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Results for “Model order reduction”

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.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Model reduction results for flexible space structures

This paper describes the novel subsystem balancing technique for obtaining reduced-order models of flexible structures, and investigates its properties fully. This method can be regarded as a combination of the best features of modal truncation (efficiency) and internal balancing (accuracy); it is particularly well suited to the typical practical case of structures which possess clusters of close modes. Numerical results are then presented demonstrating the results obtained by applying subsystem balancing to the Air Force Phillips Laboratory ASTREX testbed, the Jet Propulsion Laboratory antenna facility, and the NASA Marshall Space Flight Center ACES structure.

Williams, Trevor↗
NASA NTRS1976

Computational aspects of real-time simulation of rotary-wing aircraft

A study was conducted to determine the effects of degrading a rotating blade element rotor mathematical model suitable for real-time simulation of rotorcraft. Three methods of degradation were studied, reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments; (2) reduction of number of blades; and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which a different rotor mathematical model should be used.

Houck, J. A.↗
NASA NTRS1976

Effects of rotor model degradation on the accuracy of rotorcraft real time simulation

The effects are studied of degrading a rotating blade element rotor mathematical model to meet various real-time simulation requirements of rotorcraft. Three methods of degradation were studied: reduction of number of blades, reduction of number of blade segments, and increasing the integration interval, which has the corresponding effect of increasing blade azimuthal advance angle. The three degradation methods were studied through static trim comparisons, total rotor force and moment comparisons, single blade force and moment comparisons over one complete revolution, and total vehicle dynamic response comparisons. Recommendations are made concerning model degradation which should serve as a guide for future users of this mathematical model, and in general, they are in order of minimum impact on model validity: (1) reduction of number of blade segments, (2) reduction of number of blades, and (3) increase of integration interval and azimuthal advance angle. Extreme limits are specified beyond which the rotating blade element rotor mathematical model should not be used.

Houck, J. A.↗
NASA NTRS1990

Combined design of structures and controllers for optimal maneuverability

Approaches to the combined design of structures and controllers for achieving optimal maneuverability are presented. A maneuverability index which directly reflects the minimum time required to perform a given set of maneuvers is introduced. By designing the flexible appendages, the maneuver time of the spacecraft is minimized under the constraints of structural properties, and post maneuver spillover is kept within a specified bound. The spillover reduction is achieved by making use of an appropriate reduced order model. The distributed parameter design problem is approached using assumed shape functions, and finite element analysis with dynamic reduction. Solution procedures have been investigated. Approximate design methods have been developed to overcome the computational difficulties. Some new constraints on the modal frequencies of the spacecraft are introduced in the original optimization problem to facilitate the solution process. It is shown that the global optimal design may be obtained by tuning the natural frequencies to satisfy specific constraints. Researchers quantify the difference between a lower bound to the solution for maneuver time associated with the original problem and the estimate obtained from the modified problem, for a specified application requirement. Numerical examples are presented to demonstrate the capability of this approach.

Ling, Jer↗
NASA NTRS1992

A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
NASA NTRS1975

A study of low cost approaches to scientific experiment implementation for shuttle launched and serviced automated spacecraft

Cost reductions that can be obtained in experiment instrumentation by the use of standardized electronics and by the relaxation of instrument reliability requirements are studied. The feasibility of using standardized equipment for experiment instrumentation is assessed and a system design approach that most effectively incorporates standardized equipment is developed. The level and form of modularization that is appropriate for the standardized equipment is determined. Mission assurance aspects of instrument development are examined to determine the cost reductions that might be derived from the relaxation of reliability requirements and to formulate a systematic approach to the optimization of mission assurance cost reductions. The results of the analyses are applied to a representative model HEAO payload in order to provide a concrete example of the cost reductions that can be achieved by a standardized approach to the instrument electronics.

