Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “error vector”

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 739 records · Page 41

High-Order Polynomial Expansions (HOPE) for flux-vector splitting

The Van Leer flux splitting is known to produce excessive numerical dissipation for Navier-Stokes calculations. Researchers attempt to remedy this deficiency by introducing a higher order polynomial expansion (HOPE) for the mass flux. In addition to Van Leer's splitting, a term is introduced so that the mass diffusion error vanishes at M = 0. Several splittings for pressure are proposed and examined. The effectiveness of the HOPE scheme is illustrated for 1-D hypersonic conical viscous flow and 2-D supersonic shock-wave boundary layer interactions.

Liou, Meng-Sing↗

Evaluation of High-Resolution Ocean Surface Vector Winds Measured by QuikSCAT Scatterometer in Coastal Regions

The SeaWinds scatterometer onboard QuikSCAT covers approximately 90% of the global ocean under clear and cloudy condition in 24 h, and the standard data product has 25-km spatial resolution. Such spatial resolution is not sufficient to resolve small-scale processes, especially in coastal oceans. Based on range-compressed normalized backscatter and a modified wind retrieval algorithm, a coastal wind dataset at 12.5-km resolution was produced. Even with larger error, the high-resolution winds, in medium to high strength, would still be useful over coastal ocean. Using measurements from moored buoys from the National Buoy Data Center, the high-resolution QuikSCAT wind data are found to have similar accuracy as standard data in the open ocean. The accuracy of both high- and standard-resolution winds, particularly in wind directions, is found to degrade near shore. The increase in error is likely caused by the inadequacy of the geophysical model function/ambiguity removal scheme in addressing coastal conditions and light winds situations. The modified algorithm helps to bring the directional accuracy of the high-resolution winds to the accuracy of the standard-resolution winds in near-shore regions, particularly in the nadir and far zones across the satellite track.

scatterometer↗

D-Factor: A Quantitative Model of Application Slow-Down in Multi-Resource Shared Systems

Scheduling multiple jobs onto a platform enhances system utilization by sharing resources. The benefits from higher resource utilization include reduced cost to construct, operate, and maintain a system, which often include energy consumption. Maximizing these benefits comes at a price - resource contention among jobs increases job completion time. In this paper, we analyze slow-downs of jobs due to contention for multiple resources in a system; referred to as dilation factor. We observe that multiple-resource contention creates non-linear dilation factors of jobs. From this observation, we establish a general quantitative model for dilation factors of jobs in multi-resource systems. A job is characterized by a vector-valued loading statistics and dilation factors of a job set are given by a quadratic function of their loading vectors. We demonstrate how to systematically characterize a job, maintain the data structure to calculate the dilation factor (loading matrix), and calculate the dilation factor of each job. We validate the accuracy of the model with multiple processes running on a native Linux server, virtualized servers, and with multiple MapReduce workloads co-scheduled in a cluster. Evaluation with measured data shows that the D-factor model has an error margin of less than 16%. We also show that the model can be integrated with an existing on-line scheduler to minimize the makespan of workloads.

