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Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function ℋ2-Norm

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Title: Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function ℋ2-Norm
Authors: Rahrovani, Sadegh, 1981, Khorsand Vakilzadeh, Majid, 1984, Abrahamsson, Thomas, 1956
Source: Mechanical Systems and Signal Processing. 48(1-2):218-231
Subject Terms: Dominancy metric, Input–output relation, QR-Decomposition, Singular Value Decomposition (SVD), Modal reduction, ℋ2ℋ2-norm
Description: A main restriction in the general applicability of modal reduction techniques has been the lack of a proper dominancy analysis as well as the lack of a guaranteed bound for the approximation error. In this study, a modal dominancy approach for reduction of dynamical systems is presented. A quadratic-metric, introduced based on modal contribution to the ℋ2ℋ2-norm of the frequency response function matrix, is given in closed-form formulation. Briefly stated, a performance and error analysis of the proposed modal dominancy procedure is carried out, the problem of metric non-uniqueness as well as the treatment of structural non-minimality for a class of systems with multiple eigenvalues is described, and a method to circumvent this problem is proposed. In treating problems with high-dimensional input space, such as in moving and/or distributed loading problems, the presented method is an improvement as it incorporates information extracted from the structural and spectral properties of the input force in the modal dominancy analysis. In addition, the method׳s performance is validated for reduction of a large-scale finite element model, originated from a moving load problem in railway mechanics, and the results are compared with the balancing approach.
Access URL: https://research.chalmers.se/publication/197023
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  Label: Title
  Group: Ti
  Data: Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function ℋ2-Norm
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Rahrovani%2C+Sadegh%22">Rahrovani, Sadegh</searchLink>, 1981<br /><searchLink fieldCode="AR" term="%22Khorsand+Vakilzadeh%2C+Majid%22">Khorsand Vakilzadeh, Majid</searchLink>, 1984<br /><searchLink fieldCode="AR" term="%22Abrahamsson%2C+Thomas%22">Abrahamsson, Thomas</searchLink>, 1956
– Name: TitleSource
  Label: Source
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  Data: <i>Mechanical Systems and Signal Processing</i>. 48(1-2):218-231
– Name: Subject
  Label: Subject Terms
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Dominancy+metric%22">Dominancy metric</searchLink><br /><searchLink fieldCode="DE" term="%22Input–output+relation%22">Input–output relation</searchLink><br /><searchLink fieldCode="DE" term="%22QR-Decomposition%22">QR-Decomposition</searchLink><br /><searchLink fieldCode="DE" term="%22Singular+Value+Decomposition+%28SVD%29%22">Singular Value Decomposition (SVD)</searchLink><br /><searchLink fieldCode="DE" term="%22Modal+reduction%22">Modal reduction</searchLink><br /><searchLink fieldCode="DE" term="%22ℋ2ℋ2-norm%22">ℋ2ℋ2-norm</searchLink>
– Name: Abstract
  Label: Description
  Group: Ab
  Data: A main restriction in the general applicability of modal reduction techniques has been the lack of a proper dominancy analysis as well as the lack of a guaranteed bound for the approximation error. In this study, a modal dominancy approach for reduction of dynamical systems is presented. A quadratic-metric, introduced based on modal contribution to the ℋ2ℋ2-norm of the frequency response function matrix, is given in closed-form formulation. Briefly stated, a performance and error analysis of the proposed modal dominancy procedure is carried out, the problem of metric non-uniqueness as well as the treatment of structural non-minimality for a class of systems with multiple eigenvalues is described, and a method to circumvent this problem is proposed. In treating problems with high-dimensional input space, such as in moving and/or distributed loading problems, the presented method is an improvement as it incorporates information extracted from the structural and spectral properties of the input force in the modal dominancy analysis. In addition, the method׳s performance is validated for reduction of a large-scale finite element model, originated from a moving load problem in railway mechanics, and the results are compared with the balancing approach.
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1016/j.ymssp.2014.03.003
    Languages:
      – Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 14
        StartPage: 218
    Subjects:
      – SubjectFull: Dominancy metric
        Type: general
      – SubjectFull: Input–output relation
        Type: general
      – SubjectFull: QR-Decomposition
        Type: general
      – SubjectFull: Singular Value Decomposition (SVD)
        Type: general
      – SubjectFull: Modal reduction
        Type: general
      – SubjectFull: ℋ2ℋ2-norm
        Type: general
    Titles:
      – TitleFull: Modal Dominancy Analysis Based on Modal Contribution to Frequency Response Function ℋ2-Norm
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            NameFull: Rahrovani, Sadegh
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            NameFull: Khorsand Vakilzadeh, Majid
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            NameFull: Abrahamsson, Thomas
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            – D: 01
              M: 01
              Type: published
              Y: 2014
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            – TitleFull: Mechanical Systems and Signal Processing
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