Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix multiplication”

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 811 records · Page 45

Reducing Errors In Processing GPS Measurements

Paper presents analyses of techniques for minimization of errors in estimates based on Global Positioning System measurements at multiple locations. Presents fully-redundant double-differencing algorithm for generation of weighted, double-differenced regression system that yields minimum-variance estimates. Addresses two complications arisen in previous double-differencing approaches, namely: Rank-deficient double differencing, and nondiagonal covariance matrix.

Melbourne, W. G.↗

Unsupervised segmentation of polarimetric SAR data using the covariance matrix

A method for unsupervised segmentation of polarimetric synthetic aperture radar (SAR) data into classes of homogeneous microwave polarimetric backscatter characteristics is presented. Classes of polarimetric backscatter are selected on the basis of a multidimensional fuzzy clustering of the logarithm of the parameters composing the polarimetric covariance matrix. The clustering procedure uses both polarimetric amplitude and phase information, is adapted to the presence of image speckle, and does not require an arbitrary weighting of the different polarimetric channels; it also provides a partitioning of each data sample used for clustering into multiple clusters. Given the classes of polarimetric backscatter, the entire image is classified using a maximum a posteriori polarimetric classifier. Four-look polarimetric SAR complex data of lava flows and of sea ice acquired by the NASA/JPL airborne polarimetric radar (AIRSAR) are segmented using this technique. The results are discussed and compared with those obtained using supervised techniques.

Rignot, Eric J. M.↗

Dynamics of a spinning space station with a counterweight connected by multiple cables.

A unique and relatively simple approach is presented for obtaining the linearized equations of motion. A conservative system consisting of two rigid bodies connected by any number of massless cables with linear axial stiffness is assumed. The cable forces and torques are expanded in a Taylor series about the equilibrium values of the system coordinates which results in a cable stiffness matrix. The method of obtaining the equilibrium values of the coordinates is discussed and results are presented. The range of validity of the linear model is determined by comparing results with a digital simulation of the nonlinear system.

Nixon, D. D.↗

Development and evaluation of a list mode neutron coincidence collar for spatial response measurements of fresh fuel assemblies

A traditional safeguards neutron coincidence counting system, the Neutron Coincidence Collar, has been modified to incorporate individual preamplifiers on each of its 18 3He tubes in active interrogation mode. When used with list mode data acquisition (LMDA) and analysis, a signal from each 3He tube can be recorded and analyzed to allow a spatial response measurement to be performed on an item based on count rate and 3He tube location within the system. The ultimate goal of this project is to demonstrate the capabilities of a list mode response matrix for the nondestructive assay of fresh nuclear fuel assemblies. To enable partial defect detection of fuel pin locations and absences within an assembly, the project aims to extend well-established correlated neutron analysis techniques on a preexisting Neutron Coincidence Collar by extracting a greater number of useful signatures from the system than are currently generated. LMDA, combined with the addition of multiple preamplifiers, facilitates this capability by increasing the number of simultaneous signals that can be measured; this allows an in-depth analysis of neutron coincidence events to determine a fissioning item’s location based on the measured doubles count rate in various channel logic coincidence combinations. All of this can be done from a single measurement pulse train in offline analysis, which is the major benefit provided by LMDA. Through various stages of development and testing, a Mirion Technologies model JCC-71 Neutron Coincidence Collar has been successfully retrofit with modern electronics designed in-house at Oak Ridge National Laboratory, matching preexisting JAB-01 electronics performance, while maintaining the original system footprint. This paper presents these various stages of development and experimental evaluation of the proof of concept system.

