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 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Multi-Scale Thermo-Mechanical Modeling of Porous 3D Woven TPS Materials

This work summarizes the process to compute and analyze the thermal conductivity and mechanical properties of 3D woven TPS materials such as 3MDCP (3D Mid-Density Carbon-Phenolic). The PuMA software, developed at NASA Ames, was used to characterize different 3MDCP samples from their constituents' data, averaging their thermal conductivity and elastic properties in the three main directions to obtain their effective orthotropic thermo-mechanical properties. This was performed in multiple steps: firstly, TPS samples were digitally reconstructed using micro computed tomography (µCT) and their constituents were segmented; then, the porous matrix phase was analyzed at the micro-scale and these results were used, along with the fibers’ constituents information, to model the tows at the meso-scale; finally, results from the constituents were homogenized and used to model the thermo-mechanical behavior of the unit cell at the macro-scale. Additionally, to gain a better understanding of the tows’ morphology and distribution of the carbon-phenolic blended fibers, microscopy images of the tows’ cross-section were segmented using deep learning techniques and analyzed with PuMA. This workflow can be applied to any TPS material to computationally obtain its thermo-mechanical properties, enabling more informed TPS design and manufacturing choices.

Multi-Scale↗
NASA NTRS2011

Characterizing the Joint Effect of Diverse Test-Statistic Correlation Structures and Effect Size on False Discovery Rates in a Multiple-Comparison Study of Many Outcome Measures

In their 2009 Annals of Statistics paper, Gavrilov, Benjamini, and Sarkar report the results of a simulation assessing the robustness of their adaptive step-down procedure (GBS) for controlling the false discovery rate (FDR) when normally distributed test statistics are serially correlated. In this study we extend the investigation to the case of multiple comparisons involving correlated non-central t-statistics, in particular when several treatments or time periods are being compared to a control in a repeated-measures design with many dependent outcome measures. In addition, we consider several dependence structures other than serial correlation and illustrate how the FDR depends on the interaction between effect size and the type of correlation structure as indexed by Foerstner s distance metric from an identity. The relationship between the correlation matrix R of the original dependent variables and R~, the correlation matrix of associated t-statistics is also studied. In general R~ depends not only on R, but also on sample size and the signed effect sizes for the multiple comparisons.

Feiveson, Alan H.↗
NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for IMMAT Trials

One of many challenges in the implementation of multiple exciter testing is establishing a reasonable set of test metrics to measure the quality of testing. This is especially true in the application of Impedance Matched Multi-Axis Testing; in that it is possible to have very large spectral density matrices that serve as reference criteria. While there exist plotting schemes to view a spectral density matrix, it is often necessary to break the overlay of reference and test results into subsections of the matrices to get sufficient resolution to interpret the data. In addition, as one attempts to control multiple locations on a structure, implementation of classical single degree-of freedom test tolerances across all channels and associated cross spectra is simply not feasible. Hence it is challenging to evaluate overall test quality. The use of spectral views of the dominant singular values from the singular value decomposition of the spectral density matrices and metrics based upon them is proposed for establishing a set of compact metrics for evaluating test quality. A laboratory experiment will be included to demonstrate this proposed technique.

Impedance Matched Multi-Axis Testing↗
NASA NTRSDate not supplied

Use of Spectral Analysis of Singular Values as a Test Metric for Impedance Matched Multi-Axis Test Trials

One of many challenges in the implementation of multiple exciter testing is establishing a reasonable set of test metrics to measure the quality of testing. This is especially true in the application of Impedance Matched Multi-Axis Testing; in that it is possible to have very large spectral density matrices that serve as reference criteria. While there exist plotting schemes to view a spectral density matrix, it is often necessary to break the overlay of reference and test results into subsections of the matrices to get sufficient resolution to interpret the data. In addition, as one attempts to control multiple locations on a structure, implementation of classical single degree-of freedom test tolerances across all channels and associated cross spectra is simply not feasible. Hence it is challenging to evaluate overall test quality. The use of spectral views of the dominant singular values from the singular value decomposition of the spectral density matrices and metrics based upon them is proposed for establishing a set of compact metrics for evaluating test quality. A laboratory experiment will be included to demonstrate this proposed technique.

