Search NASA⌕ Search

SEARCH · Search NASA

Results for “sparsity”

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 145 records · Page 8

Finite element solution of optimal control problems with state-control inequality constraints

It is demonstrated that the weak Hamiltonian finite-element formulation is amenable to the solution of optimal control problems with inequality constraints which are functions of both state and control variables. Difficult problems can be treated on account of the ease with which algebraic equations can be generated before having to specify the problem. These equations yield very accurate solutions. Owing to the sparse structure of the resulting Jacobian, computer solutions can be obtained quickly when the sparsity is exploited.

Bless, Robert R.↗

Optimal matrix approximants in structural identification

Problems of model correlation and system identification are central in the design, analysis, and control of large space structures. Of the numerous methods that have been proposed, many are based on finding minimal adjustments to a model matrix sufficient to introduce some desirable quality into that matrix. In this work, several of these methods are reviewed, placed in a modern framework, and linked to other previously known ideas in computational linear algebra and optimization. This new framework provides a point of departure for a number of new methods which are introduced here. Significant among these is a method for stiffness matrix adjustment which preserves the sparsity pattern of an original matrix, requires comparatively modest computational resources, and allows robust handling of noisy modal data. Numerical examples are included to illustrate the methods presented herein.

Beattie, C. A.↗

The use of linked lists in the simulation of controller-structure interaction

An algorithm for the computer simulation of large space structures under active control is considered. Linked lists are used in a matrix data structure to implement the trapezoidal rule on system differential equations. The use of the trapezoidal rule ensures that the numerical stability is equivalent to the system stability, which is essential for this type of simulation. The sparsity of the system matrices is exploited by the linked lists, and the algorithm efficiently steps through the lists in an orderly fashion. Results of simulations on a NASA large space structure experiment are reported.

Quan, R.↗

The use of linked lists in the simulation of controller-structure interaction

An algorithm for the computer simulation of large space structures under active control is considered. Linked lists are used in a matrix data structure to implement the trapezoidal rule on the system differential equations. The use of the trapezoidal rule ensures that the numerical stability is equivalent to the system stability, which is essential for this type of simulation. The sparsity of the system matrices is exploited by the linked lists, and the algorithm efficiently steps through the lists in an orderly fashion. Results of simulations on a NASA large space structure experiment are reported.

Quan, Ralph↗

A general rough-surface inversion algorithm: Theory and application to SAR data

Rough-surface inversion has significant applications in interpretation of SAR data obtained over bare soil surfaces and agricultural lands. Due to the sparsity of data and the large pixel size in SAR applications, it is not feasible to carry out inversions based on numerical scattering models. The alternative is to use parameter estimation techniques based on approximate analytical or empirical models. Hence, there are two issues to be addressed, namely, what model to choose and what estimation algorithm to apply. Here, a small perturbation model (SPM) is used to express the backscattering coefficients of the rough surface in terms of three surface parameters. The algorithm used to estimate these parameters is based on a nonlinear least-squares criterion. The least-squares optimization methods are widely used in estimation theory, but the distinguishing factor for SAR applications is incorporating the stochastic nature of both the unknown parameters and the data into formulation, which will be discussed in detail. The algorithm is tested with synthetic data, and several Newton-type least-squares minimization methods are discussed to compare their convergence characteristics. Finally, the algorithm is applied to multifrequency polarimetric SAR data obtained over some bare soil and agricultural fields. Results will be shown and compared to ground-truth measurements obtained from these areas. The strength of this general approach to inversion of SAR data is that it can be easily modified for use with any scattering model without changing any of the inversion steps. Note also that, for the same reason it is not limited to inversion of rough surfaces, and can be applied to any parameterized scattering process.

Moghaddam, M.↗

A neural network with modular hierarchical learning

This invention provides a new hierarchical approach for supervised neural learning of time dependent trajectories. The modular hierarchical methodology leads to architectures which are more structured than fully interconnected networks. The networks utilize a general feedforward flow of information and sparse recurrent connections to achieve dynamic effects. The advantages include the sparsity of units and connections, the modular organization. A further advantage is that the learning is much more circumscribed learning than in fully interconnected systems. The present invention is embodied by a neural network including a plurality of neural modules each having a pre-established performance capability wherein each neural module has an output outputting present results of the performance capability and an input for changing the present results of the performance capabilitiy. For pattern recognition applications, the performance capability may be an oscillation capability producing a repeating wave pattern as the present results. In the preferred embodiment, each of the plurality of neural modules includes a pre-established capability portion and a performance adjustment portion connected to control the pre-established capability portion.