99 GENERAL AND MISCELLANEOUS↗

Intrafraction Variability and Deformation Quantification in the Breast

Purpose: To evaluate intrafraction variability and deformation of the lumpectomy cavity (LC), breast, and nearby organs. Methods and Materials: Sixteen left-sided postlumpectomy and 1 bilateral breast cancer cases underwent free-breathing CT (FBCT) and 10-phase 4-dimensional CT (4DCT). Deformable image registration was used for deformation analysis and contour propagation of breast, heart, lungs, and LC between end-exhale and end-inhale 4DCT phases. Respiration-induced motion was calculated via centroid analysis. Two planning target volumes (PTVs) were compared: PTV{sub FBCT} from the FBCT volume with an isotropic 10 mm expansion (5 mm excursion and 5 mm setup error) and PTV{sub 4DCT} generated from the union of 4DCT contours with isotropic 5 mm margin for setup error. Volume and geometry were evaluated via percent difference and bounding box analysis, respectively. Deformation correlations between breast/cavity, breast/lung, and breast/heart were evaluated. Associations were tested between cavity deformation and proximity to chest wall and breast surface. Results: Population-based 3-dimensional vector excursions were 2.5 ± 1.0 mm (range, 0.8-3.8 mm) for the cavity and 2.0 ± 0.8 mm (range, 0.7-3.0 mm) for the ipsilateral breast. Cavity excursion was predominantly in the anterior and superior directions (1.0 ± 0.8 mm and −1.8 ± 1.2 mm, respectively). Similarly, for all cases, LCs and ipsilateral breasts yielded median deformation values in the superior direction. For 14 of 17 patients, the LCs and breast interquartile ranges tended toward the anterior direction. The PTV{sub FBCT} was 51.5% ± 10.8% larger (P<.01) than PTV{sub 4DCT}. Bounding box analysis revealed that PTV{sub FBCT} was 9.8 ± 1.2 (lateral), 9.0 ± 2.2 (anterior–posterior), and 3.9 ± 1.8 (superior–inferior) mm larger than PTV{sub 4DCT}. Significant associations between breast and cavity deformation were found for 6 of 9 axes. No dependency was found between cavity deformation and proximity to chest wall or breast surface. Conclusions: Lumpectomy cavity and breast deformation and motion demonstrated large variability. A PTV{sub 4DCT} approach showed value in patient-specific margins, particularly if robust interfraction setup analysis can be performed.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Classical seventh-, sixth-, and fifth-order Runge-Kutta-Nystrom formulas with stepsize control for general second-order differential equations

Runge-Kutta-Nystrom formulas of the seventh, sixth, and fifth order were derived for the general second order (vector) differential equation written as the second derivative of x = f(t, x, the first derivative of x). The formulas include a stepsize control procedure, based on a complete coverage of the leading term of the local truncation error in x, and they require no more evaluations per step than the earlier Runge-Kutta formulas for the first derivative of x = f(t, x). The developed formulas are expected to be time saving in comparison to the Runge-Kutta formulas for first-order differential equations, since it is not necessary to convert the second-order differential equations into twice as many first-order differential equations. The examples shown saved from 25 percent to 60 percent more computer time than the earlier formulas for first-order differential equations, and are comparable in accuracy.

Fehlberg, E.↗

Effects of autocorrelation upon LANDSAT classification accuracy

Richmond, Virginia and Denver, Colorado were study sites in an effort to determine the effect of autocorrelation on the accuracy of a parallelopiped classifier of LANDSAT digital data. The autocorrelation was assumed to decay to insignificant levels when sampled at distances of at least ten pixels. Spectral themes developed using blocks of adjacent pixels, and using groups of pixels spaced at least 10 pixels apart were used. Effects of geometric distortions were minimized by using only pixels from the interiors of land cover sections. Accuracy was evaluated for three classes; agriculture, residential and "all other"; both type 1 and type 2 errors were evaluated by means of overall classification accuracy. All classes give comparable results. Accuracy is approximately the same in both techniques; however, the variance in accuracy is significantly higher using the themes developed from autocorrelated data. The vectors of mean spectral response were nearly identical regardless of sampling method used. The estimated variances were much larger when using autocorrelated pixels.

Craig, R. G.↗

Determination of normal modes from measured complex modes

A technique is presented for computing a set of normal modes from a set of measured complex modes. The number of elements in the modal vectors, which is equal to the number of measurements, can be larger than the number of modes under consideration. It is also shown that the practice of normal mode approximation to complex modes can lead to very large errors when the modes are too complex. A numerical example and a simulated experiment illustrate the concepts discussed and support the theory presented.

Ibrahim, S. R.↗

Oceanographic and meteorological research based on the data products of SEASAT

Reservations were expressed concerning the sum of squares wind recovery algorithm and the power law model function. The SAS sum of squares (SOS) method for recovering winds from backscatter data leads to inconsistent results when V pol and H pol winds are compared. A model function that does not use a power law and that accounts for sea surface temperature is needed and is under study both theoretically and by means of the SASS mode 4 data. Aspects of the determination of winds by means of scatterometry and of the utilization of vector wind data for meteorological forecasts are elaborated. The operational aspect of an intermittent assimilation scheme currently utilized for the specification of the initial value field is considered with focus on quantifying the absolute 12-hour linear displacement error of the movement of low centers.

