Operational modal analysis approach based on multivariable transmissibility with different transferring outputs

In recent years, transmissibility functions have been used as alternatives to identify the modal parameters of structures under operating conditions. The scalar power spectrum density transmissibility (PSDT), which relates only two responses, was proposed to extract modal parameters by combining different PSDTs with different transferring outputs. In this sense, this paper proposes extending the scalar PSDT concept to multivariable PSDT by relating multiple responses instead of only two. This extension implies the definition of a transmissibility matrix, relating the cross-spectral density matrix among the responses at coordinates Z and U with the cross-spectral density matrix among the responses at coordinates Z and K. The coordinates in Z are known as the transferring outputs. By defining the same coordinates K and U, but with different transferring outputs Z, we prove that the multivariable PSDT converges to the same matrix when it approaches the system poles. This property is used to define only one matrix with different multivariable PSDTs with same coordinates K and U, but with different transferring outputs. The resulting matrix is singular at the system poles, meaning that by applying the inverse of the matrix, the modal parameters can be identified. Here, a numeric example of a beam model subjected to excitations and data from an operational vibration bridge test shows that the proposed method is capable of identifying modal parameters. Furthermore, the results demonstrate the possibility of estimating the same modal parameters by changing only the coordinates K and U, providing greater reliability during modal parameter identification. •Multivariable transmissibility with different transferring outputs concept is proposed.•This concept is based on a relation between multiple system responses.•Multivariable transmissibility is used as a new alternative to modal identification.•Both numerical example and real vibration data are used to validate the method.