Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form

2005 ◽  
pp. 83-115 ◽  
Author(s):  
Volker Mehrmann ◽  
Tatjana Stykel
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Balanced Truncation ◽  
Large Scale Systems

Parallel Implementation of LQG Balanced Truncation for Large-Scale Systems

2008 ◽  
pp. 227-234 ◽  
Author(s):  
Jose M. Badía ◽  
Peter Benner ◽  
Rafael Mayo ◽  
Enrique S. Quintana-Ortí ◽  
Gregorio Quintana-Ortí ◽  
...  
Keyword(s):  
Large Scale ◽  
Parallel Implementation ◽  
Balanced Truncation ◽  
Large Scale Systems

Shift-Independent Model Reduction of Large-Scale Second-Order Mechanical Structures

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Masih Mahmoodi ◽  
Kamran Behdinan
Keyword(s):  
Model Reduction ◽  
Large Scale ◽  
Second Order ◽  
Computational Time ◽  
Original Structure ◽  
Fe Model ◽  
Krylov Methods ◽  
Convergence Criteria ◽  
Large Scale Systems ◽  
Reduction Techniques

Nonmodal model order reduction (MOR) techniques present accurate and efficient ways to approximate input–output behavior of large-scale mechanical structures. In this regard, Krylov-based model reduction techniques for second-order mechanical structures are typically known to require a priori knowledge of the original system parameters, such as expansion points (or eigenfrequencies). The calculation of the eigenfrequencies of the original finite-element (FE) model can be significantly time-consuming for large-scale structures. Existing iterative rational Krylov algorithm (IRKA) addresses this issue by iteratively updating the expansion points for first-order formulations until convergence criteria are achieved. Motivated by preserving the model properties of second-order systems, this paper extends the IRKA method to second-order formulations, typically encountered in mechanical structures. The proposed second-order IRKA method is implemented on a large-scale system as an example and compared with the standard Krylov and Craig-Bampton reduction techniques. The results show that the second-order IRKA method provides tangibly reduced error for a multi-input-multi-output (MIMO) mechanical structure compared to the Craig-Bampton. In addition, unlike the standard Krylov methods, the second-order IRKA does not require the information on expansion points, which eliminates the need to perform a modal analysis on the original structure. This can be especially advantageous for large-scale systems where calculations of the eigenfrequencies of the original structure can be computationally expensive. For such large-scale systems, the proposed MOR technique can lead to significant reductions of the computational time.

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.

Sign in / Sign up

Export Citation Format

Share Document