Robust multi-dataset identification with frequency domain decomposition

Right after its invention in the late nineties, the Frequency Domain Decomposition (FDD) identification technique became very popular in the operational modal analysis community due to its simplicity and robustness. The underlying idea of this technique consists of computing the singular value decomposition of the Power Spectral Densities (PSDs) estimated from the measured vibration responses with the periodogram (also known as “Welch's”) approach to identify the natural frequencies and mode shape vectors of the tested structural system. When dealing with multi-dataset output-only modal analysis, the classic approach for extracting the global mode shape vectors from all the measured datasets consists of estimating the mode shape parts corresponding to each dataset, and then scaling the different parts with the aid of the reference sensors. In this paper, two new merging approaches are proposed to scale the different mode shape parts. The first consists of (i) re-scaling the different PSDs prior to the identification; (ii) forming a global matrix containing all the re-scaled PSDs; and (iii) applying the FDD approach to the global PSD matrix to estimate the global mode shape vectors. The second merging strategy consists of (i) forming a global matrix containing all the PSDs without any prior re-scaling; (ii) applying the FDD approach to the PSD matrix to estimate the global mode shape vectors; and (iii) re-scaling the different mode shape parts by making use of the reference singular vectors. In order to illustrate the benefits of the two proposed merging approaches with regards to their classic counterpart from a practical perspective, a real-live application example is presented as the last part of the paper.