Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix factorization”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Stochastic model of the NASA/MSFC ground facility for large space structures with uncertain parameters: The maximum entropy approach, part 2

A validated technology data base is being developed in the areas of control/structures interaction, deployment dynamics, and system performance for Large Space Structures (LSS). A Ground Facility (GF), in which the dynamics and control systems being considered for LSS applications can be verified, was designed and built. One of the important aspects of the GF is to verify the analytical model for the control system design. The procedure is to describe the control system mathematically as well as possible, then to perform tests on the control system, and finally to factor those results into the mathematical model. The reduction of the order of a higher order control plant was addressed. The computer program was improved for the maximum entropy principle adopted in Hyland's MEOP method. The program was tested against the testing problem. It resulted in a very close match. Two methods of model reduction were examined: Wilson's model reduction method and Hyland's optimal projection (OP) method. Design of a computer program for Hyland's OP method was attempted. Due to the difficulty encountered at the stage where a special matrix factorization technique is needed in order to obtain the required projection matrix, the program was successful up to the finding of the Linear Quadratic Gaussian solution but not beyond. Numerical results along with computer programs which employed ORACLS are presented.

Hsia, Wei Shen↗
NASA NTRS1987

Estimation of geopotential from satellite-to-satellite range rate data: Numerical results

A technique for high-resolution geopotential field estimation by recovering the harmonic coefficients from satellite-to-satellite range rate data is presented and tested against both a controlled analytical simulation of a one-day satellite mission (maximum degree and order 8) and then against a Cowell method simulation of a 32-day mission (maximum degree and order 180). Innovations include: (1) a new frequency-domain observation equation based on kinetic energy perturbations which avoids much of the complication of the usual Keplerian element perturbation approaches; (2) a new method for computing the normalized inclination functions which unlike previous methods is both efficient and numerically stable even for large harmonic degrees and orders; (3) the application of a mass storage FFT to the entire mission range rate history; (4) the exploitation of newly discovered symmetries in the block diagonal observation matrix which reduce each block to the product of (a) a real diagonal matrix factor, (b) a real trapezoidal factor with half the number of rows as before, and (c) a complex diagonal factor; (5) a block-by-block least-squares solution of the observation equation by means of a custom-designed Givens orthogonal rotation method which is both numerically stable and tailored to the trapezoidal matrix structure for fast execution.

Thobe, Glenn E.↗
NASA NTRS1992

Electromagnetic scattering calculations on the Intel Touchstone Delta

During the first year's operation of the Intel Touchstone Delta system, software which solves the electric field integral equations for fields scattered from arbitrarily shaped objects has been transferred to the Delta. To fully realize the Delta's resources, an out-of-core dense matrix solution algorithm that utilizes some or all of the 90 Gbyte of concurrent file system (CFS) has been used. The largest calculation completed to date computes the fields scattered from a perfectly conducting sphere modeled by 48,672 unknown functions, resulting in a complex valued dense matrix needing 37.9 Gbyte of storage. The out-of-core LU matrix factorization algorithm was executed in 8.25 h at a rate of 10.35 Gflops. Total time to complete the calculation was 19.7 h-the additional time was used to compute the 48,672 x 48,672 matrix entries, solve the system for a given excitation, and compute observable quantities. The calculation was performed in 64-b precision.

Cwik, Tom↗
NASA NTRS2016

Emissions Relationships Among Western Forest Fire Plumes: II. Plume Typing for Sources of Ozone and Aerosol Absorption

Previous studies of emission factors from biomass burning are prone to largeerrors since they ignore the interplay of mixing and varying pre-fire backgroundCO2 levels. Such complications severely affected our studies of 446 forest fireplume samples measured in the Western US by the science teams of NASAs SEAC4RS and ARCTAS airborne missions. Consequently we propose a MixedEffects Regression Emission Technique (MERET) to check techniques like theNormalized Emission Ratio Method (NERM), where use of sequentialobservations cannot disentangle emissions and mixing. We also evaluate asimpler consensus technique. All techniques relate emissions to fuel burnedusing Cburn Ctot added to the fire plume, where Ctot (CO2 + CO). Mixed-effectsregression can estimate pre-fire background values of Ctot (indexed byobservation j) simultaneously with emissions factors indexed by individualspecies i, xi (Cburn )i,j., MERET and consensus require more than twoemissions indicators. Our studies excluded samples where exogenous CO orCH4 might have been fed into a fire plume, mimicking emission.We sought to let the data on 13 gases and particulate properties suggest clustersof variables and plume types, using non-negative matrix factorization (NMF).While samples were mixtures, the NMF unmixing suggested purer burn types.Particulate properties (bscat, babs, SSA, AE) and gas-phase emissions were interrelated.Finally, we sought a simple categorization useful for modeling ozone productionin plumes. Two kinds of fires produced high ozone: those with large fuel nitrogenas evidenced by remnant CH3CN in the plumes, and also those from veryintense large burns. Fire types with optimal ratios of delta-NOydelta-HCHO associate with the highest additional ozone per unit Cburn, Perhaps theseplumes exhibit limited NOx binding to reactive organics. Perhaps these plumesexhibit limited NOx binding to reactive organics.

