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

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.