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 451 records · Page 25

Rational approximations from power series of vector-valued meromorphic functions

Let F(z) be a vector-valued function, F: C yields C(sup N), which is analytic at z = 0 and meromorphic in a neighborhood of z = 0, and let its Maclaurin series be given. In this work we developed vector-valued rational approximation procedures for F(z) by applying vector extrapolation methods to the sequence of partial sums of its Maclaurin series. We analyzed some of the algebraic and analytic properties of the rational approximations thus obtained, and showed that they were akin to Pade approximations. In particular, we proved a Koenig type theorem concerning their poles and a de Montessus type theorem concerning their uniform convergence. We showed how optical approximations to multiple poles and to Laurent expansions about these poles can be constructed. Extensions of the procedures above and the accompanying theoretical results to functions defined in arbitrary linear spaces was also considered. One of the most interesting and immediate applications of the results of this work is to the matrix eigenvalue problem. In a forthcoming paper we exploited the developments of the present work to devise bona fide generalizations of the classical power method that are especially suitable for very large and sparse matrices. These generalizations can be used to approximate simultaneously several of the largest distinct eigenvalues and corresponding eigenvectors and invariant subspaces of arbitrary matrices which may or may not be diagonalizable, and are very closely related with known Krylov subspace methods.

Sidi, Avram↗

Sufficient conditions for a local minimum of the Bolza problem with multiple terminal point constraints

Sufficient conditions for a weak relative minimum are derived for a form of the Bolza problem of variational calculus. The derivation ties together first-order and second-order conditions in a unified consistent manner, addresses controllability considerations in some detail, and clarifies some small inconsistencies in earlier work. The resulting second-order conditions of optimality involve the integration of fewer backward-sweep matrix elements than the standard conditions in the literature for problems with an unspecified final time. As a result, the backward-sweep matrices have the same general structure and dimensionality whether the final time is specified or free, with the terminal values of two of three sweep matrices being more complicated in the latter case.

Wood, Lincoln J.↗

A Comparison of the Noise Characteristics of a Conventional Slat and Krueger Flap

An aeroacoustic test of two types of leading-edge high-lift devices has been conducted in the NASA Langley Quiet Flow Facility. The test compares a conventional slat with a notional equivalent-mission Krueger flap. The test matrix includes points that allow for direct comparison of the conventional and Krueger devices for equivalent-mission configurations, where the two high-lift devices satisfy the same lift requirements for a free air flight path at the same cruise airfoil angle of attack. Measurements are made for multiple Mach numbers and directivity angles. Results indicate that the Krueger flap shows similar agreement to the expected power law scaling of a conventional flap, both in terms of Strouhal number and fixed frequency (as a surrogate for Helmholtz number). Directivity patterns vary depending on the specific slat and Krueger orientations. Varying the slat gap while holding overlap constant has the same influence on both the conventional slat and Krueger flap acoustic signature. Closing the gap shows dramatic reduction in levels for both devices. Varying the Krueger overlap has a different effect on the data when compared to varying the slat overlap, but analysis is limited by acoustic sources that regularly present themselves in model-scale wind tunnel testing but are not present for full-scale vehicles. The Krueger cavity is found to have some influence on level and directivity, though not as much as the other considered parameter variations. Overall, while the spectra of the two devices are different in detail, their scaling behavior for varying parameters is extremely similar.

Bahr, Christopher J.↗

Numerically stable algorithm for discrete-ordinate-method radiative transfer in multiple scattering and emitting layered media

The transfer of monochromatic radiation in a scattering, absorbing, and emitting plane-parallel medium with a specified bidirectional reflectivity at the lower boundary is considered. The equations and boundary conditions are summarized. The numerical implementation of the theory is discussed with attention given to the reliable and efficient computation of eigenvalues and eigenvectors. Ways of avoiding fatal overflows and ill-conditioning in the matrix inversion needed to determine the integration constants are also presented.

Stamnes, Knut↗

Exercise thermoregulation after 6 h of chair rest, 6 degrees head-down bed-rest, and water immersion deconditioning in men

