Weighted Transmissibility-Based Operational Modal Analysis for Identification of Structures Using Seismic Responses
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RESEARCH PAPER
Weighted Transmissibility‑Based Operational Modal Analysis for Identification of Structures Using Seismic Responses Majid Damadipour1 · Reza Tarinejad1 · Mohammad Hossein Aminfar1 Received: 7 May 2019 / Accepted: 5 October 2020 © Shiraz University 2020
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 PIS(𝜔) 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. Keywords Short random records · Spectral leakage and dispersion · Weighted transmissibility-based · Operational modal analysis · Single loading condition · Singular values 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
* Reza Tarinejad [email protected] 1
LTI Linear time-invariant PSDTM Power spectrum density transmissibility matrix List of Symbols rth system pole 𝜆r rth mode shape 𝜙r 𝛾 Adjustable parameter used in weight function Δ Difference between the absolute values of two elements of conventional transmissibility matrix in a desired row C A proportion of Δ to the absolute value of smaller element Δ� Difference between the absolute values of two elements of weighted transmissibility matrix in a desired row C′ A proportion of Δ� to the absolute value of smaller element [U(𝜔)] Unitary matrix containing the lef
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