scholarly journals On structure-preserving transformations of the Itō generator matrix for model reduction of quantum feedback networks

2012 ◽  
Vol 370 (1979) ◽  
pp. 5422-5436 ◽  
Author(s):  
Hendra I. Nurdin ◽  
John E. Gough
Keyword(s):  
Model Reduction ◽  
Degrees Of Freedom ◽  
Generator Matrix ◽  
Structure Preserving ◽  
Adiabatic Elimination ◽  
Quantum Feedback ◽  
Feedback Networks ◽  
Generator Matrices ◽  
Standard Operations ◽  
Internal Connections

Two standard operations of model reduction for quantum feedback networks, elimination of internal connections under the instantaneous feedback limit and adiabatic elimination of fast degrees of freedom, are cast as structure-preserving transformations of Itō generator matrices. It is shown that the order in which they are applied is inconsequential.

Model reduction in power systems using a structure-preserving balanced truncation approach

2019 ◽  
Vol 177 ◽  
pp. 106002
Author(s):  
Johnny Leung ◽  
Michel Kinnaert ◽  
Jean-Claude Maun ◽  
Fortunato Villella
Keyword(s):  
Power Systems ◽  
Model Reduction ◽  
Balanced Truncation ◽  
Structure Preserving

scholarly journals Implementing model reduction to the JuliaFEM platform

2018 ◽  
Vol 51 (1) ◽  
pp. 36-54 ◽  
Author(s):  
Marja Liisa Rapo ◽  
Jukka Aho ◽  
Hannu Koivurova ◽  
Tero Frondelius
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Model Reduction ◽  
Open Source ◽  
Degrees Of Freedom ◽  
Mass Matrices ◽  
Dynamic Condensation ◽  
Dynamic Analyses ◽  
Reduction Methods ◽  
Large Model

JuliaFEM is an open source finite element method solver written in the Julia language. This paper presents an implementation of two common model reduction methods: the Guyan reduction and the Craig-Bampton method. The goal was to implement these algorithms to the JuliaFEM platform and demonstrate that the code works correctly. This paper first describes the JuliaFEM concept briefly after which it presents the theory of model reduction, and finally, it demonstrates the implemented functions in an example model. This paper includes instructions for using the implemented algorithms, and reference the code itself in GitHub. The reduced stiness and mass matrices give the same results in both static and dynamic analyses as the original matrices, which proves that the code works correctly. The code runs smoothly on relatively large model of 12.6 million degrees of freedom. In future, damping could be included in the dynamic condensation now that it has been shown to work.

System-Level Modal Representation of Flexible Multibody Systems

2009 ◽  
Author(s):  
Gert H. K. Heirman ◽  
Wim Desmet
Keyword(s):  
Model Reduction ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Flexible Multibody Systems ◽  
System Level ◽  
Algebraic Equations ◽  
Flexible Multibody ◽  
Simulation Results ◽  
Model Equations ◽  
Model Reduction Technique

The presence of both differential and algebraic equations in the model equations, as well as the number of degrees of freedom needed to accurately represent flexibility, prohibit fast simulation of flexible multibody systems (e.g. real-time). In this research, Global Modal Parametrization, a model reduction technique for flexible multibody systems is further developed to speed up simulation of flexible multibody systems. The reduction of the model is achieved by projection on a curvilinear subspace instead of a fixed vector space, requiring significantly less degrees of freedom to represent the system dynamics with the same level of accuracy. The complexity of simulation of the reduced model equations is estimated. In a numerical experiment, simulation results for the original model equations are compared with simulation results for the model equations obtained after model reduction, showing a good match. The dominant sources of error of the proposed methodology are illustrated and explained.

scholarly journals Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems

Automatica ◽  
2012 ◽  
Vol 48 (9) ◽  
pp. 1963-1974 ◽  
Author(s):  
Serkan Gugercin ◽  
Rostyslav V. Polyuga ◽  
Christopher Beattie ◽  
Arjan van der Schaft
Keyword(s):  
Model Reduction ◽  
Hamiltonian Systems ◽  
Structure Preserving

Error-Controlled Model Reduction in Flexible Multibody Dynamics

2010 ◽  
Vol 5 (3) ◽  
Author(s):  
Jörg Fehr ◽  
Peter Eberhard
Keyword(s):  
Model Reduction ◽  
Error Bounds ◽  
Degrees Of Freedom ◽  
A Priori ◽  
Reduction Process ◽  
Flexible Multibody Dynamics ◽  
Scanning Tunneling ◽  
Error Estimator ◽  
Gramian Matrix ◽  
Flexible Multibody

One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.

Sign in / Sign up

Export Citation Format

Share Document