The purpose was to investigate the mechanism for the excessive exercise hyperthermia following deconditioning (reduction of physical fitness). Rectal (Tre) and mean skin (Tsk) temperatures and thermoregulatory responses were measured in six men [mean (SD) age, 32 (6) years; mass, 78.26 (5.80) kg; surface area, 1.95 (0.11) m2; maximum oxygen uptake (VO2max), 48 (6) ml.min-1.kg-1; whilst supine in air at dry bulb temperature 23.2 (0.6) degree C, relative humidity 31.1 (11.1)% and air speed 5.6 (0.1) m.min-1] during 70 min of leg cycle exercise [51 (4)% VO2max] in ambulatory control (AC), or following 6 h of chair rest (CR), 6 degree head-down bed rest (BR), and 20 degree (WI20) and 80 degree (WI80) foot-down water immersion [water temperature, 35.0 (0.1) degree C]. Compared with the AC exercise delta Tre [mean (SD) 0.77 (0.13) degree C (*P < 0.05), after WI80 0.96 (0.13) degree C*, and after WI20 1.03 (0.09) degree C*. All Tsk responded similarly to exercise: they decreased (NS) by 0.5-0.7 degree C in minutes 4-8 and equilibrated at +0.1 to +0.5 degree C at 60-70. Skin heat conductance was not different among the five conditions (range = 147-159 kJ.m-2.h-1.degree C-1). Results from an intercorrelation matrix suggested that total body sweat rate was more closely related to Tre at 70 min (Tre70) than limb sweat rate or blood flow. Only 36% of the variability in Tre70 could be accounted for by total sweating, and less than 10% from total body dehydration. It would appear that multiple factors are involved which may include change in sensitivity of thermo- and osmoreceptors.

NASA Discipline Regulatory Physiology↗

Multiplexed Colorimetric Solid-Phase Extraction

Multiplexed colorimetric solid-phase extraction (MC-SPE) is an extension of colorimetric solid-phase extraction (C-SPE) an analytical platform that combines colorimetric reagents, solid phase extraction, and diffuse reflectance spectroscopy to quantify trace analytes in water. In CSPE, analytes are extracted and complexed on the surface of an extraction membrane impregnated with a colorimetric reagent. The analytes are then quantified directly on the membrane surface using a handheld diffuse reflectance spectrophotometer. Importantly, the use of solid-phase extraction membranes as the matrix for impregnation of the colorimetric reagents creates a concentration factor that enables the detection of low concentrations of analytes in small sample volumes. In extending C-SPE to a multiplexed format, a filter holder that incorporates discrete analysis channels and a jig that facilitates the concurrent operation of multiple sample syringes have been designed, enabling the simultaneous determination of multiple analytes. Separate, single analyte membranes, placed in a readout cartridge create unique, analyte-specific addresses at the exit of each channel. Following sample exposure, the diffuse reflectance spectrum of each address is collected serially and the Kubelka-Munk function is used to quantify each water quality parameter via calibration curves. In a demonstration, MC-SPE was used to measure the pH of a sample and quantitate Ag(I) and Ni(II).

Gazda, Daniel B.↗

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

Low thrust chemical orbit to orbit propulsion system propellant management study

Low thrust chemical propulsion systems were sized for transfer of large space systems from LEO to GEO. The influence of propellant combination, tankage and insulation requirements, and propellant management techniques on the LTPS mass and volume were studied. Liquid oxygen combined with hydrogen, methane or kerosene were the propellant combinations. Thrust levels of 445, 2230, and 4450 N were combined with 1, 4 and 8 perigee burn strategies. This matrix of systems was evaluated using multilayer insulation and spray-on-foam insulation systems. Various combinations of toroidal, cylindrical with ellipsoidal domes, and ellipsoidal tank shapes were investigated. Results indicate that low thrust (445 N) and single perigee burn approaches are considerably less efficient than the higher thrust level and multiple burn strategies. A modified propellant settling approach minimized propellant residuals and decreased system complexity, in addition, the toroid/ellipsoidal tank combination was predicted to be shortest.

Dergance, R. H.↗

Subsonic panel method for the efficient analysis of multiple geometry perturbations

An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

Bristow, D. R.↗

Iterative solution of large, sparse linear systems on a static data flow architecture - Performance studies

The applicability of static data flow architectures to the iterative solution of sparse linear systems of equations is investigated. An analytic performance model of a static data flow computation is developed. This model includes both spatial parallelism, concurrent execution in multiple PE's, and pipelining, the streaming of data from array memories through the PE's. The performance model is used to analyze a row partitioned iterative algorithm for solving sparse linear systems of algebraic equations. Based on this analysis, design parameters for the static data flow architecture as a function of matrix sparsity and dimension are proposed.

Reed, D. A.↗

Supporting Crew Autonomy in Deep Space Exploration: Preliminary Onboard Capability Requirements and Proposed Research Questions. Technical Report of the Autonomous Crew Operations Technical Interchange Meeting