Pierson, W. J., Jr.↗

Configuration management and automatic control of an augmentor wing aircraft with vectored thrust

An advanced structure for automatic flight control logic for powered-lift aircraft operating in terminal areas is under investigation at Ames Research Center. This structure is based on acceleration control; acceleration commands are constructed as the sum of acceleration on the reference trajectory and a corrective feedback acceleration to regulate path tracking errors. The central element of the structure, termed a Trimmap, uses a model of the aircraft aerodynamic and engine forces to calculate the control settings required to generate the acceleration commands. This report describes the design criteria for the Trimmap and derives a Trimmap for Ames experimental augmentor wing jet STOL research aircraft.

Cicolani, L. S.↗

Reconstruction of Charged Particle Tracks in Realistic Detector Geometry Using a Vectorized and Parallelized Kalman Filter Algorithm

One of the most computationally challenging problems expected for the High-Luminosity Large Hadron Collider (HL-LHC) is finding and fitting particle tracks during event reconstruction. Algorithms used at the LHC today rely on Kalman filtering, which builds physical trajectories incrementally while incorporating material e ects and error estimation. Recognizing the need for faster computational throughput, we have adapted Kalman-filterbased methods for highly parallel, many-core SIMD and SIMT architectures that are now prevalent in high-performance hardware. Previously we observed significant parallel speedups, with physics performance comparable to CMS standard tracking, on Intel Xeon, Intel Xeon Phi, and (to a limited extent) NVIDIA GPUs. While early tests were based on artificial events occurring inside an idealized barrel detector, we showed subsequently that our mkFit software builds tracks successfully from complex simulated events (including detector pileup) occurring inside a geometrically accurate representation of the CMS-2017 tracker. Here, we report on advances in both the computational and physics performance of mkFit, as well as progress toward integration with CMS production software. Recently we have improved the overall eciency of the algorithm by preserving short track candidates at a relatively early stage rather than attempting to extend them over many layers. Moreover, mkFit formerly produced an excess of duplicate tracks; these are now explicitly removed in an additional processing step. We demonstrate that with these enhancements, mkFit becomes a suitable choice for the first iteration of CMS tracking, and eventually for later iterations as well. We plan to test this capability in the CMS High Level Trigger during Run 3 of the LHC, with an ultimate goal of using it in both the CMS HLT and oine reconstruction for the HL-LHC CMS tracker.

Cerati, Giuseppe↗

Stochastic estimates of gradient from laser measurements for an autonomous Martian roving vehicle

The general problem of estimating the state vector x from the state equation h = Ax where h, A, and x are all stochastic, is presented. Specifically, the problem is for an autonomous Martian roving vehicle to utilize laser measurements in estimating the gradient of the terrain. Error exists due to two factors - surface roughness and instrumental measurements. The errors in slope depend on the standard deviations of these noise factors. Numerically, the error in gradient is expressed as a function of instrumental inaccuracies. Certain guidelines for the accuracy of permissable gradient must be set. It is found that present technology can meet these guidelines.

Burger, P. A.↗

Reducing Errors by Use of Redundancy in Gravity Measurements

A methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.

Kulikov, Igor↗

Impact of tether cutting on onboard navigation during the Tethered Satellite Mission-1

The first Tethered Satellite System mission (TSS-1) is manifested for Shuttle Flight STS-44 in January of 1991. The TSS mission presents a new challenge to engineers, requiring advanced guidance, navigation and control concepts. Current NASA flight rules require that the navigational state of the Orbiter at deorbit burn be known to an accuracy of 20 nautical miles. Response of the Shuttle crew to this contingency may involve cutting the tether prior to a complete retrieval. The degradation of the navigational state accuracy as modelled by Shuttle navigation system is examined. Responses to the loss of communication scenario are proposed for two cases. The first case examines navigational performance during a nominal attitude profile. The second case is identical to the first, with the inclusion of modelled tether electrodynamical forces. Comparisons of trajectories propagated from the onboard navigational state vector and a reference ephemeris state vector were performed, with the tether cut simulated at various points during the mission. Additionally, updates to the onboard navigational state via ground uplinks were provided prior to the assumed loss of communication. Through these comparisons, the onboard navigation state error was determined. Alternative responses result from efforts to minimize this error during the various phases of TSS-1 deployment. These results demonstrated existing NASA flight rules could be violated by cutting the tether, and suggests reponses to a loss of communications contingency to maintain a more accurate navigational state.

