Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear system”

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 1,207 records · Page 67

CanTrilBat and Cantera_apps v1.0 beta

This application can determine the performance and chemical behavior of batteries in 1D when they are cycled. With CanTrilBat, we are developing predictive phenomenological models for battery systems to predict operating performance and rate limiting steps in the performance of battery models. Particular attention is paid to primary and secondary chemistry mechanisms, such as the thermal runaway mechanisms experienced in secondary lithium ion batteries or self-discharge reaction mechanism that all batteries experience to one extent or another. The first application of this model has been for modeling the performance of thermal batteries. However, an implementation for secondary ion batteries is next. CanTrilBat applications solves transient problems involving batteries. It is a 1-D application that represents 3-D physical systems that can be reduced using the porous flow approximation for the anode, cathode, and separator. A control volume formulation is used to track conserved quantities. An operator-split approach is used to calculate the chemistry, diffusion and electronic transport that occurs within cathode and anode particles, allowing for the reduction in code complexity. All jacobian operations in CanTrilBat utilize numerical jacobians. A home grown predictor corrector scheme is used for time step control, and a home grown newton solver is used to relax the equations at each time step. Trilinos is used to solve for the resulting linear systems equation A block text input format is used to initialize options for the CanTriBat program. Within this block are the names of several XML input files, which specify the chemistry mechanism. These XML input files are read by low level Cantera routines, and serve to initialize the electrode and electrolyte chemistry mechanisms and transport properties. A GUI implementation has been contracted out to a university professor, but has not been implemented yet. It?s expected that CanTriBat will have the capability to do adaptive grid refinement in later versions. Grids will be halved based on an complicated set of heuristic criteria, based on how well the mesh captures changes to the first and second derivatives of selected solution components. Primary emphasis is given towards converged profiles for IV performance.

Moffat, HarryK.↗

Parallel Preconditioning for CFD Problems on the CM-5

Up to today, preconditioning methods on massively parallel systems have faced a major difficulty. The most successful preconditioning methods in terms of accelerating the convergence of the iterative solver such as incomplete LU factorizations are notoriously difficult to implement on parallel machines for two reasons: (1) the actual computation of the preconditioner is not very floating-point intensive, but requires a large amount of unstructured communication, and (2) the application of the preconditioning matrix in the iteration phase (i.e. triangular solves) are difficult to parallelize because of the recursive nature of the computation. Here we present a new approach to preconditioning for very large, sparse, unsymmetric, linear systems, which avoids both difficulties. We explicitly compute an approximate inverse to our original matrix. This new preconditioning matrix can be applied most efficiently for iterative methods on massively parallel machines, since the preconditioning phase involves only a matrix-vector multiplication, with possibly a dense matrix. Furthermore the actual computation of the preconditioning matrix has natural parallelism. For a problem of size n, the preconditioning matrix can be computed by solving n independent small least squares problems. The algorithm and its implementation on the Connection Machine CM-5 are discussed in detail and supported by extensive timings obtained from real problem data.

Simon, Horst D.↗

CanTrilBat and Cantera_apps v1.0 beta

This application can determine the performance and chemical behavior of batteries in 1D when they are cycled. With CanTrilBat, we are developing predictive phenomenological models for battery systems to predict operating performance and rate limiting steps in the performance of battery models. Particular attention is paid to primary and secondary chemistry mechanisms, such as the thermal runaway mechanisms experienced in secondary lithium ion batteries or self-discharge reaction mechanism that all batteries experience to one extent or another. The first application of this model has been for modeling the performance of thermal batteries. However, an implementation for secondary ion batteries is next. CanTrilBat applications solves transient problems involving batteries. It is a 1-D application that represents 3-D physical systems that can be reduced using the porous flow approximation for the anode, cathode, and separator. A control volume formulation is used to track conserved quantities. An operator-split approach is used to calculate the chemistry, diffusion and electronic transport that occurs within cathode and anode particles, allowing for the reduction in code complexity. All jacobian operations in CanTrilBat utilize numerical jacobians. A home grown predictor corrector scheme is used for time step control, and a home grown newton solver is used to relax the equations at each time step. Trilinos is used to solve for the resulting linear systems equation A block text input format is used to initialize options for the CanTriBat program. Within this block are the names of several XML input files, which specify the chemistry mechanism. These XML input files are read by low level Cantera routines, and serve to initialize the electrode and electrolyte chemistry mechanisms and transport properties. A GUI implementation has been contracted out to a university professor, but has not been implemented yet. It?s expected that CanTriBat will have the capability to do adaptive grid refinement in later versions. Grids will be halved based on an complicated set of heuristic criteria, based on how well the mesh captures changes to the first and second derivatives of selected solution components. Primary emphasis is given towards converged profiles for IV performance.