Communication delays are a critical challenge posed by long duration deep space exploration. Space missions historically have relied on an ever-present Mission Control Center (MCC) to direct operations in near real-time. As unanticipated anomalies that defeat fault detection and resolution systems do arise, the lack of real-time communication will significantly weaken what the MCC support represents: a reliable safety net for the flight crew through its deep and diverse areas of expertise and investigative resources. As a consequence, future space vehicles and habitats need to be equipped with capabilities to support the flight crew to operate with little or no ground support. Considerations must be given to vehicle and mission designs that will fortify the traditionally ground-centered safety net and forge new support systems, when communication delays exist. In August 2018, NASA’s Human Research Program, through its Human Factors and Behavioral Performance Element, convened a Technical Interchange Meeting (TIM) on Autonomous Crew Operations at NASA Ames Research Center. The goal of the meeting was to gather input from NASA centers, industry, academia, and branches of the Department of Defense (DoD) to address how intelligent technologies can be applied to augment onboard capabilities to support crew anomaly response. The TIM featured 24 presentations by 29 speakers and hosted a total of 59 attendees, including 43 from 5 NASA centers (Ames, Johnson, Langley, Marshall, and Jet Propulsion Lab) and 4 from the DoD (3 from Army Research Lab and 1 from Naval Postgraduate School), with remaining attendees from academia (e.g., UC Davis, CMU) and industry (e.g., IBM, Siemens). Discussions were centered around three themes: standards and guidelines, lessons learned in analog environments, and technologies. To help provide a framework for discussion, a concept matrix describing anomaly response processes was created prior to the TIM (Figure 1, page 6). The matrix captures the steps involved (monitoring and detection, diagnosis, solution development and evaluation, solution implementation and verification, resolution documentation) as well as the resources and capabilities required to support these steps (data, knowledge, analysis, synthesis, resource management). A wallpaper size printout of the matrix was utilized at the TIM to solicit attendee inputs along the three themes; the activity garnered 108 submissions of ideas. Overall, what emerged from TIM discussions was a picture of mismatch between crew anomaly response needs and support that can be provided by existing intelligent technologies. The needs are broad, spanning multiple steps and processes/resources, with many of which lacking support from existing technologies, such as knowledge management throughout the steps of problem solving (especially in resolution documentation) and manpower management. The solutions provided by existing intelligent technologies are specific to the steps/processes that they are designed to support and constrained to solving only problems similar to those that have occurred before. What is lacking from technologies is typically made up by humans, specifically their complex critical thinking, creative problem solving, and domain expertise. In the end, the TIM highlighted the pressing need to support responses to onboard anomalies during autonomous crew operations, particularly those that have eluded the system tests, inspection, and other assurance processes. Such anomalies can potentially threaten crew and vehicle safety, as well as significantly impact overall operations with additional workload. These fairly rare events are difficult to anticipate and prepare for, given the state-of-the-art in intelligent technologies. This is true even for anomalies that stem from “unknown knowns”—cases in which there is sufficient external information to characterize the problem but the overall pattern fails to be recognized by the problem solver, or in which the internal knowledge needed to solve a problem is held tacitly and potentially accessible by the problem solver but not articulated. It follows that the ability to tackle anomalies lies not only with the availability of relevant information and knowledge but also their accessibility in times of need. To that end, we propose research questions along the following three broad themes: • How intelligent technologies can help make relevant knowledge and information available? • How intelligent technologies can help make relevant knowledge and information accessible? • How intelligent technologies can help support the crew operating as a team in anomaly response processes?

autonomous crew operations↗

Electrochemical Detection of Multiple Bioprocess Analytes

An apparatus that includes highly miniaturized thin-film electrochemical sensor array has been demonstrated as a prototype of instruments for simultaneous detection of multiple substances of interest (analytes) and measurement of acidity or alkalinity in bioprocess streams. Measurements of pH and of concentrations of nutrients and wastes in cell-culture media, made by use of these instruments, are to be used as feedback for optimizing the growth of cells or the production of desired substances by the cultured cells. The apparatus is designed to utilize samples of minimal volume so as to minimize any perturbation of monitored processes. The apparatus can function in a potentiometric mode (for measuring pH), an amperometric mode (detecting analytes via oxidation/reduction reactions), or both. The sensor array is planar and includes multiple thin-film microelectrodes covered with hydrous iridium oxide. The oxide layer on each electrode serves as both a protective and electrochemical transducing layer. In its transducing role, the oxide provides electrical conductivity for amperometric measurement or pH response for potentiometric measurement. The oxide on an electrode can also serve as a matrix for one or more enzymes that render the electrode sensitive to a specific analyte. In addition to transducing electrodes, the array includes electrodes for potential control. The array can be fabricated by techniques familiar to the microelectronics industry. The sensor array is housed in a thin-film liquid-flow cell that has a total volume of about 100 mL. The flow cell is connected to a computer-controlled subsystem that periodically draws samples from the bioprocess stream to be monitored. Before entering the cell, each 100-mL sample is subjected to tangential-flow filtration to remove particles. In the present version of the apparatus, the electrodes are operated under control by a potentiostat and are used to simultaneously measure the pH and the concentration of glucose. It is anticipated that development of procedures for trapping more enzymes into hydrous iridium oxide (and possibly into other electroactive metal oxides) and of means for imparting long-term stability to the transducer layers should make it possible to monitor concentrations of products of many enzyme reactions for example, such key bioprocess analytes as amino acids, vitamins, lactose, and acetate.

