Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Sparse linear systems”

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.

208 records · Page 12
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Linear and nonlinear trending and prediction for AVHRR time series data

The variability of AVHRR calibration coefficient in time was analyzed using algorithms of linear and non-linear time series analysis. Specifically we have used the spline trend modeling, autoregressive process analysis, incremental neural network learning algorithm and redundancy functional testing. The analysis performed on available AVHRR data sets revealed that (1) the calibration data have nonlinear dependencies, (2) the calibration data depend strongly on the target temperature, (3) both calibration coefficients and the temperature time series can be modeled, in the first approximation, as autonomous dynamical systems, (4) the high frequency residuals of the analyzed data sets can be best modeled as an autoregressive process of the 10th degree. We have dealt with a nonlinear identification problem and the problem of noise filtering (data smoothing). The system identification and filtering are significant problems for AVHRR data sets. The algorithms outlined in this study can be used for the future EOS missions. Prediction and smoothing algorithms for time series of calibration data provide a functional characterization of the data. Those algorithms can be particularly useful when calibration data are incomplete or sparse.

Smid, J.↗
NASA NTRS2002

Upper-Stratospheric Ozone Trends 1979-1998

Extensive analyses of ozone observations between 1978 and 1998 measured by Dobson Umkehr, Stratospheric Aerosol and Gas Experiment (SAGE) I and II, and Solar Backscattered Ultraviolet (SBUV) and (SBUV)/2 indicate continued significant ozone decline throughout the extratropical upper stratosphere from 30-45 km altitude. The maximum annual linear decline of -0.8 +/- 0.2 %/yr(2sigma) occurs at 40 km and is well described in terms of a linear decline modulated by the 11-year solar variation. The minimum decline of -0.110.1% yr-1(2o) occurs at 25 km in midlatitudes, with remarkable symmetry between the Northern and Southern Hemispheres at 40 km altitude. Midlatitude upper-stratospheric zonal trends exhibit significant seasonal variation (+/- 30% in the Northern Hemisphere, +/- 40% in the Southern Hemisphere) with the most negative trends of -1.2%/yr occurring in the winter. Significant seasonal trends of -0.7 to -0.9%/yr occur at 40 km in the tropics between April and September. Subjecting the statistical models used to calculate the ozone trends to intercomparison tests on a variety of common data sets yields results that indicate the standard deviation between trends estimated by 10 different statistical models is less than 0.1%/yr in the annual-mean trend for SAGE data and less than 0.2%/yr in the most demanding conditions (seasons with irregular, sparse data) [World Meteorological Organization (WMO), 1998]. These consistent trend results between statistical models together with extensive consistency between the independent measurement-system trend observations by Dobson Umkehr, SAGE I and II, and SBUV and SBUV/2 provide a high degree of confidence in the accuracy of the declining ozone amounts reported here. Additional details of ozone trend results from 1978 to 1996 (2 years shorter than reported here) along with lower-stratospheric and tropospheric ozone trends, extensive intercomparisons to assess relative instrument drifts, and retrieval algorithm details are given by WMO [1998].

Newchurch, M. J.↗
NASA NTRS2014

Features of Point Clouds Synthesized from Multi-View ALOS/PRISM Data and Comparisons with LiDAR Data in Forested Areas

LiDAR waveform data from airborne LiDAR scanners (ALS) e.g. the Land Vegetation and Ice Sensor (LVIS) havebeen successfully used for estimation of forest height and biomass at local scales and have become the preferredremote sensing dataset. However, regional and global applications are limited by the cost of the airborne LiDARdata acquisition and there are no available spaceborne LiDAR systems. Some researchers have demonstrated thepotential for mapping forest height using aerial or spaceborne stereo imagery with very high spatial resolutions.For stereo imageswith global coverage but coarse resolution newanalysis methods need to be used. Unlike mostresearch based on digital surface models, this study concentrated on analyzing the features of point cloud datagenerated from stereo imagery. The synthesizing of point cloud data from multi-view stereo imagery increasedthe point density of the data. The point cloud data over forested areas were analyzed and compared to small footprintLiDAR data and large-footprint LiDAR waveform data. The results showed that the synthesized point clouddata from ALOSPRISM triplets produce vertical distributions similar to LiDAR data and detected the verticalstructure of sparse and non-closed forests at 30mresolution. For dense forest canopies, the canopy could be capturedbut the ground surface could not be seen, so surface elevations from other sourceswould be needed to calculatethe height of the canopy. A canopy height map with 30 m pixels was produced by subtracting nationalelevation dataset (NED) fromthe averaged elevation of synthesized point clouds,which exhibited spatial featuresof roads, forest edges and patches. The linear regression showed that the canopy height map had a good correlationwith RH50 of LVIS data with a slope of 1.04 and R2 of 0.74 indicating that the canopy height derived fromPRISM triplets can be used to estimate forest biomass at 30 m resolution.