Moffat, Harry K.↗

Nonlinear dynamic phenomena in the space shuttle thermal protection system

The development of an analysis for examining the nonlinear dynamic phenomena arising in the space shuttle orbiter tile/pad thermal protection system is presented. The tile/pad system consists of ceramic tiles bonded to the aluminum skin of the orbiter through a thin nylon felt pad. The pads are a soft nonlinear material which permits large strains and displays both hysteretic and nonlinear viscous damping. Application of the analysis to a square tile subjected to transverse sinusoidal motion of the orbiter skin is presented and the following nonlinear dynamic phenomena are considered: highly distorted wave forms, amplitude-dependent resonant frequencies which initially decrease and then increase with increasing amplitude of motion, magnification of substrate motion which is higher than would be expected in a similarly highly damped linear system, and classical parametric resonance instability.

Housner, J. M.↗

Dynamic analysis of nonlinear rotor-housing systems

Nonlinear analysis methods are developed which will enable the reliable prediction of the dynamic behavior of the space shuttle main engine (SSME) turbopumps in the presence of bearing clearances and other local nonlinearities. A computationally efficient convolution method, based on discretized Duhamel and transition matrix integral formulations, is developed for the transient analysis. In the formulation, the coupling forces due to the nonlinearities are treated as external forces acting on the coupled subsystems. Iteration is utilized to determine their magnitudes at each time increment. The method is applied to a nonlinear generic model of the high pressure oxygen turbopump (HPOTP). As compared to the fourth order Runge-Kutta numerical integration methods, the convolution approach proved to be more accurate and more highly efficient. For determining the nonlinear, steady-state periodic responses, an incremental harmonic balance method was also developed. The method was successfully used to determine dominantly harmonic and subharmonic responses fo the HPOTP generic model with bearing clearances. A reduction method similar to the impedance formulation utilized with linear systems is used to reduce the housing-rotor models to their coordinates at the bearing clearances. Recommendations are included for further development of the method, for extending the analysis to aperiodic and chaotic regimes and for conducting critical parameteric studies of the nonlinear response of the current SSME turbopumps.

Noah, Sherif T.↗

A stochastic approach to uncertainty in the equations of MHD kinematics

The magnetohydrodynamic (MHD) kinematics model describes the electromagnetic behavior of an electrically conducting fluid when its hydrodynamic properties are assumed to be known. In particular, the MHD kinematics equations can be used to simulate the magnetic field induced by a given velocity field. While prescribing the velocity field leads to a simpler model than the fully coupled MHD system, this may introduce some epistemic uncertainty into the model. If the velocity of a physical system is not known with certainty, the magnetic field obtained from the model may not be reflective of the magnetic field seen in experiments. Additionally, uncertainty in physical parameters such as the magnetic resistivity may affect the reliability of predictions obtained from this model. By modeling the velocity and the resistivity as random variables in the MHD kinematics model, we seek to quantify the effects of uncertainty in these fields on the induced magnetic field. We develop stochastic expressions for these quantities and investigate their impact within a finite element discretization of the kinematics equations. We obtain mean and variance data through Monte Carlo simulation for several test problems. Toward this end, we develop and test an efficient block preconditioner for the linear systems arising from the discretized equations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Applications Study of Aero-Maneuvering Orbit-to-Orbit Shuttle (AMOOS), Executive Summary

Preliminary designs and the supporting analysis for both the Aeromaneuvering Orbit-to-Orbit Shuttle (AMOOS) and the Aeromaneuvering Recovery System (AMRS) are presented. The AMOOS design is shown to yield from twice to almost three times the high energy, round-trip payloads as a purely propulsive vehicle of the same weight. Typically AMOOS can perform a crew rotation mission to equatorial geosynchronous orbit in one space shuttle launch. The flight test program analysis modeled parameters such as maximum dynamic pressure, heating rates, guidance, stability and recovery. Two model flight schedules were developed, one consisting of four flights and the other of two flights. The former is considered a very low risk, high information return program whereas the latter is a minimal cost program consistent with reasonable data returns and chance of success. The AMOOS and AMRS guidance scheme developed using linear regulator theory proved a precise and accurate guidance scheme. Both it and a classical linear system's based scheme were evaluated using 65 simulated trajectories in which the position in the entry corridor and the atmospheric density were varied randomly.

