Advancements in online modal identification: a recursive simultaneous diagonalization comprehensive framework for real-time applications

This paper introduces a recursive formulation of blind modal identification as an alternative to conventional diagonalization methods based on multi-lagged covariance matrices. While traditional blind source separation methods are effective for modal identification in structural systems, dynamic systems experiencing sudden changes or rapidly changing environmental conditions require real-time algorithms for continuous health assessment. The proposed recursive eigenspace updates on output covariance estimates, using generalized eigen perturbation, show promise in identifying modal parameters for numerically simulated systems excited with white and colored noise spectra. The paper presents a detailed framework based on recursive simultaneous diagonalization, avoiding real-time diagonalization of multi-lagged covariance matrices by incorporating two auto-covariance matrices with different lags. To evaluate the performance of the new real-time algorithm, synthesized data from a five-degrees-of-freedom system is used. A comparison with traditional independent components demonstrates the effectiveness of the proposed approach in separating closely spaced modes with high damping in real-time. Experimental investigations conducted on controlled vibroimpact test beds confirm the robustness of the proposed approach. Furthermore, the paper shows that the modal parameters obtained using the proposed method for the benchmark ASCE-SHM structure are consistent with those obtained from state-of-the-art methods. The examples presented in the paper indicate that real-time mode separation for dynamic systems in operating conditions is feasible, which is a novel contribution in the field of recursive simultaneous diagonalization.