LiDARD↗
NASA NTRS2020

Application of Low-Cost Fine Particulate Mass Monitors to Convert Satellite Aerosol Optical Depth Measurements to Surface Concentrations in North America and Africa

Low-cost particulate mass sensors provide opportunities to assess air quality at unprecedented spatial and temporal resolutions. Established traditional monitoring networks have limited spatial resolution and are simply absent in many major cities across sub-Saharan Africa (SSA). Satellites provide snapshots of regional air pollution but require ground-truthing. Low-cost monitors can supplement and extend data coverage from these sources worldwide, providing a better overall air quality picture. We investigate the utility of such a multi-source data integration approach using two case studies. First, in Pittsburgh, Pennsylvania, both traditional monitoring and dense low-cost sensor networks are compared with satellite aerosol optical depth (AOD) data from NASA's MODIS system, and a linear conversion factor is developed to convert AOD to surface fine particulate matter mass concentration (as PM2.5). With 10 or more ground monitors in Pittsburgh, there is a 2-fold reduction in surface PM2.5 estimation mean absolute error compared to using only a single ground monitor. Second, we assess the ability of combined regional-scale satellite retrievals and local-scale low-cost sensor measurements to improve surface PM2.5 estimation at several urban sites in SSA. In Rwanda, we find that combining local ground monitoring information with satellite data provides a 40 % improvement in surface PM2.5 estimation accuracy with respect to using low-cost ground monitoring data alone. A linear AOD-to-surface-PM2.5 conversion factor developed in Kigali, Rwanda, did not generalize well to other parts of SSA and varied seasonally for the same location, emphasizing the need for ongoing and localized ground-based monitoring, which can be facilitated by low-cost sensors. Overall, we find that combining ground-based low-cost sensor and satellite data, even without including additional meteorological or land use information, can improve and expand spatiotemporal air quality data coverage, especially in data-sparse regions.

AOD↗
DOE OSTI2026

Detector alignment for X-ray crystallography using Millepede-II

I describe a method for accurately refining the geometrical parameters of segmented X-ray area detectors on the basis of serial crystallography data, using 'Millepede' – an algorithm created for a very similar problem in high-energy physics. The Millepede method for serial crystallography builds on the approach of Brewster et al. [Acta Cryst. (2018), D74, 877–894], in which the detector parameters are refined simultaneously with the parameters for each individual crystal. This accounts for the mutual dependency between the parameters and thereby avoids the bias and slow convergence problems that have afflicted older approaches in which the deviations between observed and calculated Bragg peak positions were taken directly as the updates for the detector panel positions. The Millepede method uses the special structure of the least-squares normal equations to reduce them to a much smaller form that can be solved very quickly, even compared with the sparse matrix methods used previously. This makes it practical to refine the detector geometry frequently and thereby maintain accurate calibration without specialized alignment campaigns. Tilts of detector panels out of the plane can be reliably refined, as can the overall distance of the detector in the beam direction. With a simulated test case, the new method produced panel shifts within 7% of the correct values with only one iteration, and produced almost exactly correct shifts after a second iteration. A simulated out-of-plane panel rotation was correctly determined to within 0.001°. Applied to experimental data from an X-ray free-electron laser, the method increased the indexable fraction of frames from 30% to 91% in a single iteration, and to 96% after two further iterations. Computing the geometry updates on the basis of 2060 crystals took only 0.819 s on desktop computing hardware, including the time taken to read the required data from disk. The scaling was found to be very close to linear for up to 100 980 sets of crystal parameters, which took only 78.2 s to process under the same conditions. The method has been applied as part of a real-time feedback system at a synchrotron radiation beamline, in which an out-of-plane detector tilt of 0.04° was detected and corrected. Possible further applications are also described here.