Pirker, Dana M.↗

The peculiar velocities of rich clusters in the hot and cold dark matter scenarios

We present the results of a study of the peculiar velocities of rich clusters of galaxies. The peculiar motion of rich clusters in various cosmological scenarios is of interest for a number of reasons. Observationally, one can measure the peculiar motion of clusters to greater distances than galaxies because cluster peculiar motions can be determined to greater accuracy. One can also test the slope of distance indicator relations using clusters to see if galaxy properties vary with environment. We have used N-body simulations to measure the amplitude and rms cluster peculiar velocity as a function of bias parameter in the hot and cold dark matter scenarios. In addition to measuring the mean and rms peculiar velocity of clusters in the two models, we determined whether the peculiar velocity vector of a given cluster is well aligned with the gravity vector due to all the particles in the simulation and the gravity vector due to the particles present only in the clusters. We have investigated the peculiar velocities of rich clusters of galaxies in the cold dark matter and hot dark matter galaxy formation scenarios. We have derived peculiar velocities and associated errors for the scenarios using four values of the bias parameter ranging from b = 1 to b = 2.5. The growth of the mean peculiar velocity with scale factor has been determined and compared to that predicted by linear theory. In addition, we have compared the orientation of force and velocity in these simulations to see if a program such as that proposed by Bertschinger and Dekel (1989) for elliptical galaxy peculiar motions can be applied to clusters. The method they describe enables one to recover the density field from large scale redshift distance samples. The method makes it possible to do this when only radial velocities are known by assuming that the velocity field is curl free. Our analysis suggests that this program if applied to clusters is only realizable for models with a low value of the bias parameter, i.e., models in which the peculiar velocities of clusters are large enough that the errors do not render the analysis impracticable.

Rhee, George F.↗

fPINNs: Fractional Physics-Informed Neural Networks

Physics-informed neural networks (PINNs), introduced, are effective in solving integer-order partial differential equations (PDEs) based on scattered and noisy data. PINNs employ standard feedforward neural networks (NNs) with the PDEs explicitly encoded into the NN using automatic differentiation, while the sum of the mean-squared PDE residuals and the mean-squared error in initial-boundary conditions is minimized with respect to the NN parameters. Here we extend PINNs to fractional PINNs (fPINNs) to solve space-time fractional advection-diffusion equations (fractional ADEs), and we study systematically their convergence, hence explaining both fPINNs and PINNs for the first time. Specifically, we demonstrate their accuracy and effectiveness in solving multidimensional forward and inverse problems with forcing terms whose values are only known at randomly scattered spatio-temporal coordinates (black-box (BB) forcing terms). A novel element of the fPINNs is the hybrid approach that we introduce for constructing the residual in the loss function using both automatic differentiation for the integer-order operators and numerical discretization for the fractional operators. This approach bypasses the difficulties stemming from the fact that automatic differentiation is not applicable to fractional operators because the standard chain rule in integer calculus is not valid in fractional calculus. To discretize the fractional operators, we employ the Grünwald--Letnikov (GL) formula in one-dimensional fractional ADEs and the vector GL formula in conjunction with the directional fractional Laplacian in two- and three-dimensional fractional ADEs. We first consider the one-dimensional fractional Poisson equation and compare the convergence of the fPINNs against the finite difference method (FDM). We present the solution convergence using both the mean L 2 error as well as the standard deviation due to sensitivity to NN parameter initializations. Using different GL formulas we observe first-, second-, and third-order convergence rates for small size training sets but the error saturates for larger training sets. We explain these results by analyzing the four sources of numerical errors due to discretization, sampling, NN approximation, and optimization. The total error decays monotonically (below 10 –5 for a third-order GL formula) but it saturates beyond that point due to the optimization error. We also analyze the relative balance between discretization and sampling errors and observe that the sampling size and the number of discretization points (auxiliary points) should be comparable to achieve the highest accuracy. As we increase the depth of the NN up to certain value, the mean error decreases and the standard deviation increases, whereas the width has essentially no effect unless its value is either too small or too large. We next consider time-dependent fractional ADEs and compare white-box (WB) and BB forcing. We observe that for the WB forcing, our results are similar to the aforementioned cases; however, for the BB forcing fPINNs outperform FDM. Subsequently, we consider multidimensional time-, space-, and space-time-fractional ADEs using the directional fractional Laplacian and we observe relative errors of 10 –3 ~ 10 –4 . Lastly, we solve several inverse problems in one, two, and three dimensions to identify the fractional orders, diffusion coefficients, and transport velocities and obtain accurate results given proper initializations even in the presence of significant noise.

