scholarly journals Second-Order Model Reduction Based on Gramians

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Cong Teng
Keyword(s):  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Balanced Truncation ◽  
Order Model ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Large Scale Systems ◽  
Order Linear

Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds on error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.

Second Order Model Reduction Based on Diagonal Blocks of Gramians

2011 ◽  
Vol 317-319 ◽  
pp. 2359-2366
Author(s):  
Cong Teng
Keyword(s):  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Balanced Truncation ◽  
Order Model ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Large Scale Systems ◽  
New Algorithms

In this paper, some new algorithms based on diagonal blocks of reachability and observability Gramians are presented for structure preserving model order reduction on second order linear dynamical systems. They are more suitable for large scale systems compared to existing Gramian based algorithms, namely second order balanced truncation methods. In experiments, they have similar performance as the existing techniques.

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.

Time-limited Gramians-based model order reduction for second-order form systems

2018 ◽  
Vol 41 (8) ◽  
pp. 2310-2318 ◽  
Author(s):  
Shafiq Haider ◽  
Abdul Ghafoor ◽  
Muhammad Imran ◽  
Fahad Mumtaz Malik
Keyword(s):  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Reduced Order Models ◽  
Infinite Time ◽  
Model Order ◽  
Reduced Order ◽  
Order Form ◽  
Second Order Systems

A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.

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