Vibration Testing↗
NASA NTRS1994

Optimization of Residual Stresses in MMC's Using Compensating/Compliant Interfacial Layers. Part 2: OPTCOMP User's Guide

A user's guide for the computer program OPTCOMP is presented in this report. This program provides a capability to optimize the fabrication or service-induced residual stresses in uni-directional metal matrix composites subjected to combined thermo-mechanical axisymmetric loading using compensating or compliant layers at the fiber/matrix interface. The user specifies the architecture and the initial material parameters of the interfacial region, which can be either elastic or elastoplastic, and defines the design variables, together with the objective function, the associated constraints and the loading history through a user-friendly data input interface. The optimization procedure is based on an efficient solution methodology for the elastoplastic response of an arbitrarily layered multiple concentric cylinder model that is coupled to the commercial optimization package DOT. The solution methodology for the arbitrarily layered cylinder is based on the local-global stiffness matrix formulation and Mendelson's iterative technique of successive elastic solutions developed for elastoplastic boundary-value problems. The optimization algorithm employed in DOT is based on the method of feasible directions.

Pindera, Marek-Jerzy↗
NASA NTRS2006

An Analysis of Nondestructive Evaluation Techniques for Polymer Matrix Composite Sandwich Materials

Structural sandwich materials composed of triaxially braided polymer matrix composite material face sheets sandwiching a foam core are being utilized for applications including aerospace components and recreational equipment. Since full scale components are being made from these sandwich materials, it is necessary to develop proper inspection practices for their manufacture and in-field use. Specifically, nondestructive evaluation (NDE) techniques need to be investigated for analysis of components made from these materials. Hockey blades made from sandwich materials and a flat sandwich sample were examined with multiple NDE techniques including thermographic, radiographic, and shearographic methods to investigate damage induced in the blades and flat panel components. Hockey blades used during actual play and a flat polymer matrix composite sandwich sample with damage inserted into the foam core were investigated with each technique. NDE images from the samples were presented and discussed. Structural elements within each blade were observed with radiographic imaging. Damaged regions and some structural elements of the hockey blades were identified with thermographic imaging. Structural elements, damaged regions, and other material variations were detected in the hockey blades with shearography. Each technique s advantages and disadvantages were considered in making recommendations for inspection of components made from these types of materials.

Cosgriff, Laura M.↗
NASA NTRS1972

The k-space formulation of the n-dimensional scattering problem

The n-dimensional scattering problem is solved by means of a k-space formulation of the field equations, thereby replacing the conventional integral equation formulation by a set of two algebraic equations in two unknowns in two spaces (the constitutive equation being an algebraic equation in x-space). These equations are solved by an iterative method with the aid of the fast Fourier transform (FFT) algorithm connecting the two spaces, requiring very simple initial approximations. Since algebraic and FFT equations are used, the number of arithmetic multiple-add operations and storage allocations required for a numerical solution are reduced from the order of N sq (for solving the matrix equations resulting from the conventional integral equations) to the order of N(log base 2 of N) and N, respectively (where N is the number of data points required for the specification of the problem). The advantage gained in speed and storage is thus of the order of N/log base 2 of N and N, respectively. This method is thus considerably more efficient than the conventional matrix method, and permits exact numerical solutions for much larger problems. Arguments are presented toward the view that the field equations are more fundamental in k-space. The details and some numerical results of the application of this method to the three-dimensional electromagnetic scattering problems are presented as an example.

