scholarly journals Approximation and model order reduction for second order systems with Levy-noise

2015 ◽  
Author(s):  
Peter Benner ◽  
Martin Redmann
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Lévy Noise ◽  
Model Order ◽  
Second Order Systems ◽  
Levy Noise

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.

Singular perturbation approximation for linear systems with Lévy noise

2018 ◽  
Vol 18 (04) ◽  
pp. 1850033 ◽  
Author(s):  
Martin Redmann ◽  
Peter Benner
Keyword(s):  
Singular Perturbation ◽  
Linear Systems ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Lévy Noise ◽  
Model Order ◽  
Linear Evolution Equation ◽  
Levy Noise ◽  
Perturbation Approximation

To solve a stochastic linear evolution equation numerically, finite dimensional approximations are commonly used. For a good approximation, one might end up with a sequence of ordinary stochastic linear equations of high order. To reduce the high dimension for practical computations, we consider the singular perturbation approximation as a model order reduction technique in this paper. This approach is well-known from deterministic control theory and here we generalize it for controlled linear systems with Lévy noise. Additionally, we discuss properties of the reduced order model, provide an error bound, and give some examples to demonstrate the quality of this model order reduction technique.

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

scholarly journals A Structured Quasi-Arnoldi procedure for model order reduction of second-order systems

2012 ◽  
Vol 436 (8) ◽  
pp. 2780-2794 ◽  
Author(s):  
Yung-Ta Li ◽  
Zhaojun Bai ◽  
Wen-Wei Lin ◽  
Yangfeng Su
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Model Order ◽  
Second Order Systems

scholarly journals Model Reduction of Structured Dynamical Systems by Projecting onto the Dominant Eigenspace of the Gramians

2018 ◽  
Vol 10 (2) ◽  
pp. 94
Author(s):  
Shazzad Hasan ◽  
M. Monir Uddin
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Second Order ◽  
Low Rank ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Second Order Systems ◽  
Theoretical Results

This paper studies the structure preserving (second-order to second-order) model order reduction of second-order systems applying the projection onto the dominant eigenspace of the Gramians of the systems. The projectors which create the reduced order model are generated cheaply from the low-rank Gramian factors. The low-rank Gramian factors are computed efficiently by solving the corresponding Lyapunov equations of the system using the rational Krylov subspace method. The efficiency of the theoretical results are then illustrated by numerical experiments.

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