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A Comparative Study of Mode Decomposition to Relate Next-ERA, PCA, and ICA Modes

  • Conference paper
Model Validation and Uncertainty Quantification, Volume 3

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Abstract

This paper discusses a comparative study to relate parametric and non-parametric mode decomposition algorithms for response-only data. Three popular mode decomposition algorithms are included in this study: the Eigensystem Realization Algorithm with the Natural Excitation Technique (NExT-ERA) for the parametric algorithm, as well as the Principal Component Analysis (PCA) and the Independent Component Analysis (ICA) for the non-parametric algorithms. A comprehensive parametric study is provided for (i) different response types, (ii) excitation types, (iii) system damping, and (iv) sensor spatial resolution to compare the mode shapes and modal coordinates of using a 10-DOF building model. The mode decomposition results are also compared using a unique dynamic response data collected in a ship-bridge collision accident for ambient excitation with traffic loading, ambient excitation without traffic loading, and impulse excitation.

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Abbreviations

\( \ddot{X}(t),\;\dot{X}(t),\;X(t) \) :

The system acceleration, velocity and displacement, respectively.

ΨTRU :

The true mode shape determined by the modal superposition method.

\( {\hat{\Psi}}_{\ddot{X}}^{\mathrm{ERA}},\;{\hat{\Psi}}_{\dot{X}}^{\mathrm{ERA}},\;{\hat{\Psi}}_X^{\mathrm{ERA}} \) :

The mode shapes estimated with the Eigensystem Realization Algorithm with Natural Excitation Method (NExT-ERA) for \( \ddot{X}(t) \), (t), and X(t), respectively.

\( {\hat{\Psi}}_{\ddot{X}}^{\mathrm{PCA}},\;{\hat{\Psi}}_{\dot{X}}^{\mathrm{PCA}},\;{\hat{\Psi}}_X^{\mathrm{PCA}} \) :

The mode shapes estimated with the Principal Component Analysis (PCA) method for \( \ddot{X}(t) \), (t), and X(t), respectively.

\( {\hat{\Psi}}_{\ddot{X}}^{\mathrm{ICA}},\;{\hat{\Psi}}_{\dot{X}}^{\mathrm{ICA}},\;{\hat{\Psi}}_X^{\mathrm{ICA}} \) :

The mode shapes estimated with the Independent Component Analysis (ICA) method for \( \ddot{X}(t) \), (t), and X(t), respectively.

p TRU :

The true modal coordinate determined by the modal superposition method.

\( {\hat{p}}_{\ddot{X}}^{\mathrm{ERA}},\;{\hat{p}}_{\dot{X}}^{\mathrm{ERA}},\;{\hat{p}}_X^{\mathrm{ERA}} \) :

The modal coordinates estimated with the Eigensystem Realization Algorithm with Natural Excitation Method (NExT-ERA) for \( \ddot{X}(t) \), (t), and X(t), respectively.

\( {\hat{p}}_{\ddot{X}}^{\mathrm{PCA}},\;{\hat{p}}_{\dot{X}}^{\mathrm{PCA}},\;{\hat{p}}_X^{\mathrm{PCA}} \) :

The modal coordinates estimated with the Principal Component Analysis (PCA) method for \( \ddot{X}(t) \), (t), and X(t), respectively.

\( {\hat{p}}_{\ddot{X}}^{\mathrm{ICA}},\;{\hat{p}}_{\dot{X}}^{\mathrm{ICA}},\;{\hat{p}}_X^{\mathrm{ICA}} \) :

The modal coordinates estimated with the Independent Component Analysis (ICA) method for \( \ddot{X}(t) \), (t), and X(t), respectively.

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Acknowledgements

This study was supported in parts by grants from the U.S. National Science Foundation (NSF), the Air Force Office of Scientific Research (AFOSR), and the National Aeronautics and Space Administration (NASA). The assistance of A. Shakal of the California Geology Service and L.-H. Sheng of the California Department of Transportation (Caltrans) is appreciated.

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Authors and Affiliations

  1. Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL, USA

    Ayad Al-Rumaithi & Hae-Bum Yun

  2. Civil and Environmental Engineering, University of Southern California, Los Angeles, CA, USA

    Sami F. Masri

Authors
  1. Ayad Al-Rumaithi
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  2. Hae-Bum Yun
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  3. Sami F. Masri
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Correspondence to Hae-Bum Yun .

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Editors and Affiliations

  1. Civil Engineering Department, Clemson University, Clemson, South Carolina, USA

    H. Sezer Atamturktur

  2. Department of Civil and Envt. Eng., Tufts University, Medford, Massachusetts, USA

    Babak Moaveni

  3. Department of Mechanical Engineering, University of Thessaly, Volos, Greece

    Costas Papadimitriou

  4. Sandia National Laboratories, Albuquerque, New Mexico, USA

    Tyler Schoenherr

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© 2015 The Society for Experimental Mechanics, Inc.

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Al-Rumaithi, A., Yun, HB., Masri, S.F. (2015). A Comparative Study of Mode Decomposition to Relate Next-ERA, PCA, and ICA Modes. In: Atamturktur, H., Moaveni, B., Papadimitriou, C., Schoenherr, T. (eds) Model Validation and Uncertainty Quantification, Volume 3. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-15224-0_12

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  • DOI: https://doi.org/10.1007/978-3-319-15224-0_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-15223-3

  • Online ISBN: 978-3-319-15224-0

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