Moore, Angela S.↗

Heterogeneous multiphase flow properties of volcanic rocks and implications for noble gas transport from underground nuclear explosions

Of interest to the Underground Nuclear Explosion Signatures Experiment are patterns and timing of explosion-generated noble gases that reach the land surface. The impact of potentially simultaneous flow of water and gas on noble gas transport in heterogeneous fractured rock is a current scientific knowledge gap. This article presents field and laboratory data to constrain and justify a triple continua conceptual model with multimodal multiphase fluid flow constitutive equations that represents host rock matrix, natural fractures, and induced fractures from past underground nuclear explosions (UNEs) at Aqueduct and Pahute Mesas, Nevada National Security Site, Nevada, USA. Capillary pressure from mercury intrusion and direct air–water measurements on volcanic tuff core samples exhibit extreme spatial heterogeneity (i.e., variation over multiple orders of magnitude). Petrographic observations indicate that heterogeneity derives from multimodal pore structures in ash-flow tuff components and post-depositional alteration processes. Comparisons of pre- and post-UNE samples reveal different pore size distributions that are due in part to microfractures. Capillary pressure relationships require a multimodal van Genuchten (VG) constitutive model to best fit the data. Relative permeability estimations based on unimodal VG fits to capillary pressure can be different from those based on bimodal VG fits, implying the choice of unimodal vs. bimodal fits may greatly affect flow and transport predictions of noble gas signatures. The range in measured capillary pressure and predicted relative permeability curves for a given lithology and between lithologies highlights the need for future modeling to consider spatially distributed properties.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Improvements in aircraft extraction programs

Flight data from an F-8 Corsair and a Cessna 172 was analyzed to demonstrate specific improvements in the LRC parameter extraction computer program. The Cramer-Rao bounds were shown to provide a satisfactory relative measure of goodness of parameter estimates. It was not used as an absolute measure due to an inherent uncertainty within a multiplicative factor, traced in turn to the uncertainty in the noise bandwidth in the statistical theory of parameter estimation. The measure was also derived on an entirely nonstatistical basis, yielding thereby also an interpretation of the significance of off-diagonal terms in the dispersion matrix. The distinction between coefficients as linear and non-linear was shown to be important in its implication to a recommended order of parameter iteration. Techniques of improving convergence generally, were developed, and tested out on flight data. In particular, an easily implemented modification incorporating a gradient search was shown to improve initial estimates and thus remove a common cause for lack of convergence.

Balakrishnan, A. V.↗

Multiple Changes to Reusable Solid Rocket Motors, Identifying Hidden Risks

The Space Shuttle Reusable Solid Rocket Motor (RSRM) baseline is subject to various changes. Changes are necessary due to safety and quality improvements, environmental considerations, vendor changes, obsolescence issues, etc. The RSRM program has a goal to test changes on full-scale static test motors prior to flight due to the unique RSRM operating environment. Each static test motor incorporates several significant changes and numerous minor changes. Flight motors often implement multiple changes simultaneously. While each change is individually verified and assessed, the potential for changes to interact constitutes additional hidden risk. Mitigating this risk depends upon identification of potential interactions. Therefore, the ATK Thiokol Propulsion System Safety organization initiated the use of a risk interaction matrix to identify potential interactions that compound risk. Identifying risk interactions supports flight and test motor decisions. Uncovering hidden risks of a full-scale static test motor gives a broader perspective of the changes being tested. This broader perspective compels the program to focus on solutions for implementing RSRM changes with minimal/mitigated risk. This paper discusses use of a change risk interaction matrix to identify test challenges and uncover hidden risks to the RSRM program.