97 MATHEMATICS AND COMPUTING↗

Distance-preserving rigidity penalty on deformable image registration of multiple skeletal components in the neck

Purpose: This study aims at developing and testing a novel rigidity penalty suitable for the deformable registration of tightly located skeletal components in the head and neck from planning computed tomography (CT) and daily cone-beam CT (CBCT) scans of patients undergoing radiotherapy. Methods: The proposed rigidity penalty is designed to preserve intervoxel distances within each bony structure. This penalty was tested in the intensity-based B-spline deformable registration of five cervical vertebral bodies (C1–C5). The displacement vector fields (DVFs) from the registrations were compared to the DVFs generated by using rigid body motions of the cervical vertebrae, measured by the surface registration of vertebrae delineated on CT and CBCT images. Twenty five pairs of planning CT (reference) and treatment CBCTs (target) from five patients were aligned without and with the penalty. An existing penalty based on the orthonormality of the deformation gradient tensor was also tested and the effects of the penalties compared. Results: The mean magnitude of the maximum registration error with the proposed distance-preserving penalty was (0.86, 1.12, 1.33) mm compared to (2.11, 2.49, 2.46) without penalty and (1.53, 1.64, 1.64) with the existing orthonormality-based penalty. The improvement in the accuracy of the deformable image registration was also verified by comparing the Procrustes distance between the DVFs. With the proposed penalty, the average distance was 0.11 (σ 0.03 mm) which is smaller than 0.53 (0.1 mm) without penalty and 0.28 (0.04 mm) with the orthonormality-based penalty. Conclusions: The accuracy of aligning multiple bony elements was improved by using the proposed distance-preserving rigidity penalty. The voxel-based statistical analysis of the registration error shows that the proposed penalty improved the integrity of the DVFs within the vertebral bodies.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

Thermal neutron diffraction determination of the magnetic structure of EuCu{sub 2}Ge{sub 2}

The magnetic structure of EuCu{sub 2}Ge{sub 2} has been determined by flat-plate neutron powder diffraction. Two magnetic phases are present in the neutron diffraction pattern at 3.5 K. They have the same moment, within error, and a common transition temperature. Both {sup 151}Eu and {sup 153}Eu Mössbauer spectroscopy show that the two magnetic phases belong to the same crystallographic phase. Both phases can be modelled by planar helimagnetic structures: one with a propagation vector of [0.654(1), 0, 0], the other with a propagation vector of [0.410(1), 0.225(1), 0].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Sensitivity of constrained linear inversions to the selection of the Lagrange multiplier

The influence of the choice of the Lagrange multiplier on constrained linear inversions is explored, with reference made to applications in inferring the columnar aerosol size distributions from spectral aerosol optical depth measurements. A range of the Lagrange multiplier is examined to find all positive solutions for the solution vector, which represents modifying factors to the assumed form of the size distribution. An iterative method is devised to constrain the calculations to consideration of only positive quantities and a requirement that the regression fit to data be consistent with measurement errors. The determination of the variances and covariances is formulated and applied to existing data sets for optical depth. Variances in the solution are found to be large for particle radii when the information content of the data is small.

King, M. D.↗