ozone↗
NASA NTRS2017

Emissions Relationships Among Western Forest Fire Plumes: I. Emission Factors Free from Mixing Errors

Previous studies of emission factors from biomass burning are prone to largeerrors since they ignore the interplay of mixing and varying pre-fire backgroundCO2 levels. Such complications severely affected our studies of 446 forest fireplume samples measured in the Western US by the science teams of NASAsSEAC4RS and ARCTAS airborne missions. Consequently we propose a MixedEffects Regression Emission Technique (MERET) to check techniques like theNormalized Emission Ratio Method (NERM), where use of sequentialobservations cannot disentangle emissions and mixing. We also evaluate asimpler consensus technique. All techniques relate emissions to fuel burnedusing C burn = Δ Ctot added to the fire plume, where ≈ Ctot (CO2 + CO). Mixed-effectsregression can estimate pre-fire background values of Ctot (indexed byobservation j) simultaneously with emissions factors indexed by individual species i, δέλτα-xi (Cburn )i,j., MERET and consensus require more than twoemissions indicators. Our studies excluded samples where exogenous CO orCH4 might have been fed into a fire plume, mimicking emission.We sought to let the data on 13 gases and particulate properties suggest clustersof variables and plume types, using non-negative matrix factorization (NMF).While samples were mixtures, the NMF unmixing suggested purer burn types.Particulate properties (bscat, babs, SSA, AÅE) and gas-phase emissions were interrelated.Finally, we sought a simple categorization useful for modeling ozone productionin plumes. Two kinds of fires produced high ozone: those with large fuel nitrogenas evidenced by remnant CH3CN in the plumes, and also those from veryintense large burns. Fire types with optimal ratios of delta-NOydelta-HCHO associate with the highest additional ozone per unit Cburn, Perhaps theseplumes exhibit limited NOx binding to reactive organics. Perhaps these plumesexhibit limited NOx binding to reactive organics.

plumes↗
NASA NTRS2015

Techniques for Estimating Emissions Factors from Forest Burning: ARCTAS and SEAC4RS Airborne Measurements Indicate Which Fires Produce Ozone

Previous studies of emission factors from biomass burning are prone to large errors since they ignore the interplay of mixing and varying pre-fire background CO2 levels. Such complications severely affected our studies of 446 forest fire plume samples measured in the Western US by the science teams of NASA's SEAC4RS and ARCTAS airborne missions. Consequently we propose a Mixed Effects Regression Emission Technique (MERET) to check techniques like the Normalized Emission Ratio Method (NERM), where use of sequential observations cannot disentangle emissions and mixing. We also evaluate a simpler "consensus" technique. All techniques relate emissions to fuel burned using C(sub burn) = delta C(sub tot) added to the fire plume, where C(sub tot) approximately equals (CO2 + CO). Mixed-effects regression can estimate pre-fire background values of Ctot (indexed by observation j) simultaneously with emissions factors indexed by individual species i, delta epsilon lambda tau alpha−x(sub i)/(C(sub burn))i,j., MERET and "consensus" require more than two emissions indicators. Our studies excluded samples where exogenous CO or CH4 might have been fed into a fire plume, mimicking emission. We sought to let the data on 13 gases and particulate properties suggest clusters of variables and plume types, using non-negative matrix factorization (NMF). While samples were mixtures, the NMF unmixing suggested purer burn types. Particulate properties (bscat, babs, SSA, AAE) and gas-phase emissions were interrelated. Finally, we sought a simple categorization useful for modeling ozone production in plumes. Two kinds of fires produced high ozone: those with large fuel nitrogen as evidenced by remnant CH3CN in the plumes, and also those from very intense large burns. Fire types with optimal ratios of delta-NOy/delta- HCHO associate with the highest additional ozone per unit Cburn, Perhaps these plumes exhibit limited NOx binding to reactive organics. Perhaps these plumes exhibit limited NOx binding to reactive organics.