Bojarski, N. N.↗
NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗
NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗
NASA NTRS1988

An empirical model for polarized and cross-polarized scattering from a vegetation layer

An empirical model for scattering from a vegetation layer above an irregular ground surface is developed in terms of the first-order solution for like-polarized scattering and the second-order solution for cross-polarized scattering. The effects of multiple scattering within the layer and at the surface-volume boundary are compensated by using a correction factor based on the matrix doubling method. The major feature of this model is that all parameters in the model are physical parameters of the vegetation medium. There are no regression parameters. Comparisons of this empirical model with theoretical matrix-doubling method and radar measurements indicate good agreements in polarization, angular trends, and k sub a up to 4, where k is the wave number and a is the disk radius. The computational time is shortened by a factor of 8, relative to the theoretical model calculation.

Liu, H. L.↗
NASA NTRS2004

Microsystem Cooler Development

A patented microsystem Stirling cooler is under development with potential application to electronics, sensors, optical and radio frequency (RF) systems, microarrays, and other microsystems. The microsystem Stirling cooler is most suited to volume-limited applications that require cooling below the ambient or sink temperature. Primary components of the planar device include: two diaphragm actuators that replace the pistons found in traditional-scale Stirling machines; and a micro-regenerator that stores and releases thermal energy to the working gas during the Stirling cycle. The use of diaphragms eliminates frictional losses and bypass leakage concerns associated with pistons, while permitting reversal of the hot and cold sides of the device during operation to allow precise temperature control. Three candidate microregenerators were custom fabricated for initial evaluation: two constructed of porous ceramic, and one made of multiple layers of nickel and photoresist in an offset grating pattern. An additional regenerator was prepared with a random stainless steel fiber matrix commonly used in existing Stirling machines for comparison to the custom fabricated regenerators. The candidate regenerators were tested in a piezoelectric-actuated test apparatus designed to simulate the Stirling refrigeration cycle. In parallel with the regenerator testing, electrostatically-driven comb-drive diaphragm actuators for the prototype device have been designed for deep reactive ion etching (DRIE) fabrication.

Moran, Matthew E.↗
NASA NTRS2018

Electrical Properties of Unidirectional Carbon Fiber Reinforced Epoxy-Graphene Composites

This paper aims at establishing connections between electrical resistivity and stresses in carbon fiber reinforced epoxy-graphene composites. To avoid the interconnection of multiple parameters, we examined composite specimens consisting of a single strand or tow (12,000 carbon fiber filaments) embedded in an epoxy matrix containing up to 1.0 wt% of graphene (TG679) particles. The specimens show resistance increase with the tensile stress. The characteristic of the dependence varies with the content of graphene particles, tending to be linear as the percentage of graphene content increases. We did not observe any significant changes in the ultimate strength of the composite with an increase of the graphene particles concentration.

Daniel Wentzel↗
NASA NTRS2022

Deep Interacting Multiple Model Filtering

In this paper, a deep learning-based multiple model estimation framework is presented for the state estimation of hybrid dynamical systems from high dimensional observations such as camera images. A low dimensional vector which represents the measurement of the latent dynamical system and its corresponding variance are learned using a deep encoder neural network. An Interacting Multiple Model (IMM) filter is used to generate the latent state estimates and covariances using multiple dynamical models, which can be learned using backpropagation through time. The state estimates of the dynamical system and the corresponding covariance matrix are generated from the latent state estimates and covariance using a deep decoder neural network. The whole network is trained in an end-to-end manner using a loss function which minimizes the negative log-likelihood of the neural network parameters. Simulation results are presented using a 2D bouncing ball example and estimation error statistics are computed which demonstrates the accuracy and consistency of the estimation.

