Separation and identification of structural modes in largely underdetermined scenarios using frequency banding

In recent years, blind source separation (BSS) has gained significant interest in the context of operational modal analysis, as a non-parametric alternative to the identification of mechanical structures from output-only measurements. One persisting limitation of most BSS methods, however, is to they cannot identify more active modes than the number of simultaneously measured outputs. The aim of this work is to propose a solution to the largely underdetermined case – where many more modes are to be identified than the number of available measurements -- by dividing the frequency axis in subbands, such that each band provides an (over)determined problem where BSS can be applied separately. The approach comes with the proposal of a new second-order BSS that operates directly in the frequency domain and takes as an input the cross-spectral matrix of the data. A data augmentation technique is also devised to artificially increase the dimension of the measurements in severely undetermined scenarios. Finally, an identification algorithm is introduced that estimates the modal parameters of the separated structural modes. A remarkable aspect of these algorithms is that they are all based on the unified use of multi-filters designed in the frequency domain, yet with different frequency bandwidths. Another particularity of the present paper is to demonstrate the validity of the proposed approach on several benchmark databases with various degrees of difficulty including complex modes, high modal overlap, singular modes, and the presence of engine harmonics. In all cases, the proposed methodology was efficient and, above all, easy to deal with even in largely undetermined cases.