Mastering complex modes: a new method for real-time modal identification of vibrating systems

A novel algorithm for real-time modal identification in linear vibrating systems with complex modes is introduced, utilizing a combination of first order eigen-perturbation and second order separation techniques. In practical settings, structures with complex modes are frequently encountered and their presence often poses a challenge in accurately estimating the source signal in real-time. The proposed methodology addresses this issue by incorporating the right angle phase shift of the response in the sensor output and updating the second order statistics of the complex response through first order eigen-perturbation. Empirical evidence of the efficacy of the technique is demonstrated through numerical case studies and validation using various numerically modeled systems, as well as a standard ASCE-SHM benchmark problem with complex modes, highlighting the capability of the proposed method to achieve precise real-time modal property identification and online source separation with a minimal number of initially required batch data.