scholarly journals Order Reduction Methods for Solving Large-Scale Differential Matrix Riccati Equations

2020 ◽  
Vol 42 (4) ◽  
pp. A2182-A2205
Author(s):  
Gerhard Kirsten ◽  
Valeria Simoncini
Keyword(s):  
Large Scale ◽  
Order Reduction ◽  
Riccati Equations ◽  
Reduction Methods ◽  
Differential Matrix

scholarly journals A Review of Model Order Reduction Methods for Large-Scale Structure Systems

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Kuan Lu ◽  
Kangyu Zhang ◽  
Haopeng Zhang ◽  
Xiaohui Gu ◽  
Yulin Jin ◽  
...  
Keyword(s):  
Complex Systems ◽  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Large Scale Structure ◽  
Scale Structure ◽  
High Dimensional ◽  
Model Order ◽  
Reduction Methods ◽  
Proper Orthogonal

The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

scholarly journals Low-rank approximate solutions to large-scale differential matrix Riccati equations

2018 ◽  
Vol 45 (2) ◽  
pp. 233-254 ◽  
Author(s):  
Y. Guldoğan ◽  
M. Hached ◽  
K. Jbilou ◽  
M. Kurulay
Keyword(s):  
Large Scale ◽  
Approximate Solutions ◽  
Riccati Equations ◽  
Low Rank ◽  
Differential Matrix

scholarly journals A comparison of second-order model order reduction methods for an artificial fishtail

2019 ◽  
Vol 67 (8) ◽  
pp. 648-667 ◽  
Author(s):  
Jens Saak ◽  
Dirk Siebelts ◽  
Steffen W. R. Werner
Keyword(s):  
Model Order Reduction ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Scale Model ◽  
Order Model ◽  
Model Order ◽  
Reduction Methods ◽  
Second Order Model

Abstract In order to apply control theory in small autonomous vehicles, mathematical models with small numbers of states are required for using the limited computational power in embedded programming. In this paper, we consider an artificial fishtail as an example for a complex mechanical system with a second-order large-scale model, which is derived by using the finite element method. To meet the above limitations, the several hundreds of thousands of degrees of freedom need to be reduced to merely a handful of surrogate degrees of freedom. We seek to achieve this task by various second-order model order reduction methods. All methods are applied on the fishtail’s matrices and their results are evaluated and compared in the frequency domain as well as in the time domain.

Embedded order reduction of hierarchical systems within an mCCM framework

2018 ◽  
Vol 37 (4) ◽  
pp. 1535-1544
Author(s):  
Michael Popp ◽  
Wolfgang Mathis
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Piecewise Linear ◽  
Hierarchical Structures ◽  
Order Reduction ◽  
Hierarchical Level ◽  
Hierarchical Systems ◽  
Content Type ◽  
Reduction Methods ◽  
Interconnected Dynamical Systems

Purpose The purpose of this paper is to present the embedding of linear and nonlinear order reduction methods in a theoretical framework for handling hierarchically interconnected dynamical systems. Design/methodology/approach Based on the component connection modeling (CCM), a modified framework called mCCM for describing interconnected dynamic systems especially with hierarchical structures is introduced and used for order reduction purposes. The balanced truncation method for linear systems and the trajectory piecewise linear reduction scheme are used for the order reduction of systems described within the mCCM framework. Findings It is shown that order reduction methods can be embedded into the context of interconnected dynamical systems with the benefit of having a further degree of freedom in form of the hierarchical level, on which the order reduction is performed. Originality/value The aspect of hierarchy within system descriptions is exploited for order reduction purposes. This distinguishes the presented approach from common methods, which already start with single large-scale systems without explicitly considering hierarchical structures.

THE NEW ALGORITHM OF SOLVING HARMONIC BALANCE EQUATIONS

2019 ◽  
Author(s):  
Vladimir Lantsov ◽  
A. Papulina
Keyword(s):  
Harmonic Balance ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Balance Equations ◽  
Model Order ◽  
Cad Systems ◽  
Computational Costs ◽  
Reduction Methods ◽  
Model Equations

The new algorithm of solving harmonic balance equations which used in electronic CAD systems is presented. The new algorithm is based on implementation to harmonic balance equations the ideas of model order reduction methods. This algorithm allows significantly reduce the size of memory for storing of model equations and reduce of computational costs.

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