Enhanced Power Spectral Density Transmissibility Matrix for Operational Modal Analysis of Structures

Abstract

The approach for identifying modal parameters of a structure from power spectral density transmissibility matrices, called the PSDTM-SVD method, is improved to identify modal parameters (including damping ratios) in a condition when the structure is not completely loaded. Therefore, an enhanced PSDTM-SVD method is proposed based on the use of a modified Moore-Penrose inverse to evaluate the singularity of the transmissibility matrices at the system poles and thus determine natural frequencies, mode shapes, and damping ratios. In the inverse modified operation, it is necessary to use a maximum number of singular values, which depends on the rank of the transmissibility matrix. One cause of the reduction of the matrix rank is the number of uncorrelated loads present in the structure. In this way, we propose a procedure for the automatic identification of the number of singular values that must be used in the Moore-Penrose inverse. Different numerical examples of a beam model subjected to colored noise excitations and data from an operational vibration bridge test showed that the proposed method is capable of identifying modal parameters.