Modal parameter identification based on combining transmissibility functions and blind source separation techniques

Transmissibility-based operational modal analysis is a recent and alternative approach used to identify the modal parameters of structures under operational conditions. This approach is advantageous compared with traditional operational modal analysis because it does not make any assumptions about the excitation spectrum (i.e., white noise with a flat spectrum). However, common methodologies do not include a procedure to extract closely spaced modes with low signal-to-noise ratios. This issue is relevant when considering that engineering structures generally have closely spaced modes and that their measured responses present high levels of noise. Therefore, to overcome these problems, a new combined method for modal parameter identification is proposed in this work. The proposed method combines blind source separation (BSS) techniques and transmissibility-based methods. Here, BSS techniques were used to recover source signals, and transmissibility-based methods were applied to estimate modal information from the recovered source signals. To achieve this combination, a new method to define a transmissibility function was proposed. The suggested transmissibility function is based on the relationship between the power spectral density (PSD) of mixed signals and the PSD of signals from a single source. The numerical responses of a truss structure with high levels of added noise and very closely spaced modes were processed using the proposed combined method to evaluate its ability to identify modal parameters in these conditions. Colored and white noise excitations were used for the numerical example. The proposed combined method was also used to evaluate the modal parameters of an experimental test on a structure containing closely spaced modes. The results showed that the proposed combined method is capable of identifying very closely spaced modes in the presence of noise and, thus, may be potentially applied to improve the identification of damping ratios.