Topic

# Model order reduction

About: Model order reduction is a(n) research topic. Over the lifetime, 3938 publication(s) have been published within this topic receiving 44916 citation(s).

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TL;DR: The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.

Abstract: Recent results on singular perturbations are surveyed as a tool for model order reduction and separation of time scales in control system design. Conceptual and computational simplifications of design procedures are examined by a discussion of their basic assumptions. Over 100 references are organized into several problem areas. The content of main theorems is presented in a tutorial form aimed at a broad audience of engineers and applied mathematicians interested in control, estimation and optimization of dynamic systems.

860 citations

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TL;DR: This paper presents an approach to the nonlinear model reduction based on representing the non linear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection, and shows that the macromodels obtained are significantly more accurate than models obtained with linear or the recently developed quadratic reduction techniques.

Abstract: In this paper, we present an approach to nonlinear model reduction based on representing a nonlinear system with a piecewise-linear system and then reducing each of the pieces with a Krylov projection. However, rather than approximating the individual components as piecewise linear and then composing hundreds of components to make a system with exponentially many different linear regions, we instead generate a small set of linearizations about the state trajectory which is the response to a "training input." Computational results and performance data are presented for an example of a micromachined switch and selected nonlinear circuits. These examples demonstrate that the macromodels obtained with the proposed reduction algorithm are significantly more accurate than models obtained with linear or recently developed quadratic reduction techniques. Also, we propose a procedure for a posteriori estimation of the simulation error, which may be used to determine the accuracy of the extracted trajectory piecewise-linear reduced-order models. Finally, it is shown that the proposed model order reduction technique is computationally inexpensive, and that the models can be constructed "on the fly," to accelerate simulation of the system response.

593 citations

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TL;DR: This paper revisits a new model reduction methodology based on the use of separated representations, the so called Proper Generalized Decomposition—PGD, which allows to treat efficiently models defined in degenerated domains as well as the multidimensional models arising from multiddimensional physics or from the standard ones when some sources of variability are introduced in the model as extra-coordinates.

Abstract: This paper revisits a new model reduction methodology based on the use of separated representations, the so called Proper Generalized Decomposition—PGD. Space and time separated representations generalize Proper Orthogonal Decompositions—POD—avoiding any a priori knowledge on the solution in contrast to the vast majority of POD based model reduction technologies as well as reduced bases approaches. Moreover, PGD allows to treat efficiently models defined in degenerated domains as well as the multidimensional models arising from multidimensional physics (quantum chemistry, kinetic theory descriptions,…) or from the standard ones when some sources of variability are introduced in the model as extra-coordinates.

506 citations

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24 Sep 2014

Abstract: Basic Concepts.- to Model Order Reduction.- Linear Systems, Eigenvalues, and Projection.- Theory.- Structure-Preserving Model Order Reduction of RCL Circuit Equations.- A Unified Krylov Projection Framework for Structure-Preserving Model Reduction.- Model Reduction via Proper Orthogonal Decomposition.- PMTBR: A Family of Approximate Principal-components-like Reduction Algorithms.- A Survey on Model Reduction of Coupled Systems.- Space Mapping and Defect Correction.- Modal Approximation and Computation of Dominant Poles.- Some Preconditioning Techniques for Saddle Point Problems.- Time Variant Balancing and Nonlinear Balanced Realizations.- Singular Value Analysis and Balanced Realizations for Nonlinear Systems.- Research Aspects and Applications.- Matrix Functions.- Model Reduction of Interconnected Systems.- Quadratic Inverse Eigenvalue Problem and Its Applications to Model Updating - An Overview.- Data-Driven Model Order Reduction Using Orthonormal Vector Fitting.- Model-Order Reduction of High-Speed Interconnects Using Integrated Congruence Transform.- Model Order Reduction for MEMS: Methodology and Computational Environment for Electro-Thermal Models.- Model Order Reduction of Large RC Circuits.- Reduced Order Models of On-Chip Passive Components and Interconnects, Workbench and Test Structures.

489 citations

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Abstract: We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in ð0; 1� , based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, and a mechanical chaotic ‘‘jerk’’ model. In both models, numerical simulations are used to demonstrate that for different types of model nonlinearities, and using the proper control parameters, chaotic attractors are obtained with system orders as low as 2.1. Consequently, we present a conjecture that third-order chaotic nonlinear systems can still produce chaotic behavior with a total system order of 2 þ e ,1 > e > 0, using the appropriate control parameters. The effect of fractional order on the chaotic range of the control parameters is studied. It is demonstrated that as the order is decreased, the chaotic range of the control parameter is affected by contraction and translation. Robustness against model order reduction is demonstrated. 2002 Elsevier Science Ltd. All rights reserved.

410 citations