On shift selection for Krylov subspace based model order reduction

Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequ...

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Bibliographic Details
Published in:Multibody system dynamics Vol. 58; no. 3-4; pp. 231 - 251
Main Authors: Frie Lennart, Eberhard, Peter
Format: Journal Article
Language:English
Published: Dordrecht Springer Nature B.V 01.01.2023
Subjects:
Algorithms
Approximation
Decomposition
Differential equations
Errors
Finite element method
Helicopters
Mathematical analysis
Mathematical models
Mechanical systems
Model reduction
Multibody systems
Reduced order models
Singular value decomposition
Subspaces
Transfer functions
ISSN:1384-5640, 1573-272X
Online Access:Get full text
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Summary:Mechanical systems are often modeled with the multibody system method or the finite element method and numerically described with systems of differential equations. Increasing demands on detail and the resulting high complexity of these systems make the use of model order reduction inevitable. Frequently, moment matching based on Krylov subspaces is used for the reduction. There, the transfer functions of the full system and of the reduced system are matched at distinct frequency shifts. The selection of these shifts, however, is not trivial. In this contribution we suggest an algorithm that evaluates an increasing number of shifts iteratively until a reduced model that approximates the full model in a subspace with very low approximation error is found. Thereafter, the projection matrix that spans this subspace is decomposed with singular value decomposition and only most important directions are retained. In this way, small reduced models with good approximation properties that do not exceed a predefined error bound can be found or low-error models for a given reduced order can be generated. The evaluation of more shifts than necessary and further reduction by means of singular value decomposition is the novelty of this contribution. In this paper, this novel approach is extensively studied and, furthermore, applied to the numerical example of an industrial helicopter model.
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ISSN:1384-5640
1573-272X
DOI:10.1007/s11044-022-09872-7