White, J.↗

Scaled ILU Smoothers for Navier-Stokes Pressure Projection

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) V-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES+AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

algebraic multigrid↗

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the embedded discrete fracture model (EDFM) and the embedded finite element method (EFEM) for the flow and the mechanics, respectively. This nonconforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finite volumes that exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an extended finite element approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

58 GEOSCIENCES↗

Fidelity Analysis of Sampled Imaging Systems

Many modeling, simulation and performance analysis studies of sampled imaging systems are inherently incomplete because they are conditioned on a discrete-input, discrete-output model that only accounts for blurring during image acquisition and additive noise. For those sampled imaging systems where the effects of digital image acquisition, digital filtering and reconstruction are significant, the modeling, simulation and performance analysis should be based on a more comprehensive continuous-input, discrete-processing, continuous-output end-to-end model. This more comprehensive model should properly account for the low-pass filtering effects of image acquisition prior to sampling, the potentially important noiselike effects of the aliasing caused by sampling, additive noise due to device electronics and quantization, the generally high-boost filtering effects of digital processing, and the low-pass filtering effects of image reconstruction. This model should not, however, be so complex as to preclude significant mathematical analysis, particularly the mean-square (fidelity) type of analysis so common in linear system theory. We demonstrate that, although the mathematics of such a model is more complex, the increase in complexity is not so great as to prevent a complete fidelity-metric analysis at both the component level and at the end-to-end system level: that is, computable mean-square-based fidelity metrics are developed by which both component-level and system-level performance can be quantified. In addition, we demonstrate that system performance can be assessed qualitatively by visualizing the output image as the sum of three component images, each of which relates to a corresponding fidelity metric. The cascaded, or filtered, component accounts for the end-to-end system filtering of image acquisition, digital processing, and image reconstruction; the random noise component accounts for additive random noise, modulated by digital processing and image reconstruction filtering; and the aliased noise component accounts for the frequency folding effect of sampling, modulated by digital processing and image reconstruction filtering.

Park, Stephen K.↗

Validation & Verification of Electrical Components B2 Test Facility

The research focus of this project is to assist in the closure of Measurement, Monitoring and Control System (MMCS) and other electrical requirements in support of the B2 Space Launch System (SLS) Core Stage Green Run Test Project. Alongside this goal I am to understand project management tools to analyze and control activities/tasks associated with those items. The project I am working on will assist electrical engineers in developing and or identifying closure rationale for the MMCS and electrical requirements. Also as serving the role of a training project manager, I am to develop and maintain a method for tracking progress with estimate completion dates specifically identifying those items during this performance window. The methods I used in order to perform the research consisted of worddocuments, excel sheets, and pdf documents needed for review. For example, documents consisted of: a SLS Core Stage Green Run Facility Requirement Document (FRD) identifying the SSC MMCS and electrical requirements, a Stage Controller to SSC Interface Control Document (ICD) identifying the SSC requirements, and the B2 SLS Core Stage Green Run Test project System Requirements Document (SRD) which identifies the MMCS and electrical requirements. The files were sent to me by both mentors, Mr. Barry Robinson and Ms. Dawn Davis. Overall, the review process for the word documents and excel spreadsheets proved to be successful. The data for the electrical components were accurate and were consistent with the original recorded data. However, the consistency with the pdf documents did not follow up all the way. Attention to this mistake was made and further revisions were done in order for the data to agree with each other. Furthermore, an itinerary was designed using Microsoft Outlook in order to track progress with estimated completion dates. This project contributes to NASA/Center Missions and Goals through the Waterfall Model. The Waterfall Model is a linear system used for engineering design. In the Waterfall Model, the fourth step is Verification and Validation. This involves installation, testing, and debugging of the B2 SLS Core Stage electrical components. For the SLS Core Stage Green Run Test Project, each requirement contained in this approved requirements set will have at least one Verification Item (VI) assigned to it. During the design phase, VIs will mostly consist of Analysis or Inspection types. Design phase VIs and closure information will be documented in Dynamics Data Management System (DDMS) in the form of analysis reports and design documentation.