Baldi, Pierre F.↗

Tensor-GMRES method for large sparse systems of nonlinear equations

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Feng, Dan↗

An efficiency study of the simultaneous analysis and design of structures

The efficiency of the Simultaneous Analysis and Design (SAND) approach in the minimum weight optimization of structural systems subject to strength and displacement constraints as well as size side constraints is investigated. SAND allows for an optimization to take place in one single operation as opposed to the more traditional and sequential Nested Analysis and Design (NAND) method, where analyses and optimizations alternate. Thus, SAND has the advantage that the stiffness matrix is never factored during the optimization retaining its original sparsity. One of SAND's disadvantages is the increase in the number of design variables and in the associated number of constraint gradient evaluations. If SAND is to be an acceptable player in the optimization field, it is essential to investigate the efficiency of the method and to present a possible cure for any inherent deficiencies.

Striz, Alfred G.↗

Dispersed ion structures at the poleward edge of the auroral oval: Low-altitude observations and numerical modeling

We have compared the AUREOL 3 (A3) observations of auroral ion precipitation, particularly ion beams, with the results from the global kinetic model of magnetotail plasma of Ashour-Abdalla et al. (1993). We have identified 101 energetic keV H(+) velocity dispersed precipitating ion structures (VDIS) with fluxes above 10(exp -3) ergs./sq cm./s in the A3 record between the end of 1981 and mid-1984. These beams display a systematic increase in energy with increasing latitude and were observed in a narrow region within less than 1 deg in latitude of the polar cap boundary. The VDIS are the most distinctive feature in the auroral zone of the plasma sheet boundary layer. We report first on a statistical analysis of the possible ralationships between magnetic activity or substorm phase and the VDIS properties. Our particle simulations of the precipitating ions have been extended by using a series of modified versions of the Tsyganenko (1989) magnetic field model and by varying the cross-magnetosphere electric field. In the simulations, plasma from a mantle source is subject to strong nonlinear acceleration, forming beams which flow along the PSBL. Only 3 to 4% of these beams precipitate into the ionosphere to form the VDIS while the majority return to the equatorial plane after mirroring and form the thermalized central plasma sheet. The final energy and the dispersion of the beams in the model depend on the amplitude of the cross-tail electric field. Two unsual observations of low-energy (less than 5 keV) O(+) VDIS, shifted by 4 deg 5 deg in invariant latitude equatorward of H(+) VDIS are analyzed in detail. The sparsity of such O(+) events and the absence of the changes in the flux and frequency of occurrence indicate a solar wind origin for the plasma. Finally, large-scale kinetic modeling, even with its simplifications and assumptions (e.g., static magnetic field, solar wind source), reproduces low-altitude auroral ion features fairly well; it may therefore be presented as an appropriate framework into which data on energization and transport of the hot plasma, obtained in the equatorial plane, could be inserted in the near future.

Bosqued, J. M.↗

Modular, Hierarchical Learning By Artificial Neural Networks

Modular and hierarchical approach to supervised learning by artificial neural networks leads to neural networks more structured than neural networks in which all neurons fully interconnected. These networks utilize general feedforward flow of information and sparse recurrent connections to achieve dynamical effects. The modular organization, sparsity of modular units and connections, and fact that learning is much more circumscribed are all attractive features for designing neural-network hardware. Learning streamlined by imitating some aspects of biological neural networks.

Baldi, Pierre F.↗

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Molenaar, J.↗

Rhenium Mechanical Properties and Joining Technology

Iridium-coated rhenium (Ir/Re) provides thermal margin for high performance and long life radiation cooled rockets. Two issues that have arisen in the development of flight Ir/Re engines are the sparsity of rhenium (Re) mechanical property data (particularly at high temperatures) required for engineering design, and the inability to directly electron beam weld Re chambers to C103 nozzle skirts. To address these issues, a Re mechanical property database is being established and techniques for creating Re/C103 transition joints are being investigated. This paper discusses the tensile testing results of powder metallurgy Re samples at temperatures from 1370 to 2090 C. Also discussed is the evaluation of Re/C103 transition pieces joined by both, explosive and diffusion bonding. Finally, the evaluation of full size Re transition pieces, joined by inertia welding, as well as explosive and diffusion bonding, is detailed.

Reed, Brian D.↗

PLATSIM: A Simulation and Analysis Package for Large-Order Flexible Systems

The software package PLATSIM provides efficient time and frequency domain analysis of large-order generic space platforms. PLATSIM can perform open-loop analysis or closed-loop analysis with linear or nonlinear control system models. PLATSIM exploits the particular form of sparsity of the plant matrices for very efficient linear and nonlinear time domain analysis, as well as frequency domain analysis. A new, original algorithm for the efficient computation of open-loop and closed-loop frequency response functions for large-order systems has been developed and is implemented within the package. Furthermore, a novel and efficient jitter analysis routine which determines jitter and stability values from time simulations in a very efficient manner has been developed and is incorporated in the PLATSIM package. In the time domain analysis, PLATSIM simulates the response of the space platform to disturbances and calculates the jitter and stability values from the response time histories. In the frequency domain analysis, PLATSIM calculates frequency response function matrices and provides the corresponding Bode plots. The PLATSIM software package is written in MATLAB script language. A graphical user interface is developed in the package to provide convenient access to its various features.