Ghananeel Rotithor↗
NASA NTRS2017

A Framework for Extending the Science Traceability Matrix: Application to the Planned Europa Mission

One of the most critical functions of the systems engineering requirements process for a large multi-instrument science-driven space mission is to successfully communicate customer expectations into a comprehensive and traceable science requirements flowdown. These requirements are essential to communicating the constraints on the scope of the science investigations and clarifying how multiple instruments contribute to a given science goal. They also provide insight into how the science goals of the whole mission are affected by design choices. There is little specific guidance available on best practices for developing this science-driven flowdown. A unified Science Traceability Matrix (USTM) contains a significant amount of information that can be leveraged for that purpose, but the USTM was not designed to directly produce a complete science requirements flowdown. Thus, starting with the principles codified in a USTM, the authors propose a framework that directly maps into the requirements flowdown and supports broader systems engineering processes while retaining its meaning to the science team. This Science Traceability and Alignment Framework, or STAF, defines a set of common definitions and valid relationships to structure communication across the project. In addition, STAF populates a network of information that can be useful to support complex mission analysis activities such as fault protection. This work discusses the highest-level implementation of the STAF, the project-domain or P-STAF, which describes an approach to decomposing customer requirements into science requirements. The planned Europa Mission is used as a case study for the implementation of this framework and its potential benefits to a project.

Susca, Sara↗
NASA NTRS2001

Optimization of an oligonucleotide microchip for microbial identification studies: a non-equilibrium dissociation approach

The utility of a high-density oligonucleotide microarray (microchip) for identifying strains of five closely related bacilli (Bacillus anthracis, Bacillus cereus, Bacillus mycoides, Bacillus medusa and Bacillus subtilis) was demonstrated using an approach that compares the non-equilibrium dissociation rates ('melting curves') of all probe-target duplexes simultaneously. For this study, a hierarchical set of 30 oligonucleotide probes targeting the 16S ribosomal RNA of these bacilli at multiple levels of specificity (approximate taxonomic ranks of domain, kingdom, order, genus and species) was designed and immobilized in a high-density matrix of gel pads on a glass slide. Reproducible melting curves for probes with different levels of specificity were obtained using an optimized salt concentration. Clear discrimination between perfect match (PM) and mismatch (MM) duplexes was achieved. By normalizing the signals to an internal standard (a universal probe), a more than twofold discrimination (> 2.4x) was achieved between PM and 1-MM duplexes at the dissociation temperature at which 50% of the probe-target duplexes remained intact. This provided excellent differentiation among representatives of different Bacillus species, both individually and in mixtures of two or three. The overall pattern of hybridization derived from this hierarchical probe set also provided a clear 'chip fingerprint' for each of these closely related Bacillus species.

Non-NASA Center↗
NASA NTRS1984

Ratioed scatter diagrams - An erotetic method for phase identification on complex surfaces using scanning Auger microscopy

By ratioing multiple Auger intensities and plotting a two-dimensional occupational scatter diagram while digitally scanning across an area, the number and elemental association of surface phases can be determined. This can prove a useful tool in scanning Auger microscopic analysis of complex materials. The technique is illustrated by results from an anomalous region on the reaction zone of a SiC/Ti-6Al-4V metal matrix composite material. The anomalous region is shown to be a single phase associated with sulphur and phosphorus impurities. Imaging of a selected phase from the ratioed scatter diagram is possible and may be a useful technique for presenting multiple scanning Auger images.

Browning, R.↗
NASA NTRS1990

Statistical significance test for transition matrices of atmospheric Markov chains

Low-frequency variability of large-scale atmospheric dynamics can be represented schematically by a Markov chain of multiple flow regimes. This Markov chain contains useful information for the long-range forecaster, provided that the statistical significance of the associated transition matrix can be reliably tested. Monte Carlo simulation yields a very reliable significance test for the elements of this matrix. The results of this test agree with previously used empirical formulae when each cluster of maps identified as a distinct flow regime is sufficiently large and when they all contain a comparable number of maps. Monte Carlo simulation provides a more reliable way to test the statistical significance of transitions to and from small clusters. It can determine the most likely transitions, as well as the most unlikely ones, with a prescribed level of statistical significance.

Vautard, Robert↗