Smith, Eric A.↗
DOE OSTI2022

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Elucidating the Role of Hydrogen at c‐In 2 O 3 /a‐In 2 O 3− x Interface

Ab initio molecular dynamics simulations and hybrid functional electronic structure calculations are employed to determine the formation, the structural and electronic properties, and the dynamics of covalent (In—OH) and ionic (In—H—In) hydrogen defects at crystalline-In 2 O 3 /amorphous-In 2 O 3−x interface. This comprehensive computational study considers (i) various interstitial and substitutional hydrogen site locations within the crystalline, amorphous, and interfacial regions; (ii) several oxygen-to-hydrogen ratios; and (iii) possible defect charged states. The results reveal hydrogen's inability to fully passivate the undercoordinated under-shared in atoms in amorphous highly substoichiometric oxide, giving rise to the formation of deep electron traps even in net-charge neutral structures. These trap defects are found to be sensitive to photoexcitation, in contrast to In—OH with H's electronic states located below the valence band and to In—H—In, where H is found to maintain its charge state upon illumination. Nevertheless, H plays a critical role in photoinduced conductivity and its relaxation by promoting In—O coordination transformations at the interfacial region, including deterioration of the crystalline layer. Finally, the results help identify mobile H species and metastable H defect complexes (such as In—H—H—In, In—OH–H—In, and In—OH–O—In) that are responsible for long relaxation times of the conductivity decay.

H defects↗
DOE OSTI2021

Equivalence principle in Reissner–Nordström geometry

The Equivalence Principle is a key element in the development of General Relativity. In one of its formulations, the Equivalence Principle states that a reference frame at rest in a uniform gravitational field is equivalent to a reference frame in uniformly accelerated motion in the absence of any gravitation field. We analyze the spacetime surrounding a non-rotating spherically symmetric charged body, known as Reissner–Nordström geometry, and exhibit a coordinate transformation, which makes explicit its compatibility with the Equivalence Principle. We revisit the Schwarzschild case, previously analyzed in the literature. We also consider second order terms of the relevant expansion parameters in the approximate metric, which is needed for the computed curvature quantities to be correct at zeroth order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Intrepid MCMC: Metropolis-Hastings with exploration

In engineering examples, one often encounters the need to sample from unnormalized distributions with complex shapes that may also be implicitly defined through a physical or numerical simulation model, making it computationally expensive to evaluate the associated density function. For such cases, MCMC has proven to be an invaluable tool. Random-walk Metropolis Methods (also known as Metropolis-Hastings (MH)), in particular, are highly popular for their simplicity, flexibility, and ease of implementation. However, most MH algorithms suffer from significant limitations when attempting to sample from distributions with multiple modes (particularly disconnected ones). Here, in this paper, we present Intrepid MCMC - a novel MH scheme that utilizes a simple coordinate transformation to significantly improve the mode-finding ability and convergence rate to the target distribution of random-walk Markov chains while retaining most of the simplicity of the vanilla MH paradigm. Through multiple examples, we showcase the improvement in the performance of Intrepid MCMC over vanilla MH for a wide variety of target distribution shapes. We also provide an analysis of the mixing behavior of the Intrepid Markov chain, as well as the efficiency of our algorithm for increasing dimensions. A thorough discussion is presented on the practical implementation of the Intrepid MCMC algorithm. Finally, its utility is highlighted through a Bayesian parameter inference problem for a two-degree-of-freedom oscillator under free vibration.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Data-driven surrogate modeling of hPIC ion energy-angle distributions for high-dimensional sensitivity analysis of plasma parameters' uncertainty

In this work, we present a data-driven strategy for effective construction of a surrogate model in high-dimensional parameter space for the ion energy-angle distribution (IEAD) output of hPIC simulations of plasma-surface interactions. The methodology is based on a bin-by-bin least-squares fitting of the IEAD in the parameter space. The fitting is performed in a transformed coordinate system to normalize the IEAD, and it employs sparse grids for sampling the parameter space to overcome sampling challenges in high dimensions. The surrogate model is significantly cheaper computationally than direct hPIC simulations yet maintains high fidelity to them, providing a fast emulator for hPIC simulations. Sensitivity analysis based on the surrogate model is utilized to characterize the dependence of the ion impact angle and energy moments on the physical parameters.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

An efficient, conservative, time-implicit solver for the fully kinetic arbitrary-species 1D-2V Vlasov-Ampère system

In this paper, we consider the solution of the fully kinetic (including electrons) Vlasov-Ampère system in a one-dimensional physical space and two-dimensional velocity space (1D-2V) for an arbitrary number of species with a time-implicit Eulerian algorithm. The problem of velocity-space meshing for disparate thermal and bulk velocities is dealt with by an adaptive coordinate transformation of the Vlasov equation for each species, which is then discretized, including the resulting inertial terms. Mass, momentum, and energy are conserved, and Gauss's law is enforced to within the nonlinear convergence tolerance of the iterative solver through a set of nonlinear constraint functions while permitting significant flexibility in choosing discretizations in time, configuration, and velocity space. We mitigate the temporal stiffness introduced by, e.g., the plasma frequency through the use of high-order/low-order (HOLO) acceleration of the iterative implicit solver. We present several numerical results for canonical problems of varying degrees of complexity, including the multiscale ion-acoustic shock wave problem, which demonstrate the efficacy, accuracy, and efficiency of the scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations

We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.

Novikau, I [Lawrence Livermore National Laboratory↗
DOE OSTI2026

A novel conditional formulation of the Vlasov–Ampère equations: a conservative, positivity, asymptotic and Gauss law preserving scheme

We propose a novel reformulation of the Vlasov–Ampère equations for plasmas that reveals discrete symmetries that enables simultaneous conservation of mass, momentum and energy; preservation of Gauss’s law; positivity of the distribution function; and consistency with quasi-neutral asymptotics. The approach employs variable and coordinate transformations to yield a coupled system comprising a modified Vlasov equation and associated moment–field equations. The modified Vlasov equation advances a conditional distribution function that excludes mass, momentum and energy densities, which are instead evolved through moment equations enforcing the relevant symmetries, conservation laws and involution constraints. This reformulation aligns naturally with a recent slow-manifold reduction technique, which separates fast electron time scales and simplifies the treatment of the quasi-neutral limit within the reduced moment–field subsystem. Using this framework, we develop a numerical method for the reduced 1D1V subsystem that, for the first time in the literature, satisfies all key physical constraints while maintaining a quasi-neutral asymptotic behaviour. The advantages of the method are demonstrated on canonical electrostatic test problems, including the multiscale ion acoustic shock wave.

1D1V↗