Millepede-II↗
NASA NTRS2007

Validation of the Pulmonary Function System for Use on the International Space Station

Aerobic deconditioning occurs during long duration space flight despite the use of exercise countermeasures (Convertino, 1996). As a part of International Space Station (ISS) medical operations, periodic tests designed to estimate aerobic capacity are performed to track changes in aerobic fitness and to determine the effectiveness of exercise countermeasures. These tests are performed prior to, during, and after missions of greater than 30 days in duration. Crewmembers selected for missions aboard the ISS perform a graded exercise test on a cycle ergometer approximately 270 days prior to their scheduled launch date in order to measure peak oxygen consumption (VO2PK) and peak heart rate (HRpk). Approximately 30 to 45 days prior to launch, crewmembers perform a submaximal cycle ergometer test at work rates set to elicit 25, 50 and 75% of their pre-flight VO2PK. This test, known as the Periodic Fitness Evaluation (PFE), serves as a baseline measure to which subsequent in-and post-flight exercise tests are compared. While onboard the ISS, crewmembers are normally scheduled to perform the PFE beginning with flight day (FD) 14 and every 30 days thereafter. The PFE is also conducted 5 and 30 days following flight. Using PFE data, aerobic fitness is estimated by quantifying the VO2 vs. HR relationship using linear regression and calculating the VO2 that would occur at the crewmember s previously measured HRpk. Currently, for data collected during flight, this technique assumes that the pre- vs. in-flight oxygen consumption per given cycle workload is similar. However, the validity of this assumption is based upon a sparse amount of data collected during the Skylab era (Michel, et al. 1977). The method of using heart rate and cycle ergometer work rates has been used to estimate aerobic fitness in normal gravity (Astrand and Ryhming, 1954; Lee, 1993). Due to spaceflight induced physiological alterations, such as shifts in extracellular fluid (e.g. plasma) volume, this method may not be valid during space flight. In addition, the ergometer onboard ISS is vibration-isolated and moves with the astronaut s application of force into the pedals. The effect of this movement on the VO2 of cycle exercise on ISS has not been quantified.

McCleary, Frank A.↗
DOE OSTI2023

Sparsity of the electron repulsion integral tensor using different localized virtual orbital representations in local second-order Møller–Plesset theory

Utilizing localized orbitals, local correlation theory can reduce the unphysically high system-size scaling of post-Hartree–Fock (post-HF) methods to linear scaling in insulating molecules. The sparsity of the four-index electron repulsion integral (ERI) tensor is central to achieving this reduction. For second-order Møller–Plesset theory (MP2), one of the simplest post-HF methods, only the (ia|jb) ERIs are needed, coupling occupied orbitals i, j and virtuals a, b. In this paper, we compare the numerical sparsity (called the “ragged list”) and two other approaches revealing the low-rank sparsity of the ERI. The ragged list requires only one set of (localized) virtual orbitals, and we find that the orthogonal valence virtual-hard virtual set of virtuals originally proposed by Subotnik et al. gives the sparsest ERI tensor. To further compress the ERI tensor, the pair natural orbital (PNO) type representation uses different sets of virtual orbitals for different occupied orbital pairs, while the occupied-specific virtual (OSV) approach uses different virtuals for each occupied orbital. Here, our results indicate that while the low-rank PNO representation achieves significant rank reduction, it also requires more memory than the ragged list. The OSV approach requires similar memory to that of the ragged list, but it involves greater algorithmic complexity. An approximation (called the “fixed sparsity pattern”) for solving the local MP2 equations using the numerically sparse ERI tensor is proposed and tested to be sufficiently accurate and to have highly controllable error. A low-scaling local MP2 algorithm based on the ragged list and the fixed sparsity pattern is therefore promising.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Open momentum space method for the Hofstadter butterfly and the quantized Lorentz susceptibility

