Structure preserving model order reduction of a class of second-order descriptor systems via balanced truncation

2020 ◽  
Vol 152 ◽  
pp. 185-198
Author(s):  
M. Monir Uddin
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Descriptor Systems ◽  
Balanced Truncation ◽  
Model Order ◽  
Structure Preserving

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 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.

Frequency Interval Gramians Based Structure Preserving Model Order Reduction for Second Order Systems

2017 ◽  
Vol 20 (2) ◽  
pp. 790-801 ◽  
Author(s):  
Shafiq Haider ◽  
Abdul Ghafoor ◽  
Muhammad Imran ◽  
Fahad Mumtaz Malik
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Frequency Interval ◽  
Model Order ◽  
Structure Preserving ◽  
Second Order Systems

Laguerre-Gramian-based structure-preserving model order reduction for second-order form systems

2021 ◽  
pp. 014233122110507
Author(s):  
Liu Dai ◽  
Zhi-Hua Xiao ◽  
Ren-Zheng Zhang ◽  
Yao-Lin Jiang
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Low Rank ◽  
Main Task ◽  
Model Order ◽  
Structure Preserving ◽  
First Order ◽  
Order Form ◽  
Order Representation

A new structure-preserving model order reduction technique based on Laguerre-Gramian for second-order form systems is presented in this article. The main task of the proposed approach is to use the Laguerre polynomial expansion of the matrix exponential function to obtain the approximate low-rank decomposition of the Gramians for the equivalent first-order representation of the original second-order form system. The approximate balanced system is generated by a balancing transformation which is directly computed from the expansion coefficients of impulse responses in the space spanned by Laguerre polynomials, without computing the full Gramians for the first-order representation. Then, the reduced second-order model is constructed by truncating the states with small approximate Hankel singular values (HSVs). The above method has a disadvantage that it may unexpectedly result in unstable systems although the original one is stable. Therefore, modified reduction procedure combined with the dominant subspace projection method is presented to alleviate the limitation. Finally, two numerical experiments are provided to demonstrate the effectiveness of the algorithms.

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