fires↗
NASA NTRS2016

Techniques for Estimating Emissions Factors from Forest Burning: ARCTAS and SEAC4RS Airborne Measurements Indicate which Fires Produce Ozone

Previous studies of emission factors from biomass burning are prone to large errors since they ignore the interplay of mixing and varying pre-fire background CO2 levels. Such complications severely affected our studies of 446 forest fire plume samples measured in the Western US by the science teams of NASA's SEAC4RS and ARCTAS airborne missions. Consequently we propose a Mixed Effects Regression Emission Technique (MERET) to check techniques like the Normalized Emission Ratio Method (NERM), where use of sequential observations cannot disentangle emissions and mixing. We also evaluate a simpler "consensus" technique. All techniques relate emissions to fuel burned using C(burn) = delta C(tot) added to the fire plume, where C(tot) approximately equals (CO2 = CO). Mixed-effects regression can estimate pre-fire background values of C(tot) (indexed by observation j) simultaneously with emissions factors indexed by individual species i, delta, epsilon lambda tau alpha-x(sub I)/C(sub burn))I,j. MERET and "consensus" require more than emissions indicators. Our studies excluded samples where exogenous CO or CH4 might have been fed into a fire plume, mimicking emission. We sought to let the data on 13 gases and particulate properties suggest clusters of variables and plume types, using non-negative matrix factorization (NMF). While samples were mixtures, the NMF unmixing suggested purer burn types. Particulate properties (b scant, b abs, SSA, AAE) and gas-phase emissions were interrelated. Finally, we sought a simple categorization useful for modeling ozone production in plumes. Two kinds of fires produced high ozone: those with large fuel nitrogen as evidenced by remnant CH3CN in the plumes, and also those from very intense large burns. Fire types with optimal ratios of delta-NOy/delta- HCHO associate with the highest additional ozone per unit Cburn, Perhaps these plumes exhibit limited NOx binding to reactive organics. Perhaps these plumes exhibit limited NOx binding to reactive organics

ozone↗
NASA NTRS2011

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗
NASA NTRS1985

Study of the lithology, petrology and rock chemistry for the Pyramid Mountains, New Mexico

Rock and soil samples were collected at 24 sites within the Pyramid Mountains of southwestern New Mexico. The site locations are specified as 10-acre plots within the Section, Township, and Range land survey system. Hand specimen are described. The specimen were analyzed by X-ray fluorescence. The technique is designed to obtain good analysis for silica. The other elements are run so that matrix factor logic can be used to adjust the silica intensities, and to compensate for the element interaction.

Grant, S. K.↗
NASA NTRS1991

Spatial operator approach to flexible multibody system dynamics and control

The inverse and forward dynamics problems for flexible multibody systems were solved using the techniques of spatially recursive Kalman filtering and smoothing. These algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. These identities are easily derived using the spatial operator algebra developed by the author. Current work is aimed at computational experiments with the described algorithms and at modelling for control design of limber manipulator systems. It is also aimed at handling and manipulation of flexible objects.

Rodriguez, G.↗
NASA NTRS1990

Spatial operator approach to flexible manipulator inverse and forward dynamics

This study extends to flexible multibody manipulators the recent results of the author on the use of spatially recursive filtering and smoothing techniques for robot arm dynamics. The configuration analyzed is that of a mechanical system of flexible bodies joined together by articulated joints. The inverse and forward dynamics problems are solved using the techniques of spatially recursive Kalman filtering and smoothing. The algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. The identities are easily derived using a spatial operator algebra developed by the author.

Rodriguez, G.↗
NASA NTRS1991

Generalized covariance analysis for partially autonomous deep space missions

A new covariance analysis method is presented that is suitable for the evaluation of multiple impulsive controllers acting on some stochastic process x. The method accommodates batch and sequential estimators with equal ease and accounts for time-delay effects in a natural manner. The formalism is developed in terms of a generalized state vector that is formed from the system state vector x, augmented by various fixed epoch estimates, and a data vector formed from discrete time observations of the system. Recursions are developed for time transition, measurement incorporation, and impulsive control updating of the generalized covariance matrix. Means of limiting the dimensional growth of the generalized state vector via the processes of estimator epoch adjustment and measurement vector deflation are described and the application of numerically stable matrix factorization methods to the generalized covariance recursions is outlined. The method is applied to the Magellan spacecraft to demonstrate the capability of ground-based optimal estimation and control of gyro/star scanner misalignment.

