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Weighted Transmissibility-Based Operational Modal Analysis for Identification of Structures Using Seismic Responses

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Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

Abstract

Transmissibility-based operational modal analysis is an effective approach to identify the modal parameters using the output-only data from the ambient vibrations. This approach, based on the SVD technique, has a good ability to determine the vibrational modes with high certainty. However, the results of the present research indicate that the transmissibility approach has not an appropriate performance in identifying the vibrational modes using the short random records such as seismic records. These records have a high spectral leakage and dispersion due to the non-periodic harmonic components caused by the vibrational characteristics of the system and the strong ambient excitations (e.g., earthquake). In this paper, an efficient approach called weighted transmissibility-based operational modal analysis is proposed to properly identify the natural frequencies and mode shapes using the short seismic records. The proposed approach combines the single-reference weighted transmissibility functions associated with different transferring outputs obtained from single loading condition in a unique matrix formulation. It extracts the vibrational modes using the efficient \({\text{PIS}}\left( \omega \right)\) function calculated by the singular values of the weighted transmissibility matrices. In this research, several theoretical examples, including 2-DOF, 3-DOF, 5-DOF and 10-DOF systems, have been provided to indicate the capabilities of the proposed approach in identifying the modal parameters of structural systems.

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Abbreviations

OMA:

Operational modal analysis

TOMA:

Transmissibility-based operational modal analysis

SVD:

Singular value decomposition

WTOMA:

Weighted transmissibility-based operational modal analysis

PIS:

Product of inverse of second singular values

DOF:

Degrees of freedom

PSD:

Power spectral density

PSDT:

Power spectrum density transmissibility

WTM:

Weighted transmissibility matrix

NWT:

Normalized weighted transmissibility

ANWT:

Averaged normalized weighted transmissibility

LTI:

Linear time-invariant

PSDTM:

Power spectrum density transmissibility matrix

\(\lambda_{r}\) :

rth system pole

\(\phi_{\text{r}}\) :

rth mode shape

\(\gamma\) :

Adjustable parameter used in weight function

\(\Delta\) :

Difference between the absolute values of two elements of conventional transmissibility matrix in a desired row

\(C\) :

A proportion of \(\Delta\) to the absolute value of smaller element

\(\Delta^{\prime }\) :

Difference between the absolute values of two elements of weighted transmissibility matrix in a desired row

\(C^{\prime }\) :

A proportion of \(\Delta^{\prime }\) to the absolute value of smaller element

\(\left[ {U\left( \omega \right)} \right]\) :

Unitary matrix containing the left singular vectors

\(\left[ {V\left( \omega \right)} \right]\) :

Unitary matrix containing the right singular vectors

\(\left[ {S\left( \omega \right)} \right]\) :

Diagonal matrix containing the singular values

\(\left[ {S\left( \omega \right)} \right]^{\dag }\) :

Inverse of the diagonal matrix \(\left[ {S\left( \omega \right)} \right]\)

\(\left[ {{\text{WTM}}\left( \omega \right)} \right]^{\dag }\) :

Pseudo-inverse of weighted transmissibility matrix

\(\left[ M \right]\) :

Mass matrix

\(\left[ K \right]\) :

Stiffness matrix

\(\left[ C \right]\) :

Damping matrix

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Authors and Affiliations

  1. University of Tabriz, Tabriz, East Azerbaijan, Iran

    Majid Damadipour, Reza Tarinejad & Mohammad Hossein Aminfar

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  1. Majid Damadipour
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  2. Reza Tarinejad
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  3. Mohammad Hossein Aminfar
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Correspondence to Reza Tarinejad.

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Damadipour, M., Tarinejad, R. & Aminfar, M.H. Weighted Transmissibility-Based Operational Modal Analysis for Identification of Structures Using Seismic Responses. Iran J Sci Technol Trans Civ Eng 45, 43–59 (2021). https://doi.org/10.1007/s40996-020-00509-3

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  • DOI: https://doi.org/10.1007/s40996-020-00509-3

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