Greenhalgh, Phillip O.↗

High-Time-Resolution Study of Magnetic Holes in the Solar Wind

The objectives of this investigation are to determine the internal plasma structure of kinetic-scale and larger scale magnetic holes, and to determine their stability, their source mechanism(s), and their spatial extent. It is also of importance to determine the relationship between kinetic-scale holes and long-duration holes. As smaller and smaller magnetic depressions are investigated in order to make this a complete study, a robust criterion is necessary for distinguishing magnetic holes from random or unresolvable fluctuations in the interplanetary magnetic field. In order to resolve this ambiguity, we obtained from the MFI experiments magnetic field measurements from the WIND spacecraft at a time resolution of 46 to 184 ms over certain periods. We have also devised a measure of certainty for magnetic hole detections. The certainty factor, q, is defined as the difference between the mean magnetic field in the hole and the local magnetic field, in units of the local standard deviation of the field strength. For fullest generality, it is necessary to calculate this q over the range of available scales of interest, from 60 ms up to 300 s. This technique establishes a two dimensional matrix of relative probabilities that a hole of some duration (d) might exist in the data set at a given time (t). In identifying q-peaks in time and duration, we also come upon a natural method for distinguishing holes with internal structure from multiple holes in close proximity or holes nested inside of others. If two q-peaks are more than a half-width apart, they are simply said to be separate events.

Lazarus, Alan↗

Sensitivity Equation Derivation for Transient Heat Transfer Problems

The focus of the paper is on the derivation of sensitivity equations for transient heat transfer problems modeled by different discretization processes. Two examples will be used in this study to facilitate the discussion. The first example is a coupled, transient heat transfer problem that simulates the press molding process in fabrication of composite laminates. These state equations are discretized into standard h-version finite elements and solved by a multiple step, predictor-corrector scheme. The sensitivity analysis results based upon the direct and adjoint variable approaches will be presented. The second example is a nonlinear transient heat transfer problem solved by a p-version time-discontinuous Galerkin's Method. The resulting matrix equation of the state equation is simply in the form of Ax = b, representing a single step, time marching scheme. A direct differentiation approach will be used to compute the thermal sensitivities of a sample 2D problem.

Hou, Gene↗

The OMPS Limb Profiler Instrument: Two-Dimensional Retrieval Algorithm

The upcoming Ozone Mapper and Profiler Suite (OMPS), which will be launched on the NPOESS Preparatory Project (NPP) platform in early 2011, will continue monitoring the global distribution of the Earth's middle atmosphere ozone and aerosol. OMPS is composed of three instruments, namely the Total Column Mapper (heritage: TOMS, OMI), the Nadir Profiler (heritage: SBUV) and the Limb Profiler (heritage: SOLSE/LORE, OSIRIS, SCIAMACHY, SAGE III). The ultimate goal of the mission is to better understand and quantify the rate of stratospheric ozone recovery. The focus of the paper will be on the Limb Profiler (LP) instrument. The LP instrument will measure the Earth's limb radiance (which is due to the scattering of solar photons by air molecules, aerosol and Earth surface) in the ultra-violet (UV), visible and near infrared, from 285 to 1000 nm. The LP simultaneously images the whole vertical extent of the Earth's limb through three vertical slits, each covering a vertical tangent height range of 100 km and each horizontally spaced by 250 km in the cross-track direction. Measurements are made every 19 seconds along the orbit track, which corresponds to a distance of about 150km. Several data analysis tools are presently being constructed and tested to retrieve ozone and aerosol vertical distribution from limb radiance measurements. The primary NASA algorithm is based on earlier algorithms developed for the SOLSE/LORE and SAGE III limb scatter missions. All the existing retrieval algorithms rely on a spherical symmetry assumption for the atmosphere structure. While this assumption is reasonable in most of the stratosphere, it is no longer valid in regions of prime scientific interest, such as polar vortex and UTLS regions. The paper will describe a two-dimensional retrieval algorithm whereby the ozone distribution is simultaneously retrieved vertically and horizontally for a whole orbit. The retrieval code relies on (1) a forward 2D Radiative Transfer code (to model limb radiances within a non-uniform atmosphere and evaluate 2D analytical partial derivatives) and (2) an optimal estimator inversion routine. The algorithm uses the typically sparse nature of the kernel matrices as well as fast matrix inversion techniques to allow for fast inversion of limb data with efficient memory management (as was done for MIPAS data processing). While the method has so far only been developed in the context of Single Scatter, the paper will show how the CPU intensive Multiple Scatter modeling can be implemented using parallel CPU processing. Initial results will be presented in terms of retrieved ozone profiles and code performance.

