Search NASA⌕ Search

SEARCH · Search NASA

Results for “Linear interpolation”

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 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Data smoothing and error detection based on linear interpolation

A method is presented, based on linear interpolation, for detecting and correcting bad data points in a set of data without contaminating the good data points. The method used is not concerned with the small random errors usually attributed to a noisy system. It assumes that the data points which are in error are relatively isolated from each other and that the number of such points is small compared to the total number of data points.

Guerra, V. M.↗
DOE OSTI2015

Evaluation of linear interpolation method for missing value on solar radiation dataset in Perlis

This paper intends to reveal the ability of the linear interpolation method to predict missing values in solar radiation time series. Reliable dataset is equally tends to complete time series observed dataset. The absence or presence of radiation data alters long-term variation of solar radiation measurement values. Based on that change, the opportunities to provide bias output result for modelling and the validation process is higher. The completeness of the observed variable dataset has significantly important for data analysis. Occurrence the lack of continual and unreliable time series solar radiation data widely spread and become the main problematic issue. However, the limited number of research quantity that has carried out to emphasize and gives full attention to estimate missing values in the solar radiation dataset.

42 ENGINEERING↗
NASA NTRS1979

Differences between measured and linearly interpolated synoptic variables over a 12-h period during AVE 4

Results of analyses revealed that nonlinear changes or differences formed centers or systems, that were mesosynoptic in nature. These systems correlated well in space with upper level short waves, frontal zones, and radar observed convection, and were very systematic in time and space. Many of the centers of differences were well established in the vertical, extending up to the tropopause. Statistical analysis showed that on the average nonlinear changes were larger in convective areas than nonconvective regions. Errors often exceeding 100 percent were made by assuming variables to change linearly through a 12-h period in areas of thunderstorms, indicating that these nonlinear changes are important in the development of severe weather. Linear changes, however, accounted for more and more of an observed change as the time interval (within the 12-h interpolation period) increased, implying that the accuracy of linear interpolation increased over larger time intervals.

Dupuis, L. R.↗
DOE OSTI2016

SU-G-IeP2-08: Investigation On Signal Detectability in Volumetric Cone Beam CT Images with Anatomical Background

Purpose: To investigate the slice direction dependent detectability in cone beam CT images with anatomical background. Methods: We generated 3D anatomical background images using breast anatomy model. To generate 3D breast anatomy, we filtered 3D Gaussian noise with a square root of 1/f{sup 3}, and then assigned the attenuation coefficient of glandular (0.8cm{sup −1}) and adipose (0.46 cm{sup −1}) tissues based on voxel values. Projections were acquired by forward projection, and quantum noise was added to the projection data. The projection data were reconstructed by FDK algorithm. We compared the detectability of a 3 mm spherical signal in the image reconstructed from four different backprojection Methods: Hanning weighted ramp filter with linear interpolation (RECON1), Hanning weighted ramp filter with Fourier interpolation (RECON2), ramp filter with linear interpolation (RECON3), and ramp filter with Fourier interpolation (RECON4), respectively. We computed task SNR of the spherical signal in transverse and longitudinal planes using channelized Hotelling observer with Laguerre-Gauss channels. Results: Transverse plane has similar task SNR values for different backprojection methods, while longitudinal plane has a maximum task SNR value in RECON1. For all backprojection methods, longitudinal plane has higher task SNR than transverse plane. Conclusion: In this work, we investigated detectability for different slice direction in cone beam CT images with anatomical background. Longitudinal plane has a higher task SNR than transverse plane, and backprojection with hanning weighted ramp filter with linear interpolation method (i.e., RECON1) produced the highest task SNR among four different backprojection methods. This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the IT Consilience Creative Programs(IITP-2015-R0346-15-1008) supervised by the IITP (Institute for Information & Communications Technology Promotion), Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the MSIP (2015R1C1A1A01052268) and framework of international cooperation program managed by NRF (NRF-2015K2A1A2067635).

60 APPLIED LIFE SCIENCES↗
NASA NTRS2018

Deriving Three Dimensional Reservoir Bathymetry from Multi-Satellite Datasets

We evaluate different techniques that rebuild reservoir bathymetry by combining multi-satellite imagery of surface water elevation and extent. Digital elevation models (DEMs) are processed in two distinct ways in order to determine 3-D reservoir bathymetry. They are defined as (a) linear extrapolation and (b) linear interpolation. The first one linearly extrapolates the land slope, defining the bottom as the intersection of all extrapolated lines. The second linearly interpolates the uppermost and lowermost pixels of the reservoir's main river, repeating the process for all other tributaries. A visible bathymetry, resulting from the combination of radar altimetry and water extent masks, can be coupled with the DEM, improving the accuracy of techniques (a) and (b). Envisat-and Altika-based altimetric time series is combined to a Landsat-based water extent database over the2002-2016 period in order to generate the visible bathymetry, and topography is derived from the 3-arcsecHydroSHEDS DEM. Fourteen 3-D bathymetries derived from the combination of these techniques and datasets, plus the inclusion of upstream and downstream riverbed elevations, are evaluated over Lake Mead. Accuracy is measured using ground observations, and show that metrics improve as a function of added data requirement and processing. Best bathymetry estimates are obtained when the visible bathymetry, linear extrapolation technique and riverbed elevation are combined. Water storage variability is also evaluated and shows that best results are derived from the aforementioned combination. This study contributes to our understanding and representation of reservoir water impoundment impacts on the hydrological cycle.

