Results 11  20
of
286
Projection Frameworks for Model Reduction of Weakly . . .
, 2000
"... In this paper we present a generalization of popular linear model reduction methods, such as Lanczos and Arnoldibased algorithms based on rational approximation, to systems whose response to interesting external inputs can be described by a few terms in a functional series expansion such as a Volt ..."
Abstract

Cited by 41 (1 self)
 Add to MetaCart
In this paper we present a generalization of popular linear model reduction methods, such as Lanczos and Arnoldibased algorithms based on rational approximation, to systems whose response to interesting external inputs can be described by a few terms in a functional series expansion such as a Volterra series. The approach allows automatic generation of macromodels that include frequencydependent nonlinear effects.
Generalized spectral decomposition method for solving stochastic finite element equations: invariant subspace problem and dedicated algorithms
, 2008
"... ..."
The method of proper orthogonal decomposition for dynamical characterization and order reduction of mechanical systems: an overview
 Nonlinear Dynamics
, 2005
"... Abstract. Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theo ..."
Abstract

Cited by 34 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting highdimensional data into a lowerdimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study. Key words: dynamic characterization, order reduction, proper orthogonal decomposition 1.
Reduced Order Controllers for Spatially Distributed Systems via Proper Orthogonal Decomposition
, 1999
"... A method for reducing controllers for systems described by partial differential equations (PDEs) is presented. This approach differs from an often used method of reducing the model and then designing the controller. The controller reduction is accomplished by projection of a large scale finite eleme ..."
Abstract

Cited by 29 (4 self)
 Add to MetaCart
(Show Context)
A method for reducing controllers for systems described by partial differential equations (PDEs) is presented. This approach differs from an often used method of reducing the model and then designing the controller. The controller reduction is accomplished by projection of a large scale finite element approximation of the PDE controller onto low order bases that are computed using the proper orthogonal decomposition (POD). Two methods for constructing input collections for POD, and hence low order bases, are discussed and computational results are included. The first uses the method of snapshots found in POD literature. The second is a new idea that uses an integral representation of the feedback control law. Specifically, the kernels, or functional gains, are used as data for POD. A low order controller derived by applying the POD process to functional gains avoids subjective criteria associated with implementing a time snapshot approach and performs favorably.
Galactic dynamics
 A&A, 96, 164 Combes, F.,2004 IAU Symp 222
, 1987
"... dynamic patterns from infectious disease data using ..."
Abstract

Cited by 27 (0 self)
 Add to MetaCart
dynamic patterns from infectious disease data using
Optimal Control of Vortex Shedding Using Low Order Models Part II: ModelBased Control
"... this paper we describe investigations into this approach. Given the form of our low order models, with flow velocities represented in terms of the mean flow and a sum of "modes" (POD basis functions), a natural control aim is the reduction of the wake unsteadiness, associated with the mode ..."
Abstract

Cited by 26 (0 self)
 Add to MetaCart
this paper we describe investigations into this approach. Given the form of our low order models, with flow velocities represented in terms of the mean flow and a sum of "modes" (POD basis functions), a natural control aim is the reduction of the wake unsteadiness, associated with the mode amplitudes. In the light of the introductory discussion in Part I, we cannot expect to suppress the unsteadiness entirely, but we can hope to reduce it. We also note from Part I that cylinder rotation tends, in general, to increase the level of wake unsteadiness, (the most extreme manifestation being lockedon flow), so that achieving reductions via this approach will be a clear demonstration of the success of the control method. The first requirement here is a suitable formulation for the modelbased control, and 30 W. R. Graham, J. Peraire and K. Y. Tang
Centroidal Voronoi tessellationbased reducedorder modeling of complex systems
"... Abstract. A reducedorder modeling methodology based on centroidal Voronoi tessellations (CVTs) is introduced. CVTs are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. For discrete data sets, CVTs ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
(Show Context)
Abstract. A reducedorder modeling methodology based on centroidal Voronoi tessellations (CVTs) is introduced. CVTs are special Voronoi tessellations for which the generators of the Voronoi diagram are also the centers of mass (means) of the corresponding Voronoi cells. For discrete data sets, CVTs are closely related to the hmeans and kmeans clustering techniques. A discussion of reducedorder modeling for complex systems such as fluid flows is given to provide a context for the application of reducedorder bases. Then, detailed descriptions of CVTbased reducedorder bases and how they can be constructed from snapshot sets and how they can be applied to the lowcost simulation of complex systems are given. Subsequently, some concrete incompressible flow examples are used to illustrate the construction and use of CVTbased reducedorder bases. The CVTbased reducedorder modeling methodology is shown to be effective for these examples.
Model Reduction via the KarhunenLoeve Expansion Part I: An Exposition
 Tech. Rep. T.R. 9632, Inst. Systems Research
, 1996
"... In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases. In Part I of ..."
Abstract

Cited by 23 (5 self)
 Add to MetaCart
(Show Context)
In formulating mathematical models for dynamical systems, obtaining a high degree of qualitative correctness (i.e. predictive capability) may not be the only objective. The model must be useful for its intended application, and models of reduced complexity are attractive in many cases. In Part I of this paper we provide an exposition of some techniques that are useful in finding models of reduced complexity for dynamical systems involving flows. The material presented here is not new. The techniques we discuss are based on classical theory such as the KarhunenLoeve expansion and the method of Galerkin, and the more recent concept of "coherent structures". They have been heavily exploited in a wide range of areas in science and engineering. The attempt here is to present this collection of important methods and ideas together, at a high level of detail, in coherent form, and in the context of model reduction for simulation and control. In this manner we lead in to Part II which illustr...
Reduced Order Model Feedback Control Design: Computational Studies for Thin Cylindrical Shells
 IEEE Trans. Auto. Contr
, 1998
"... Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system considered is a thin cylindrical shell with surfacemounted piezoceramic actuators. DonnellMushtari equations, modifi ..."
Abstract

Cited by 20 (11 self)
 Add to MetaCart
(Show Context)
Reduced order models employing the Lagrange and POD reduced basis methods in numerical approximation and feedback control of systems are presented and numerically tested. The system considered is a thin cylindrical shell with surfacemounted piezoceramic actuators. DonnellMushtari equations, modified to include KelvinVoigt damping, are used to model the system dynamics. Basis functions constructed from Fourier polynomials tensored with cubic splines are employed in the Galerkin expansion of the full order model. Reduced basis elements are then formed from full order approximations of the exogenously excited shell taken at different time instances. Numerical examples illustrating the features of the reduced basis methods are presented. To investigate the behavior of the methods when executed on physical systems, the numerical implementation of reduced order control gains in the full order model is developed and numerical examples are presented. 1 Research supported in part by the U.S...