Fast Bayesian modal identification of structures using known single-input forced vibration data

Modal identification aims to identify the modal parameters of constructed structures based on vibration data. Forced vibration tests allow one to obtain data with a higher signal-to-noise ratio compared with free or ambient vibration tests. Modal identification techniques for forced vibration data exist, but they do not provide a rigorous quantification of the remaining uncertainties of the modal parameters, which is becoming important in modern structural health monitoring and uncertainty propagation. This paper develops a Bayesian approach that properly accounts for uncertainty in accordance with probability logic for modal identification using forced vibration data. The posterior probability density function of the modal parameters to be identified given the data is derived based on the assumed model and the collected data. An efficient algorithm is developed that allows practical implementation in the case of a single shaker. It is applicable for both separated and closely-spaced modes even with a large number of measured degrees of freedom. The proposed method is verified and investigated using synthetic and field test data.