Bastian, Tyler↗

On the stability of robotic systems with random communication rates

Control problems of sampled data systems which are subject to random sample rate variations and delays are studied. Due to the rapid growth of the use of computers more and more systems are controlled digitally. Complex systems such as space telerobotic systems require the integration of a number of subsystems at different hierarchical levels. While many subsystems may run on a single processor, some subsystems require their own processor or processors. The subsystems are integrated into functioning systems through communications. Communications between processes sharing a single processor are also subject to random delays due to memory management and interrupt latency. Communications between processors involve random delays due to network access and to data collisions. Furthermore, all control processes involve delays due to casual factors in measuring devices and to signal processing. Traditionally, sampling rates are chosen to meet the worst case communication delay. Such a strategy is wasteful as the processors are then idle a great proportion of the time; sample rates are not as high as possible resulting in poor performance or in the over specification of control processors; there is the possibility of missing data no matter how low the sample rate is picked. Asymptotical stability with probability one for randomly sampled multi-dimensional linear systems is studied. A sufficient condition for the stability is obtained. This condition is so simple that it can be applied to practical systems. A design procedure is also shown.

Kobayashi, H.↗

Simulation and Analysis of Technology and Operational Procedures to Reduce the Combined Effects of Emissions and Contrails

The development and evaluation of concepts and technology to support future air traffic management systems require a hierarchy of models ranging from real-time simulations to extensive field evaluations. Air traffic simulation models such as Airspace Concept Evaluation System, Center Tracon Automation System, Future Air traffic management Concept Evaluation Tool and others are used to design air traffic systems balancing the conflicting objectives of maximizing safety, meeting future demands for airports and airspace and increase efficiency of traffic flows in the presence of uncertain weather. The impact of aviation emissions and contrails on climate imposes another constraint on the design of aircraft and aviation operations. The understanding of the complex interaction between physical climate system, the carbon and other greenhouse gas emissions and aviation activity can be improved by the development of integrated assessment models that include emission and climate models together with air traffic simulations. The modeling of aircraft emissions and their interaction with each other to change the concentration levels of different gasses in the atmosphere and the resulting impact of the radiative forcing on the equilibrium of the Earth's atmosphere is complex and requires the use of coupled atmosphere-ocean general circulation models together with three-dimensional models of carbon cycle and chemistry of other non-CO2 greenhouse gases. These models are computationally intensive and unsuitable for studies involving the generation of multiple scenarios. Simple emission and climate models, based on the input-output relations of linear systems, capture the fundamental emission to climate impact behavior by careful selection of key variables and their dynamics. The impact of various greenhouse gases depends on the total concentration, effect per unit change in atmospheric concentration and the spatial distribution of the gas. All these quantities are influenced by the lifetime of the gas. The impact of a greenhouse gas depends on the interval of assessment, which may vary from a few decades to a few centuries. Climate metrics are aimed at providing a common scale to compare different greenhouse gases. If the metrics are to be used as a tool in developing and evaluating aviation operations, they should be transparent and easy to apply. Global Warming Potential and Aggregate Global Temperature Potential are some of the commonly used metrics. This paper integrates a national-level air traffic simulation and optimization capability with simple climate models and carbon cycle models, and climate metrics to assess the impact of aviation on climate. The capability brings together metrics, which are useful in aviation operations together with metrics used in climate studies. The capability can be used to make trade-offs between extra fuel cost and reduction in climate impact. There is considerable uncertainty in our understanding of the radiative forcing associated with emissions and contrails. The parameters in the simulation can be used to evaluate the effect of various uncertainties in emission models and contrails. It can also be used to evaluate the impact of different decision horizons. Alternatively, the optimization results from the simulation can be used as inputs to other tools that monetize global climate impacts like the FAA's Aviation Environmental Portfolio Management Tool for Impacts.

