Frequency-Domain Fast Maximum Likelihood Estimation of Complex Modes

Proportional damping is usually assumed in modal analysis for civil structures. However, this model may not capture the true dynamic characteristics of structures, e.g., when damper is introduced to suppress the vibration. In this condition, it is better to use the non-proportional damping model, which results in the more general complex modes. This paper aims at developing a fast-maximum likelihood estimation of complex modes when only structural output data are available. Starting with the state space representation, a frequency-domain probabilistic model is first formulated to model the structural ambient vibration. Modal parameters are then identified by employing the principle of maximum likelihood estimation, and the expectation-maximization algorithm is applied. An efficient and numerically robust implementation is provided so that the operation can be done in seconds. The modal identification of the Guangzhou TV tower is used to illustrate its performance to the practical civil structures.