Rauh, R. David↗

Incorporation of Plasticity and Damage Into an Orthotropic Three-Dimensional Model with Tabulated Input Suitable for Use in Composite Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive industries. While there are several composite material models currently available within commercial transient dynamic finite element codes, several features have been identified as being lacking in the currently available material models that could substantially enhance the predictive capability of the impact simulations. A specific desired feature pertains to the incorporation of both plasticity and damage within the material model. Another desired feature relates to using experimentally based tabulated stress-strain input to define the evolution of plasticity and damage as opposed to specifying discrete input properties (such as modulus and strength) and employing analytical functions to track the response of the material. To begin to address these needs, a combined plasticity and damage model suitable for use with both solid and shell elements is being developed for implementation within the commercial code LS-DYNA. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain-hardening based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. The effective plastic strain is computed by using the non-associative flow rule in combination with appropriate numerical methods. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used, in which a load in one direction results in a stiffness reduction in multiple coordinate directions. A specific laminated composite is examined to demonstrate the process of characterizing and analyzing the response of a composite using the developed model.

Impact↗

An Investigation of Theories of Failure for Ceramic Matrix Composites

In order to further advance the understanding of the mechanical behavior of ceramic matrix composites (CMCs), acoustic emission (AE) techniques were imple mented to monitor and identify damage mechanisms in CMCs under tensile loading. In addition to real-time AE monitoring techniques, a data acquisition system was developed and implemented in order to capture AE waveforms resulting from stress-induced damage. Waveforms were inspected for multiple events, separated in distinct events, and then analyzed to determine waveform characteristics in the time and frequency domains. Waveform characteristics included peak amplitude, event duration, MARSE, energy, and dominant and centroidal frequency. In addition to conventional methods for determining a damage discrimination criteria, a study of the distribution and correlation the waveform characteristics was performed to aid in the determination of a damage discrimination criteria. The damage discrimination criteria was tested for "uniqueness", i.e., the effectiveness of the criteria to identify and monitor damage independent of the stress-strain relationship. Insitu radiography was used to substantiate the damage accumulation.

Hemann, John H.↗

On practical stability.

In this paper, a class of nonlinear nonautonomous systems with multiple nonlinearities is considered. Sufficient conditions are developed for a type of practical stability with specified settling time. The conditions are independent of the actual form of nonlinear characteristics so that they can be interpreted as conditions for 'absolute' practical stability. The stability test is reduced to verification of the Hurwitz property of a constant matrix. This makes the stability analysis of the considered class of nonlinear systems convenient for machine computations. The proposed practical stability analysis is applied to a third-order system with several nonlinearities.

Grujic, L. T.↗

Polarimetry with multiple mirror telescopes

The polarizations of multiple mirror telescopes are calculated using Mueller calculus. It is found that the Multiple Mirror Telescope (MMT) produces a constant depolarization that is a function of wavelength and independent of sky position. The efficiency and crosstalk are modeled and experimentally verified. The two- and four-mirror new generation telescopes are found to produce sinusoidal depolarization for which an accurate interpretation of the incident Stokes vector requires inverse matrix calculations. Finally, the depolarization of f/1 paraboloids is calculated and found to be less than 0.1 percent at 3000 A.

West, S. C.↗

The role of equiaxed particles on the yield stress of composites

Possible explanations are investigated for the yield strength enhancement of discontinuously reinforced Al alloy matrix MMCs, for the case of low temperature yield behavior where deformation occurs by dislocation slide. The Al alloys contain 0.1-10 micron diameter equiaxed particle discontinuous reinforcements of TiB2, Al2O3, and TiC. Attention is given to a single dislocation-particle interaction model, and both dislocation pile-up and forest-hardening multiple-dislocation particle interaction models.

Aikin, R. M., Jr.↗

Composite plates impact damage - An atlas

The present volume on impact damage in composite plates presents an extensive compendium of visual and graphic data regarding a variety of material and impactor parameters. The photographs are taken with X-ray and C-scan imaging in conjunction with a dye penetrant to show matrix cracks and delaminations. Impact and static-loading tests are performed on plates of graphite-epoxy, graphite-toughened epoxy, and graphite-PEEK materials. The images are presented to yield specific visual data regarding such parameters as impactor velocity, thickness of the back ply group, impactor nose radius, and the effects of multiple delaminations. The images are grouped in eight subsets that correspond to parameters including plate length, material, and the difference in fiber orientation between adjacent ply groups. This substantial volume represents a systematic effort to study the effects of several material parameters on impact damage.

Finn, Scott R.↗