Source record↗
NASA NTRS1990

Optimal model reduction and frequency-weighted extension

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗
NASA NTRS1989

Optimal aeroassisted coplanar orbital transfer using an energy model

The atmospheric portion of the trajectories for the aeroassisted coplanar orbit transfer was investigated. The equations of motion for the problem are expressed using reduced order model and total vehicle energy, kinetic plus potential, as the independent variable rather than time. The order reduction is achieved analytically without an approximation of the vehicle dynamics. In this model, the problem of coplanar orbit transfer is seen as one in which a given amount of energy must be transferred from the vehicle to the atmosphere during the trajectory without overheating the vehicle. An optimal control problem is posed where a linear combination of the integrated square of the heating rate and the vehicle drag is the cost function to be minimized. The necessary conditions for optimality are obtained. These result in a 4th order two-point-boundary-value problem. A parametric study of the optimal guidance trajectory in which the proportion of the heating rate term versus the drag varies is made. Simulations of the guidance trajectories are presented.

Halyo, Nesim↗
NASA NTRS1987

Modeling and control of beam-like structures

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for beam-like continua. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗
NASA NTRS1988

Modal cost analysis for simple continua

The most popular finite element codes are based upon appealing theories of convergence of modal frequencies. For example, the popularity of cubic elements for beam-like structures is due to the rapid convergence of modal frequencies and stiffness properties. However, for those problems in which the primary consideration is the accuracy of response of the structure at specified locations, it is more important to obtain accuracy in the modal costs than in the modal frequencies. The modal cost represents the contribution of a mode in the norm of the response vector. This paper provides a complete modal cost analysis for simple continua such as beam-like structures. Upper bounds are developed for mode truncation errors in the model reduction process and modal cost analysis dictates which modes to retain in order to reduce the model for control design purposes.

Hu, A.↗
NASA NTRS1989

The determination of third order linear models from a seventh order nonlinear jet engine model

Results are presented that demonstrate how good reduced-order models can be obtained directly by recursive parameter identification using input/output (I/O) data of high-order nonlinear systems. Three different methods of obtaining a third-order linear model from a seventh-order nonlinear turbojet engine model are compared. The first method is to obtain a linear model from the original model and then reduce the linear model by standard reduction techniques such as residualization and balancing. The second method is to identify directly a third-order linear model by recursive least-squares parameter estimation using I/O data of the original model. The third method is to obtain a reduced-order model from the original model and then linearize the reduced model. Frequency responses are used as the performance measure to evaluate the reduced models. The reduced-order models along with their Bode plots are presented for comparison purposes.

Lalonde, Rick J.↗
NASA NTRS2007

Model Checker for Java Programs

Java Pathfinder (JPF) is a verification and testing environment for Java that integrates model checking, program analysis, and testing. JPF consists of a custom-made Java Virtual Machine (JVM) that interprets bytecode, combined with a search interface to allow the complete behavior of a Java program to be analyzed, including interleavings of concurrent programs. JPF is implemented in Java, and its architecture is highly modular to support rapid prototyping of new features. JPF is an explicit-state model checker, because it enumerates all visited states and, therefore, suffers from the state-explosion problem inherent in analyzing large programs. It is suited to analyzing programs less than 10kLOC, but has been successfully applied to finding errors in concurrent programs up to 100kLOC. When an error is found, a trace from the initial state to the error is produced to guide the debugging. JPF works at the bytecode level, meaning that all of Java can be model-checked. By default, the software checks for all runtime errors (uncaught exceptions), assertions violations (supports Java s assert), and deadlocks. JPF uses garbage collection and symmetry reductions of the heap during model checking to reduce state-explosion, as well as dynamic partial order reductions to lower the number of interleavings analyzed. JPF is capable of symbolic execution of Java programs, including symbolic execution of complex data such as linked lists and trees. JPF is extensible as it allows for the creation of listeners that can subscribe to events during searches. The creation of dedicated code to be executed in place of regular classes is supported and allows users to easily handle native calls and to improve the efficiency of the analysis.