HydroSHEDS↗
DOE OSTI2014

SU-E-T-140: Dynamic Wave Arc Trajectory Verification Using KV X-Ray Fluoroscopy

Purpose: Purpose: This study investigates the geometric accuracy of simultaneous Gantry/Ring rotation during Dynamic Wave Arc (DWA) delivery. Methods: The Vero SBRT system consists of a 6MV LINAC mounted on an O-ring gantry that can rotate around the vertical axis (±60°), similar to couch rotation on C-arm gantries. To provide CBCT and fluoroscopy imaging functionalities, two orthogonal kV imaging units are attached to the O-ring at −45°/+45° from the beam axis.Dynamic Wave Arc maximizes Vero's motion capabilities by employing synchronized gantry and ring motion on a complex non-coplanar trajectory in combination with aperture based optimized MLC segments.Four wave arc trajectories (T1-4) were delivered using a cubic phantom with a configuration of five lead beads. O-ring gantry position information was retrieved through continuous dual-source kV X-ray image acquisition during DWA. An in-house algorithm read in the image set, extracted the projected marker positions and determined the angulation through reconstruction of the beam source position. The geometric error was quantified as the distance between the independently detected positions from kV-images and reference trajectory derived from the treatment plan in the Ring-Gantry space. Results: The average displacement between the 3D gantry/ring positions reconstructed from the fluoroscopy images and the reference trajectory was 0.346 mm (SD 0,171) for T1. A mean offset of 0.348 mm (SD 0,182) and 0.357 mm (SD 0.194) was observed for trajectory T2(2segmens) and T3(4segments), respectively. The saw shape T4 presented a mean geometric error of 0.363 (SD 0.156). The overall systematic error of 0.350 was caused by the difference between planned reference trajectory created by linear interpolation between CP, and the machine delivery following a spline curve. Conclusion: An independent geometric QA approach has been developed for DWA delivery verification, successfully applied on diverse trajectories and disclosed that the Vero system is capable of accurately follow complex trajectories.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
NASA NTRS1994

Noise and drift analysis of non-equally spaced timing data

Generally, it is possible to obtain equally spaced timing data from oscillators. The measurement of the drifts and noises affecting oscillators is then performed by using a variance (Allan variance, modified Allan variance, or time variance) or a system of several variances (multivariance method). However, in some cases, several samples, or even several sets of samples, are missing. In the case of millisecond pulsar timing data, for instance, observations are quite irregularly spaced in time. Nevertheless, since some observations are very close together (one minute) and since the timing data sequence is very long (more than ten years), information on both short-term and long-term stability is available. Unfortunately, a direct variance analysis is not possible without interpolating missing data. Different interpolation algorithms (linear interpolation, cubic spline) are used to calculate variances in order to verify that they neither lose information nor add erroneous information. A comparison of the results of the different algorithms is given. Finally, the multivariance method was adapted to the measurement sequence of the millisecond pulsar timing data: the responses of each variance of the system are calculated for each type of noise and drift, with the same missing samples as in the pulsar timing sequence. An estimation of precision, dynamics, and separability of this method is given.

Vernotte, F.↗
DOE OSTI2017

Kernel reconstruction methods for Doppler broadening — Temperature interpolation by linear combination of reference cross sections at optimally chosen temperatures

This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T j ). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T 0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T j ). The choice of the L 2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T j ) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T min ,T max ]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope 238 U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of 238 U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2015

SU-E-I-10: Investigation On Detectability of a Small Target for Different Slice Direction of a Volumetric Cone Beam CT Image