impact of aviation on the environment↗

Continuously varying skin potentials elicited by sinusoidally varying electric shock potentials

An investigation was carried out to determine whether a form of quasi-linear systems analysis can be applied to electrodormal responses to yield new insights into the nature of the response mechanisms and their interrelationships. The response investigated was the electrodermal response (galvanic skin potential, GSP) as elicited by an electric shock stimulus applied to the skin. The response subsequent to this stimulation was examined and its characteristics measured. A series of experimental runs on three Ss was accomplished, using sinusoidal modulation envelopes of frequencies. Results showed that it was possible to drive the GSP and to achieve relatively high coherence between the driving frequency and the response itself. The analysis was limited to Fourier analysis of the response in order to determine the relative energies at the driving frequency and at successive harmonics of that driving frequency, and correlational analysis in order to determine the degree of linear relationship between the driving frequency and the driven response.

Senders, J. W.↗

Studies of the dynamics of the twin-lift system

A full set of equations of motion for the twin lift system, linearized about a hover trim condition were derived and presented. It is shown that this full set of equations of motion decouples into simpler sets of equations of motion if the aerodynamic coupling derivatives of the helicopters are neglected. One of these decoupled sets of equations of motion (referred to as the planar set) was studied at length. The other decoupled set (referred to as the nonplanar set) is examined here. It is shown that when the geometric configuration of the twin-lift is symmetric that a further decoupling is possible into antisymmetric and symmetric sets of equations. One set of these reduced equations of motion referred to as the antisymmetric set is directly equivalent to the longitudinal motion of a single helicopeter with a sling load. The second set, referred to as the symmetric set corresponds to the rotation of the entire system without load motion. As in the case of the planar symmetric motion, the location of the tether attachment point influences the stability of the nonplanar symmetric mode. The trend is opposite however in the nonplanar case in that an attachment point below the helicopter center of gravity gives a favorable effect on the stability. The effect is not as strong however as the unfavorable effect on the planar symmetric mode.

Curtiss, H. C., Jr.↗

Current Pressure Transducer Application of Model-based Prognostics Using Steady State Conditions

Prognostics is the process of predicting a system's future states, health degradation/wear, and remaining useful life (RUL). This information plays an important role in preventing failure, reducing downtime, scheduling maintenance, and improving system utility. Prognostics relies heavily on wear estimation. In some components, the sensors used to estimate wear may not be fast enough to capture brief transient states that are indicative of wear. For this reason it is beneficial to be capable of detecting and estimating the extent of component wear using steady-state measurements. This paper details a method for estimating component wear using steady-state measurements, describes how this is used to predict future states, and presents a case study of a current/pressure (I/P) Transducer. I/P Transducer nominal and off-nominal behaviors are characterized using a physics-based model, and validated against expected and observed component behavior. This model is used to map observed steady-state responses to corresponding fault parameter values in the form of a lookup table. This method was chosen because of its fast, efficient nature, and its ability to be applied to both linear and non-linear systems. Using measurements of the steady state output, and the lookup table, wear is estimated. A regression is used to estimate the wear propagation parameter and characterize the damage progression function, which are used to predict future states and the remaining useful life of the system.

Fault Estimation↗

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗

Maneuver simulations of flexible spacecraft by solving TPBVP

The optimal control of large angle rapid maneuvers and vibrations of a Shuttle mast reflector system is considered. The nonlinear equations of motion are formulated by using Lagrange's formula, with the mast modeled as a continuous beam. The nonlinear terms in the equations come from the coupling between the angular velocities, the modal coordinates, and the modal rates. Pontryagin's Maximum Principle is applied to the slewing problem, to derive the necessary conditions for the optimal controls, which are bounded by given saturation levels. The resulting two point boundary value problem (TPBVP) is then solved by using the quasilinearization algorithm and the method of particular solutions. In the numerical simulations, the structural parameters and the control limits from the Spacecraft Control Lab Experiment (SCOLE) are used. In the 2-D case, only the motion in the plane of an Earth orbit or the single axis slewing motion is discussed. In the 3-D slewing, the mast is modeled as a continuous beam subjected to 3-D deformations. The numerical results for both the linearized system and the nonlinear system are presented to compare the differences in their time response.

Bainum, Peter M.↗