Visser, Willem↗
NASA NTRS1993

Digraph reliability model processing advances and applications

This paper describes a new algorithm, called SourceDoubls, which efficiently solves for singletons and doubletons of a digraph reliability model. Compared with previous methods, the SourceDoubls algorithm provides up to a two order of magnitude reduction in the amount of time required to solve large digraph models. This significant increase in model solution speed allows complex digraphs containing thousands of nodes to be used as knowledge bases for real time automated monitoring and diagnosis applications. Currently, an application to provide monitoring and diagnosis of the Space Station Freedom Data Management System is under development at NASA/Ames Research Center and NASA/Johnson Space Center. This paper contains an overview of this system and provides details of how it will use digraph models processed by the SourceDoubls algorithm to accomplish its task.

Iverson, D. L.↗
NASA NTRS2005

Cycle-averaged dynamics of a periodically driven, closed-loop circulation model

Time-varying elastance models have been used extensively in the past to simulate the pulsatile nature of cardiovascular waveforms. Frequently, however, one is interested in dynamics that occur over longer time scales, in which case a detailed simulation of each cardiac contraction becomes computationally burdensome. In this paper, we apply circuit-averaging techniques to a periodically driven, closed-loop, three-compartment recirculation model. The resultant cycle-averaged model is linear and time invariant, and greatly reduces the computational burden. It is also amenable to systematic order reduction methods that lead to further efficiencies. Despite its simplicity, the averaged model captures the dynamics relevant to the representation of a range of cardiovascular reflex mechanisms. c2004 Elsevier Ltd. All rights reserved.

Non-NASA Center↗
NASA NTRS2024

A Uniform Analysis of Debris Discs with the Gemini Planet Imager II: Constraints on Dust Density Distribution Using Empirically Informed Scattering Phase Functions

Spatially resolved images of debris discs are necessary to determine disc morphological properties and the scattering phase function (SPF) thatantifies the brightness of scattered light as a function of phase angle. Current high-contrast imaging instruments have successfully resolved several dozens of debris discs around other stars, but few studies have investigated trends in the scattered-light, resolved population of debris discs in a uniform and consistent manner. We have combined Karhunen-Loeve Image Projection (KLIP) with radiative-transfer disc forward modelling in order to obtain the highest-quality image reductions and constrain disc morphological properties of eight debris discs imaged by the Gemini Planet Imager at H -band with a consistent and uniformly applied approach. In describing the scattering properties of our models, we assume a common SPF informed from solar system dust scattering measurements and apply it to all systems. We identify a diverse range of dust density properties among the sample, including critical radius, radial width, and vertical width. We also identify radially narrow and vertically extended discs that may have resulted from substellar companion perturbations, along with a tentative positive trend in disc eccentricity with relative disc width. We also find that using a common SPF can achieve reasonable model fits for discs that are axisymmetric and asymmetric when fitting models to each side of the disc independently, suggesting that scattering behaviour from debris discs may be similar to Solar system dust.

scattering↗
NASA NTRS2018

Hybrid Reduced Order Model for N2-N2 Interactions for Application to Dissociation and Energy Transfer Processes

This work presents a general framework for model reduction of non-equilibrium energy transfer and dissociation processes. The multi-group maximum-entropy method is coupled with the quasi-classical trajectory method to directly construct a reduced order model for chemical non-equilibrium. Kinetic data is calculated by applying detailed balance at a microscopic level, overcoming the limitation of calculating recombination kinetic data. This approach enables the construction of a reduced order model for kinetics which bypasses the need to compute state-to-state kinetic data. This physics based reduced order model ensures that an equilibrium distribution is reached given infinite time, while allowing for non-equilibrium distributions during the relaxation and dissociation processes. A proof-of-concept test case demonstrates the applicability of this model by comparison with state-to-state kinetic data for the N2(Chi (sup 1) Sigma ((sub g), (sup plus sign)) minus N ((exp 4) S (sub u)) system with excellent agreement.

Maximum Entropy↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