Boone, Jack N.↗
NASA NTRS1991

Parallel variable-band Choleski solvers for computational structural analysis applications on vector multiprocessor supercomputers

A Choleski method used to solve linear systems of equations that arise in large scale structural analyses is described. The method uses a novel variable-band storage scheme and is structured to exploit fast local memory caches while minimizing data access delays between main memory and vector registers. Several parallel implementations of this method are described for the CRAY-2 and CRAY Y-MP computers demonstrating the use of microtasking and autotasking directives. A portable parallel language, FORCE, is also used for two different parallel implementations, demonstrating the use of CRAY macrotasking. Results are presented comparing the matrix factorization times for three representative structural analysis problems from runs made in both dedicated and multi-user modes on both the CRAY-2 and CRAY Y-MP computers. CPU and wall clock timings are given for the various parallel methods and are compared to single processor timings of the same algorithm. Computation rates over 1 GIGAFLOP (1 billion floating point operations per second) on a four processor CRAY-2 and over 2 GIGAFLOPS on an eight processor CRAY Y-MP are demonstrated as measured by wall clock time in a dedicated environment. Reduced wall clock times for the parallel methods relative to the single processor implementation of the same Choleski algorithm are also demonstrated for runs made in multi-user mode.

Poole, E. L.↗
NASA NTRS1995

A case study of view-factor rectification procedures for diffuse-gray radiation enclosure computations

The view factors which are used in diffuse-gray radiation enclosure calculations are often computed by approximate numerical integrations. These approximately calculated view factors will usually not satisfy the important physical constraints of reciprocity and closure. In this paper several view-factor rectification algorithms are reviewed and a rectification algorithm based on a least-squares numerical filtering scheme is proposed with both weighted and unweighted classes. A Monte-Carlo investigation is undertaken to study the propagation of view-factor and surface-area uncertainties into the heat transfer results of the diffuse-gray enclosure calculations. It is found that the weighted least-squares algorithm is vastly superior to the other rectification schemes for the reduction of the heat-flux sensitivities to view-factor uncertainties. In a sample problem, which has proven to be very sensitive to uncertainties in view factor, the heat transfer calculations with weighted least-squares rectified view factors are very good with an original view-factor matrix computed to only one-digit accuracy. All of the algorithms had roughly equivalent effects on the reduction in sensitivity to area uncertainty in this case study.

Taylor, Robert P.↗
NASA NTRS1994

FFT Computation with Systolic Arrays, A New Architecture

The use of the Cooley-Tukey algorithm for computing the l-d FFT lends itself to a particular matrix factorization which suggests direct implementation by linearly-connected systolic arrays. Here we present a new systolic architecture that embodies this algorithm. This implementation requires a smaller number of processors and a smaller number of memory cells than other recent implementations, as well as having all the advantages of systolic arrays. For the implementation of the decimation-in-frequency case, word-serial data input allows continuous real-time operation without the need of a serial-to-parallel conversion device. No control or data stream switching is necessary. Computer simulation of this architecture was done in the context of a 1024 point DFT with a fixed point processor, and CMOS processor implementation has started.

Boriakoff, Valentin↗
NASA NTRS2001

Biomaterials and bone mechanotransduction

Bone is an extremely complex tissue that provides many essential functions in the body. Bone tissue engineering holds great promise in providing strategies that will result in complete regeneration of bone and restoration of its function. Currently, such strategies include the transplantation of highly porous scaffolds seeded with cells. Prior to transplantation the seeded cells are cultured in vitro in order for the cells to proliferate, differentiate and generate extracellular matrix. Factors that can affect cellular function include the cell-biomaterial interaction, as well as the biochemical and the mechanical environment. To optimize culture conditions, good understanding of these parameters is necessary. The new developments in bone biology, bone cell mechanotransduction, and cell-surface interactions are reviewed here to demonstrate that bone mechanotransduction is strongly influenced by the biomaterial properties.

Review↗