Here we develop a generic k ∙ p open momentum space method for calculating the Hofstadter butterfly of both continuum (moiré) models and tight-binding models, where the quasimomentum is directly substituted by the Landau level (LL) operators. By taking a LL cutoff (and a reciprocal lattice cutoff for continuum models), one obtains the Hofstadter butterfly with in-gap spectral flows. For continuum models such as the moiré model for twisted bilayer graphene, our method gives a sparse Hamiltonian, making it much more efficient than existing methods. The spectral flows in the Hofstadter gaps can be understood as edge states on a momentum space boundary, from which one can determine the two integers (t ν , s ν ) of a gap ν satisfying the Diophantine equation. The spectral flows can also be removed to obtain a clear Hofstadter butterfly. While t ν is known as the Chern number, our theory identifies s ν as a dual Chern number for the momentum space, which corresponds to a quantized Lorentz susceptibility γ xy = eBs ν .

2-dimensional systems↗
NASA NTRS1997

Controls/CFD Interdisciplinary Research Software Generates Low-Order Linear Models for Control Design From Steady-State CFD Results

The NASA Lewis Research Center is developing analytical methods and software tools to create a bridge between the controls and computational fluid dynamics (CFD) disciplines. Traditionally, control design engineers have used coarse nonlinear simulations to generate information for the design of new propulsion system controls. However, such traditional methods are not adequate for modeling the propulsion systems of complex, high-speed vehicles like the High Speed Civil Transport. To properly model the relevant flow physics of high-speed propulsion systems, one must use simulations based on CFD methods. Such CFD simulations have become useful tools for engineers that are designing propulsion system components. The analysis techniques and software being developed as part of this effort are an attempt to evolve CFD into a useful tool for control design as well. One major aspect of this research is the generation of linear models from steady-state CFD results. CFD simulations, often used during the design of high-speed inlets, yield high resolution operating point data. Under a NASA grant, the University of Akron has developed analytical techniques and software tools that use these data to generate linear models for control design. The resulting linear models have the same number of states as the original CFD simulation, so they are still very large and computationally cumbersome. Model reduction techniques have been successfully applied to reduce these large linear models by several orders of magnitude without significantly changing the dynamic response. The result is an accurate, easy to use, low-order linear model that takes less time to generate than those generated by traditional means. The development of methods for generating low-order linear models from steady-state CFD is most complete at the one-dimensional level, where software is available to generate models with different kinds of input and output variables. One-dimensional methods have been extended somewhat so that linear models can also be generated from two- and three-dimensional steady-state results. Standard techniques are adequate for reducing the order of one-dimensional CFD-based linear models. However, reduction of linear models based on two- and three-dimensional CFD results is complicated by very sparse, ill-conditioned matrices. Some novel approaches are being investigated to solve this problem.

Melcher, Kevin J.↗
DOE OSTI2023

WeakIdent: Weak formulation for identifying differential equation using narrow-fit and trimming

Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differential equation is a linear combination of various differential terms, the identification problem can be formulated as solving a linear system, with the feature matrix consisting of linear and nonlinear terms multiplied by a coefficient vector. This product is equal to the time derivative term, and thus generates dynamical behaviors. The goal is to identify the correct terms that form the equation to capture the dynamics of the given data. We propose a general and robust framework to recover differential equations using a weak formulation with two new mechanisms, narrow-fit and trimming, for both ordinary and partial differential equations (ODEs and PDEs). The weak formulation facilitates an efficient and robust way to handle noise, and two new mechanisms, narrow-fit and trimming, improve the coefficient support and value recoveries respectively. For each sparsity level, Subspace Pursuit is utilized to find an initial set of support from the large dictionary. Then, we focus on highly dynamic regions (rows of the feature matrix), and error normalize the feature matrix in the narrow-fit step. The support is further updated via trimming the terms that contribute the least. Finally, the support set of features with the smallest Cross-Validation error is chosen as the result. A comprehensive set of numerical experiments are presented for both systems of ODEs and PDEs with various noise levels. The proposed method gives a robust recovery of the coefficients, and a significant denoising effect which can handle up to 100% noise-to-signal ratio for some equations. We compare the proposed method with several state-of-the-art algorithms for the recovery of differential equations.

97 MATHEMATICS AND COMPUTING↗