Modal assurance distribution of multivariate signals for modal identification of time-varying dynamic systems

Most time–frequency representations (TFRs) and signal analysis methods used for the identification of dynamic systems through non-parametric techniques are based on univariate signals. However, combining the information obtained from different sensors to investigate the overall behavior of the monitored structure is not trivial, as different recordings may show different features. Moreover, methods based upon the analysis of the energy density distribution in the time–frequency plane generally suffer from problems related to crossing and closely-spaced modes. In this paper, a new time–frequency representation of multivariate and multicomponent signals based on the modal assurance criterion (MAC) is presented. The analysis of the modal assurance distribution (MAD) thus obtained enables the extraction of decoupled modal responses, which can then be used to evaluate the instantaneous modal parameters of time-varying systems. To this end, a decomposition algorithm based on modal assurance (DAMA) is proposed, employing the watershed segmentation of the MAD. The results for two case studies, a finite element model and a full-scale experimental benchmark, are shown, considering both the original MAD and two enhanced versions, here proposed to improve its readability. The results are compared with those obtained from modern and widely used techniques, showing the promising efficacy of the proposed method for signals with time-varying frequency and amplitude, even in the presence of narrow-band disturbances and white noise, as well as with vanishing modes.