Purpose: To investigate the detectability of a small target for different slice direction of a volumetric cone beam CT image and its impact on dose reduction. Methods: Analytic projection data of a sphere object (1 mm diameter, 0.2/cm attenuation coefficient) were generated and reconstructed by FDK algorithm. In this work, we compared the detectability of the small target from four different backprojection Methods: hanning weighted ramp filter with linear interpolation (RECON 1), hanning weighted ramp filter with Fourier interpolation (RECON2), ramp filter with linear interpolation (RECON 3), and ramp filter with Fourier interpolation (RECON4), respectively. For noise simulation, 200 photons per measurement were used, and the noise only data were reconstructed using FDK algorithm. For each reconstructed volume, axial and coronal slice were extracted and detection-SNR was calculated using channelized Hotelling observer (CHO) with dense difference-of-Gaussian (D-DOG) channels. Results: Detection-SNR of coronal images varies for different backprojection methods, while axial images have a similar detection-SNR. Detection-SNR{sup 2} ratios of coronal and axial images in RECON1 and RECON2 are 1.33 and 1.15, implying that the coronal image has a better detectability than axial image. In other words, using coronal slices for the small target detection can reduce the patient dose about 33% and 15% compared to using axial slices in RECON 1 and RECON 2. Conclusion: In this work, we investigated slice direction dependent detectability of a volumetric cone beam CT image. RECON 1 and RECON 2 produced the highest detection-SNR, with better detectability in coronal slices. These results indicate that it is more beneficial to use coronal slice to improve detectability of a small target in a volumetric cone beam CT image. This research was supported by the MSIP (Ministry of Science, ICT and Future Planning), Korea, under the IT Consilience Creative Program (NIPA-2014-H0201-14-1002) supervised by the NIPA (National IT Industry Promotion Agency). Authors declares that s/he has no conflict of Interest in relation to the work in this abstract.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Evaluation of Accuracy and Performance of a Bilinear Interpolator with Dense EOS Tables in xRage

This study investigates the performance and accuracy of simulations using air and deuterium equation-of-state (EOS) tables that have been densified coupled with linear interpolation, as opposed to the default rational interpolation used in EOSPAC. EOS tables that are densified by adding in more temperature and density points that have been calculated by the rational function interpolator are able to improve the accuracy of the linear interpolator by over 50%. There was no change in runtime performance for a simulation using a dense EOS table with linear interpolation. In a memory limited case, dense EOS tables had no apparent effect on the simulation runtime or memory usage.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Assimilating irregularly spaced sparsely observed turbulent signals with hierarchical Bayesian reduced stochastic filters

In this paper, we consider a practical filtering approach for assimilating irregularly spaced, sparsely observed turbulent signals through a hierarchical Bayesian reduced stochastic filtering framework. The proposed hierarchical Bayesian approach consists of two steps, blending a data-driven interpolation scheme and the Mean Stochastic Model (MSM) filter. We examine the potential of using the deterministic piecewise linear interpolation scheme and the ordinary kriging scheme in interpolating irregularly spaced raw data to regularly spaced processed data and the importance of dynamical constraint (through MSM) in filtering the processed data on a numerically stiff state estimation problem. In particular, we test this approach on a two-layer quasi-geostrophic model in a two-dimensional domain with a small radius of deformation to mimic ocean turbulence. Our numerical results suggest that the dynamical constraint becomes important when the observation noise variance is large. Second, we find that the filtered estimates with ordinary kriging are superior to those with linear interpolation when observation networks are not too sparse; such robust results are found from numerical simulations with many randomly simulated irregularly spaced observation networks, various observation time intervals, and observation error variances. Third, when the observation network is very sparse, we find that both the kriging and linear interpolations are comparable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Overset meshes for incompressible flows: On preserving accuracy of underlying discretizations

This study on overset meshes for incompressible-flow simulations is motivated by accurate prediction of wind farm aerodynamics involving large motions and deformations of components with complex geometry. Specifically, using first-order hyperbolic and elliptic equation proxies for the incompressible Navier-Stokes (NS) equations, we investigate the influence of information exchange between overset meshes on numerical performance where the underlying discretization is second-order accurate. The first aspect of information exchange surrounds interpolation of solution where we examine Lagrange and point-cloud-based interpolation for creating constraint equations between overset meshes. To maintain overall second-order accuracy, higher-order interpolation is required for elliptic problems, but linear interpolation is sufficient for hyperbolic problems in first-order form. Higher-order point-cloud-based interpolation provides a pathway to maintaining accuracy in unstructured meshes, but at higher complexity. The second aspect of information exchange focuses on comparing the approaches of overset single system (OSS) and overset Additive Schwarz (OAS) for coupling the linear systems of the overlapping meshes. While the former involves a single linear system, in the latter the discrete linear systems are solved separately, and solving the global system is accomplished through outer iterations and sequential information exchange in a Jacobi fashion. For the test cases studied, accuracy for hyperbolic problems is maintained by performing two outer iterations, whereas many outer iterations are required for elliptic systems. The order-of-accuracy studies explored here are critical for verifying the overset-mesh coupling algorithms used in engineering simulations. Accuracy of these simulations themselves is, however, quantified using engineering quantities of interest such as drag, power, etc. Consequently, we conclude with numerical experiments using NS equations for incompressible flows where we show that linear interpolation and few outer iterations are sufficient for achieving asymptotic convergence of engineering quantities of interest.

97 MATHEMATICS AND COMPUTING↗