Rault, Didier F.↗

Durability of Ceramic Matrix Composites in Combustion Environments

SiO2 scale volatility and the resulting recession of SiC has been previously identified for CVD, as well as sintered, SiC and Si3N4 materials. Linear weight loss and surface recession of SiC was observed as a result of SiO2 volatility for both fuel-lean and fuel-rich gas mixtures. A strong Arrhenius temperature dependence exist and parametric studies using multiple linear regression were used to develop recession relationships as a function of e(sup -Q/RT) central dot P(sup X)V(sup y) for both lean and rich combustion conditions. Recession of 0.2 - 2.0 micron/hr is predicted for typical combustion conditions at 1200 - 1400 C, with a somewhat higher absolute recession rate and activation energy for rich combustion versus lean.

Robinson, Raymond C.↗

Exponential time differencing for the tracer equations appearing in primitive equation ocean models

The tracer equations are part of the primitive equations used in ocean modeling and describe the transport of tracers, such as temperature, salinity or chemicals, in the ocean. Depending on the number of tracers considered, several equations may be added to and coupled to the dynamics system. In many relevant situations, the time-step requirements of explicit methods imposed by the transport and mixing in the vertical direction are more restrictive than those for the horizontal, and this may cause the need to use very small time steps if a fully explicit method is employed. To overcome this issue, we propose an exponential time differencing (ETD) solver where the vertical terms (transport and diffusion) are treated with a matrix exponential, whereas the horizontal terms are dealt with in an explicit way. In this work, we investigate numerically the computational speed-ups that can be obtained over other semi-implicit methods, and we analyze the advantages of the method in the case of multiple tracers.

42 ENGINEERING↗

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Binning is Sinning: Redemption for Hubble Diagram Using Photometrically Classified Type Ia Supernovae

Bayesian Estimation Applied to Multiple Species (BEAMS) is implemented in the BEAMS with Bias Corrections (BBC) framework to produce a redshift-binned Hubble diagram (HD) for Type Ia supernovae (SNe Ia). BBC corrects for selection effects and non–SN Ia contamination, and systematic uncertainties are described by a covariance matrix with dimension matching the number of BBC redshift bins. For spectroscopically confirmed SN Ia samples, a recent "Binning is Sinning" article showed that an unbinned HD and covariance matrix reduces the systematic uncertainty by a factor of ~1.5 compared to the binned approach. Here we extend their analysis to obtain an unbinned HD for a photometrically identified sample processed with BBC. To test this new method, we simulate and analyze 50 samples corresponding to the Dark Energy Survey (DES) with a low-redshift anchor; the simulation includes SNe Ia, and contaminants from core-collapse SNe and peculiar SNe Ia. The analysis includes systematic uncertainties for calibration and measures the dark energy equation of state parameter (w). Compared to a redshift-binned HD, the unbinned HD with nearly 2000 events results in a smaller systematic uncertainty, in qualitative agreement with BHS21, and averaging results among the 50 samples we find no evidence for a w-bias. To reduce computation time for fitting an unbinned HD with large samples, we propose an HD-rebinning method that defines the HD in bins of redshift, color, and stretch; the rebinned HD results in similar uncertainty as the unbinned case, and shows no evidence for a w-bias.

79 ASTRONOMY AND ASTROPHYSICS↗

Acoustic theory of axisymmetric multisectioned ducts

Equations are developed for the acoustic field in a duct system which is made up of a number of connected circular and annular ducts. These equations are suitable for finding the acoustic field inside of and radiated from an aircraft turbofan engine. Acoustic modes are used as generalized coordinates in order to develop a set of matrix equations for the acoustic field. Equations for these modes are given for circular and annular ducts with uniform flow. Modal source equations are derived for point acoustic sources. General equations for mode transmission and reflection are developed and detailed equations are derived for ducts with multiple sections of acoustic treatment and for ducts with circumferential splitter rings. The general theory is applied to the special case of a uniform area circular duct with multisection liners and it is shown that the mode reflection effects are proportional to differences of the acoustic admittances of adjacent liners. A numerical example is given which shows that multisection liners may provide greater noise suppression than uniform liners.