Maghami, Peiman G.↗

Algorithms for Efficient Computation of Transfer Functions for Large Order Flexible Systems

An efficient and robust computational scheme is given for the calculation of the frequency response function of a large order, flexible system implemented with a linear, time invariant control system. Advantage is taken of the highly structured sparsity of the system matrix of the plant based on a model of the structure using normal mode coordinates. The computational time per frequency point of the new computational scheme is a linear function of system size, a significant improvement over traditional, still-matrix techniques whose computational times per frequency point range from quadratic to cubic functions of system size. This permits the practical frequency domain analysis of systems of much larger order than by traditional, full-matrix techniques. Formulations are given for both open- and closed-loop systems. Numerical examples are presented showing the advantages of the present formulation over traditional approaches, both in speed and in accuracy. Using a model with 703 structural modes, the present method was up to two orders of magnitude faster than a traditional method. The present method generally showed good to excellent accuracy throughout the range of test frequencies, while traditional methods gave adequate accuracy for lower frequencies, but generally deteriorated in performance at higher frequencies with worst case errors being many orders of magnitude times the correct values.

Maghami, Peiman G.↗

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Kandil, Osama A.↗

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

El Nino and the Global Ocean Observing System

Until a decade ago, an often-quoted expression in oceanography is that very few observations are recorded throughout the ocean. Now, the sentiment is no longer valid in the uppermost 10% of the tropical Pacific Ocean nor at the surface of the global ocean. One of the remarkable legacies of the 1985-1994 Tropical Oceans Global Atmosphere (TOGA) Program is an in situ marine meteorological and upper oceanographic measurement array throughout the equatorial Pacific to monitor the development and maintenance of El Nino episodes. The TOGA Observing System, which initially consisted of moored- and drifting-buoy arrays, a network of commercial ships, and coastal and island stations, now includes a constellation of satellites and data-assimilating models to simulate subsurface oceanographic conditions. The El Nino and La Nina tropical Pacific Ocean observing system represents the initial phase of an integrated global ocean observing system. Remarkable improvements have been made in ocean model simulation of subsurface currents, but some problems persist. For example, the simulation of the South Equatorial Current (SEC) remains an important challenge in the 2S-2N Pacific equatorial wave guide. During El Nino the SEC at the equator is reduced and sometimes the direction is reversed, becoming eastward. Both conditions allow warm water stored in the western Pacific to invade the eastern region, creating an El Nino episode. Assimilation of data is a tenet of faith to correct simulation errors caused by deficiencies in surface fluxes (especially wind stress) and parameterizations of subgrid-scale physical processes. In the first of two numerical experiments, the Pacific SEC was simulated with and without assimilation of subsurface temperature data. Along the equator, a very weak SEC occurred throughout the eastern Pacific, independent of assimilation of data. However, as displayed in the diagram, in the western Pacific there was no satisfactory agreement between the two simulations. To help determine reliability of the simulated SEC in the western Pacific, current measurements recorded during the 9-19 October 1994 voyage of the French research vessel L'Atalante are also shown in the diagram. With data assimilation, the simulated SEC was in much better agreement with L'Atalante observations. The simulated SEC with data assimilation was far from perfect, in part because of the sparsity of subsurface temperature observations. In the next experiment, TOPEX/POSEIDON sea surface height data in combination with subsurface temperatures will be assimilated to assess further improvement of the simulation of the SEC.

Halpern, David↗

Model Refinement Using Eigensystem Assignment

IA novel approach for the refinement of finite-element-based analytical models of flexible structures is presented. The proposed approach models the possible refinements in the mass, damping, and stiffness matrices of the finite element model in the form of a constant gain feedback with acceleration, velocity, and displacement measurements, respectively. Once the free elements of the structural matrices have been defined, the problem of model refinement reduces to obtaining position, velocity, and acceleration gain matrices with appropriate sparsity that reassign a desired subset of the eigenvalues of the model, along with partial mode shapes, from their baseline values to those obtained from system identification test data. A sequential procedure is used to assign one conjugate pair of eigenvalues at each step using symmetric output feedback gain matrices, and the eigenvectors are partially assigned, while ensuring that the eigenvalues assigned in the previous steps are not disturbed. The procedure can also impose that gain matrices be dissipative to guarantee the stability of the refined model. A numerical example, involving finite element model refinement for a structural testbed at NASA Langley Research Center (Controls-Structures-Interaction Evolutionary model) is presented to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