Zorumski, W. E.↗

Generalizing mkFit and its Application to HL-LHC

mkFit is an implementation of the Kalman filter-based track reconstruction algorithm that exploits both thread- and data-level parallelism. In the past few years the project transitioned from the R&D phase to deployment in the Run-3 offline workflow of the CMS experiment. The CMS tracking performs a series of iterations, targeting reconstruction of tracks of increasing difficulty after removing hits associated to tracks found in previous iterations. mkFit has been adopted for several of the tracking iterations, which contribute to the majority of reconstructed tracks. When tested in the standard conditions for production jobs, speedups in track pattern recognition are on average of the order of 3.5x for the iterations where it is used (3-7x depending on the iteration). Multiple factors contribute to the observed speedups, including vectorization and a lightweight geometry description, as well as improved memory management and single precision. Efficient vectorization is achieved with both the icc and the gcc (default in CMSSW) compilers and relies on a dedicated library for small matrix operations, Matriplex, which has recently been released in a public repository. While the mkFit geometry description already featured levels of abstraction from the actual Phase-1 CMS tracker, several components of the implementations were still tied to that specific geometry. We have further generalized the geometry description and the configuration of the run-time parameters, in order to enable support for the Phase-2 upgraded tracker geometry for the HL-LHC and potentially other detector configurations. The implementation strategy and high-level code changes required for the HL-LHC geometry are presented. Speedups in track building from mkFit imply that track fitting becomes a comparably time consuming step of the tracking chain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Multi-energy ion irradiation effects and distinctive features of color center generation in yttria-stabilized zirconia driven by structural discrepancy

Regarding a requirement for inert matrix fuel (IMF) to burn minor actinides and plutonium and high-level waste immobilization, Yttria-stabilized zirconia (ZrO 2 -6.5 wt% Y 2 O 3 ) (YSZ) crystals with cubic phase are selected to comprehensively evaluate the irradiation resistance by irradiation-induced structural discrepancies across multiple energy conditions. Electronic excitation and nuclear collisions reveal distinct color centers, influenced by varying component ratios that reflect their formation mechanisms. Key factors driving ultra-fast structural transitions include collision cascades, pressure waves, and energy dissipation from electronic excitation. In this work, we find that in the electronic energy loss (E ele )-dominant region, internal latent tracks with unique surface nanostructures emerge, distinct from the defect clusters seen in the nuclear energy loss (E nuc )-dominant region, while the threshold for latent track formation and melting are identified. In conclusion, structural discrepancies driven by different energy-loss mechanisms promote the generation of singly ionized and nearest-neighbor doubly ionized oxygen vacancies, which respectively dominate the formation of F⁺ and T-centers, resulting in bandgap narrowing (4.80 eV → 4.73 eV), and furthermore triggering visible light emission (2.17 eV → 2.20 eV) in irradiated YSZ crystals, thus, enabling the design of novel irradiation-tailored material functionalities.

36 MATERIALS SCIENCE↗

Optical Modeling Activities for the James Webb Space Telescope (JWST) Project: Determining Image Motion and Wavefront Error Over an Extended Field of View with a Segmented Optical System - II

This is part two of a series on the optical modeling activities for JWST. Starting with the linear optical model discussed in part one, we develop centroid and wavefront error sensitivities for the special case of a segmented optical system such as JWST, where the primary mirror consists of 18 individual segments. Our approach extends standard sensitivity matrix methods used for systems consisting of monolithic optics, where the image motion is approximated by averaging ray coordinates at the image and residual wavefront error is determined with global tip/tilt removed. We develop an exact formulation using the linear optical model, and extend it to cover multiple field points for performance prediction at each instrument aboard JWST. This optical model is then driven by thermal and dynamic structural perturbations in an integrated modeling environment. Results are presented.

Howard, Joseph M.↗